mcmc_based_searches.py 78.4 KB
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""" Searches using MCMC-based methods """

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import sys
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import os
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import copy
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import logging
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from collections import OrderedDict
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import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import emcee
import corner
import dill as pickle

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from core import BaseSearchClass, ComputeFstat, SemiCoherentSearch
from optimal_setup_functions import get_V_estimate
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from core import tqdm, args, earth_ephem, sun_ephem
from optimal_setup_functions import get_optimal_setup
import helper_functions
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class MCMCSearch(BaseSearchClass):
    """ MCMC search using ComputeFstat"""
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    @helper_functions.initializer
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    def __init__(self, label, outdir, theta_prior, tref, minStartTime,
                 maxStartTime, sftfilepath=None, nsteps=[100, 100],
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                 nwalkers=100, ntemps=1, log10temperature_min=-5,
                 theta_initial=None, scatter_val=1e-10,
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                 binary=False, BSGL=False, minCoverFreq=None,
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                 maxCoverFreq=None, detectors=None, earth_ephem=None,
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                 sun_ephem=None, injectSources=None, assumeSqrtSX=None):
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        """
        Parameters
        label, outdir: str
            A label and directory to read/write data from/to
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        sftfilepath: str
            File patern to match SFTs
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        theta_prior: dict
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            Dictionary of priors and fixed values for the search parameters.
            For each parameters (key of the dict), if it is to be held fixed
            the value should be the constant float, if it is be searched, the
            value should be a dictionary of the prior.
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        theta_initial: dict, array, (None)
            Either a dictionary of distribution about which to distribute the
            initial walkers about, an array (from which the walkers will be
            scattered by scatter_val, or  None in which case the prior is used.
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        tref, minStartTime, maxStartTime: int
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            GPS seconds of the reference time, start time and end time
        nsteps: list (m,)
            List specifying the number of steps to take, the last two entries
            give the nburn and nprod of the 'production' run, all entries
            before are for iterative initialisation steps (usually just one)
            e.g. [1000, 1000, 500].
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        nwalkers, ntemps: int,
            The number of walkers and temperates to use in the parallel
            tempered PTSampler.
        log10temperature_min float < 0
            The  log_10(tmin) value, the set of betas passed to PTSampler are
            generated from np.logspace(0, log10temperature_min, ntemps).
        binary: Bool
            If true, search over binary parameters
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        detectors: str
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            Two character reference to the data to use, specify None for no
            contraint.
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        minCoverFreq, maxCoverFreq: float
            Minimum and maximum instantaneous frequency which will be covered
            over the SFT time span as passed to CreateFstatInput
        earth_ephem, sun_ephem: str
            Paths of the two files containing positions of Earth and Sun,
            respectively at evenly spaced times, as passed to CreateFstatInput
            If None defaults defined in BaseSearchClass will be used

        """

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        if os.path.isdir(outdir) is False:
            os.mkdir(outdir)
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        self.add_log_file()
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        logging.info(
            'Set-up MCMC search for model {} on data {}'.format(
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                self.label, self.sftfilepath))
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        self.pickle_path = '{}/{}_saved_data.p'.format(self.outdir, self.label)
        self.unpack_input_theta()
        self.ndim = len(self.theta_keys)
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        if self.log10temperature_min:
            self.betas = np.logspace(0, self.log10temperature_min, self.ntemps)
        else:
            self.betas = None
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        if earth_ephem is None:
            self.earth_ephem = self.earth_ephem_default
        if sun_ephem is None:
            self.sun_ephem = self.sun_ephem_default

        if args.clean and os.path.isfile(self.pickle_path):
            os.rename(self.pickle_path, self.pickle_path+".old")

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        self.log_input()

    def log_input(self):
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        logging.info('theta_prior = {}'.format(self.theta_prior))
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        logging.info('nwalkers={}'.format(self.nwalkers))
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        logging.info('scatter_val = {}'.format(self.scatter_val))
        logging.info('nsteps = {}'.format(self.nsteps))
        logging.info('ntemps = {}'.format(self.ntemps))
        logging.info('log10temperature_min = {}'.format(
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            self.log10temperature_min))
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    def inititate_search_object(self):
        logging.info('Setting up search object')
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        self.search = ComputeFstat(
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            tref=self.tref, sftfilepath=self.sftfilepath,
            minCoverFreq=self.minCoverFreq, maxCoverFreq=self.maxCoverFreq,
            earth_ephem=self.earth_ephem, sun_ephem=self.sun_ephem,
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            detectors=self.detectors, BSGL=self.BSGL, transient=False,
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            minStartTime=self.minStartTime, maxStartTime=self.maxStartTime,
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            binary=self.binary, injectSources=self.injectSources,
            assumeSqrtSX=self.assumeSqrtSX)
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    def logp(self, theta_vals, theta_prior, theta_keys, search):
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        H = [self.generic_lnprior(**theta_prior[key])(p) for p, key in
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             zip(theta_vals, theta_keys)]
        return np.sum(H)

    def logl(self, theta, search):
        for j, theta_i in enumerate(self.theta_idxs):
            self.fixed_theta[theta_i] = theta[j]
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        FS = search.compute_fullycoherent_det_stat_single_point(
            *self.fixed_theta)
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        return FS

    def unpack_input_theta(self):
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        full_theta_keys = ['F0', 'F1', 'F2', 'Alpha', 'Delta']
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        if self.binary:
            full_theta_keys += [
                'asini', 'period', 'ecc', 'tp', 'argp']
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        full_theta_keys_copy = copy.copy(full_theta_keys)

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        full_theta_symbols = ['$f$', '$\dot{f}$', '$\ddot{f}$', r'$\alpha$',
                              r'$\delta$']
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        if self.binary:
            full_theta_symbols += [
                'asini', 'period', 'period', 'ecc', 'tp', 'argp']

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        self.theta_keys = []
        fixed_theta_dict = {}
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        for key, val in self.theta_prior.iteritems():
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            if type(val) is dict:
                fixed_theta_dict[key] = 0
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                self.theta_keys.append(key)
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            elif type(val) in [float, int, np.float64]:
                fixed_theta_dict[key] = val
            else:
                raise ValueError(
                    'Type {} of {} in theta not recognised'.format(
                        type(val), key))
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            full_theta_keys_copy.pop(full_theta_keys_copy.index(key))
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        if len(full_theta_keys_copy) > 0:
            raise ValueError(('Input dictionary `theta` is missing the'
                              'following keys: {}').format(
                                  full_theta_keys_copy))

        self.fixed_theta = [fixed_theta_dict[key] for key in full_theta_keys]
        self.theta_idxs = [full_theta_keys.index(k) for k in self.theta_keys]
        self.theta_symbols = [full_theta_symbols[i] for i in self.theta_idxs]

        idxs = np.argsort(self.theta_idxs)
        self.theta_idxs = [self.theta_idxs[i] for i in idxs]
        self.theta_symbols = [self.theta_symbols[i] for i in idxs]
        self.theta_keys = [self.theta_keys[i] for i in idxs]

    def check_initial_points(self, p0):
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        for nt in range(self.ntemps):
            logging.info('Checking temperature {} chains'.format(nt))
            initial_priors = np.array([
                self.logp(p, self.theta_prior, self.theta_keys, self.search)
                for p in p0[nt]])
            number_of_initial_out_of_bounds = sum(initial_priors == -np.inf)

            if number_of_initial_out_of_bounds > 0:
                logging.warning(
                    'Of {} initial values, {} are -np.inf due to the prior'
                    .format(len(initial_priors),
                            number_of_initial_out_of_bounds))

                p0 = self.generate_new_p0_to_fix_initial_points(
                    p0, nt, initial_priors)

    def generate_new_p0_to_fix_initial_points(self, p0, nt, initial_priors):
        logging.info('Attempting to correct intial values')
        idxs = np.arange(self.nwalkers)[initial_priors == -np.inf]
        count = 0
        while sum(initial_priors == -np.inf) > 0 and count < 100:
            for j in idxs:
                p0[nt][j] = (p0[nt][np.random.randint(0, self.nwalkers)]*(
                             1+np.random.normal(0, 1e-10, self.ndim)))
            initial_priors = np.array([
                self.logp(p, self.theta_prior, self.theta_keys,
                          self.search)
                for p in p0[nt]])
            count += 1

        if sum(initial_priors == -np.inf) > 0:
            logging.info('Failed to fix initial priors')
        else:
            logging.info('Suceeded to fix initial priors')

        return p0
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    def OLD_run_sampler_with_progress_bar(self, sampler, ns, p0):
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        for result in tqdm(sampler.sample(p0, iterations=ns), total=ns):
            pass
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        return sampler

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    def setup_convergence_testing(
            self, convergence_period=10, convergence_length=10,
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            convergence_burnin_fraction=0.25, convergence_threshold_number=10,
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            convergence_threshold=1.2, convergence_prod_threshold=2,
            convergence_plot_upper_lim=2):
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        """
        If called, convergence testing is used during the MCMC simulation

        This uses the Gelmanr-Rubin statistic based on the ratio of between and
        within walkers variance. The original statistic was developed for
        multiple (independent) MCMC simulations, in this context we simply use
        the walkers

        Parameters
        ----------
        convergence_period: int
            period (in number of steps) at which to test convergence
        convergence_length: int
            number of steps to use in testing convergence - this should be
            large enough to measure the variance, but if it is too long
            this will result in incorect early convergence tests
        convergence_burnin_fraction: float [0, 1]
            the fraction of the burn-in period after which to start testing
        convergence_threshold_number: int
            the number of consecutive times where the test passes after which
            to break the burn-in and go to production
        convergence_threshold: float
            the threshold to use in diagnosing convergence. Gelman & Rubin
            recomend a value of 1.2, 1.1 for strict convergence
        convergence_prod_threshold: float
            the threshold to test the production values with
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        convergence_plot_upper_lim: float
            the upper limit to use in the diagnostic plot
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        """
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        if convergence_length > convergence_period:
            raise ValueError('convergence_length must be < convergence_period')
        logging.info('Setting up convergence testing')
        self.convergence_length = convergence_length
        self.convergence_period = convergence_period
        self.convergence_burnin_fraction = convergence_burnin_fraction
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        self.convergence_prod_threshold = convergence_prod_threshold
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        self.convergence_diagnostic = []
        self.convergence_diagnosticx = []
        self.convergence_threshold_number = convergence_threshold_number
        self.convergence_threshold = convergence_threshold
        self.convergence_number = 0
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        self.convergence_plot_upper_lim = convergence_plot_upper_lim
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    def get_convergence_statistic(self, i, sampler):
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        s = sampler.chain[0, :, i-self.convergence_length+1:i+1, :]
        within_std = np.mean(np.var(s, axis=1), axis=0)
        per_walker_mean = np.mean(s, axis=1)
        mean = np.mean(per_walker_mean, axis=0)
        between_std = np.sqrt(np.mean((per_walker_mean-mean)**2, axis=0))
        W = within_std
        B_over_n = between_std**2 / self.convergence_period
        Vhat = ((self.convergence_period-1.)/self.convergence_period * W
                + B_over_n + B_over_n / float(self.nwalkers))
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        c = np.sqrt(Vhat/W)
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        self.convergence_diagnostic.append(c)
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        self.convergence_diagnosticx.append(i - self.convergence_length/2)
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        return c

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    def burnin_convergence_test(self, i, sampler, nburn):
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        if i < self.convergence_burnin_fraction*nburn:
            return False
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        if np.mod(i+1, self.convergence_period) != 0:
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            return False
        c = self.get_convergence_statistic(i, sampler)
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        if np.all(c < self.convergence_threshold):
            self.convergence_number += 1
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        else:
            self.convergence_number = 0
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        return self.convergence_number > self.convergence_threshold_number

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    def prod_convergence_test(self, i, sampler, nburn):
        testA = i > nburn + self.convergence_length
        testB = np.mod(i+1, self.convergence_period) == 0
        if testA and testB:
            self.get_convergence_statistic(i, sampler)

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    def check_production_convergence(self, k):
        bools = np.any(
            np.array(self.convergence_diagnostic)[k:, :]
            > self.convergence_prod_threshold, axis=1)
        if np.any(bools):
            logging.warning(
                '{} convergence tests in the production run of {} failed'
                .format(np.sum(bools), len(bools)))

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    def run_sampler(self, sampler, p0, nprod=0, nburn=0):
        if hasattr(self, 'convergence_period'):
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            logging.info('Running {} burn-in steps with convergence testing'
                         .format(nburn))
            iterator = tqdm(sampler.sample(p0, iterations=nburn), total=nburn)
            for i, output in enumerate(iterator):
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                if self.burnin_convergence_test(i, sampler, nburn):
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                    logging.info(
                        'Converged at {} before max number {} of steps reached'
                        .format(i, nburn))
                    self.convergence_idx = i
                    break
            iterator.close()
            logging.info('Running {} production steps'.format(nprod))
            j = nburn
            k = len(self.convergence_diagnostic)
            for result in tqdm(sampler.sample(output[0], iterations=nprod),
                               total=nprod):
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                self.prod_convergence_test(j, sampler, nburn)
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                j += 1
            self.check_production_convergence(k)
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            return sampler
        else:
            for result in tqdm(sampler.sample(p0, iterations=nburn+nprod),
                               total=nburn+nprod):
                pass
            return sampler
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    def run(self, proposal_scale_factor=2, create_plots=True, **kwargs):
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        self.old_data_is_okay_to_use = self.check_old_data_is_okay_to_use()
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        if self.old_data_is_okay_to_use is True:
            logging.warning('Using saved data from {}'.format(
                self.pickle_path))
            d = self.get_saved_data()
            self.sampler = d['sampler']
            self.samples = d['samples']
            self.lnprobs = d['lnprobs']
            self.lnlikes = d['lnlikes']
            return

        self.inititate_search_object()

        sampler = emcee.PTSampler(
            self.ntemps, self.nwalkers, self.ndim, self.logl, self.logp,
            logpargs=(self.theta_prior, self.theta_keys, self.search),
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            loglargs=(self.search,), betas=self.betas, a=proposal_scale_factor)
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        p0 = self.generate_initial_p0()
        p0 = self.apply_corrections_to_p0(p0)
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        self.check_initial_points(p0)

        ninit_steps = len(self.nsteps) - 2
        for j, n in enumerate(self.nsteps[:-2]):
            logging.info('Running {}/{} initialisation with {} steps'.format(
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                j, ninit_steps, n))
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            sampler = self.run_sampler(sampler, p0, nburn=n)
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            logging.info("Mean acceptance fraction: {}"
                         .format(np.mean(sampler.acceptance_fraction, axis=1)))
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            if self.ntemps > 1:
                logging.info("Tswap acceptance fraction: {}"
                             .format(sampler.tswap_acceptance_fraction))
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            if create_plots:
                fig, axes = self.plot_walkers(sampler,
                                              symbols=self.theta_symbols,
                                              **kwargs)
                fig.tight_layout()
                fig.savefig('{}/{}_init_{}_walkers.png'.format(
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                    self.outdir, self.label, j), dpi=400)
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            p0 = self.get_new_p0(sampler)
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            p0 = self.apply_corrections_to_p0(p0)
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            self.check_initial_points(p0)
            sampler.reset()

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        if len(self.nsteps) > 1:
            nburn = self.nsteps[-2]
        else:
            nburn = 0
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        nprod = self.nsteps[-1]
        logging.info('Running final burn and prod with {} steps'.format(
            nburn+nprod))
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        sampler = self.run_sampler(sampler, p0, nburn=nburn, nprod=nprod)
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        logging.info("Mean acceptance fraction: {}"
                     .format(np.mean(sampler.acceptance_fraction, axis=1)))
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        if self.ntemps > 1:
            logging.info("Tswap acceptance fraction: {}"
                         .format(sampler.tswap_acceptance_fraction))
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        if create_plots:
            fig, axes = self.plot_walkers(sampler, symbols=self.theta_symbols,
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                                          nprod=nprod, **kwargs)
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            fig.tight_layout()
            fig.savefig('{}/{}_walkers.png'.format(self.outdir, self.label),
                        dpi=200)
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        samples = sampler.chain[0, :, nburn:, :].reshape((-1, self.ndim))
        lnprobs = sampler.lnprobability[0, :, nburn:].reshape((-1))
        lnlikes = sampler.lnlikelihood[0, :, nburn:].reshape((-1))
        self.sampler = sampler
        self.samples = samples
        self.lnprobs = lnprobs
        self.lnlikes = lnlikes
        self.save_data(sampler, samples, lnprobs, lnlikes)

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    def plot_corner(self, figsize=(7, 7),  tglitch_ratio=False,
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                    add_prior=False, nstds=None, label_offset=0.4,
                    dpi=300, rc_context={}, **kwargs):

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        if self.ndim < 2:
            with plt.rc_context(rc_context):
                fig, ax = plt.subplots(figsize=figsize)
                ax.hist(self.samples, bins=50, histtype='stepfilled')
                ax.set_xlabel(self.theta_symbols[0])

            fig.savefig('{}/{}_corner.png'.format(
                self.outdir, self.label), dpi=dpi)
            return

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        with plt.rc_context(rc_context):
            fig, axes = plt.subplots(self.ndim, self.ndim,
                                     figsize=figsize)

            samples_plt = copy.copy(self.samples)
            theta_symbols_plt = copy.copy(self.theta_symbols)
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            theta_symbols_plt = [s.replace('_{glitch}', r'_\textrm{glitch}')
                                 for s in theta_symbols_plt]
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            if tglitch_ratio:
                for j, k in enumerate(self.theta_keys):
                    if k == 'tglitch':
                        s = samples_plt[:, j]
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                        samples_plt[:, j] = (
                            s - self.minStartTime)/(
                                self.maxStartTime - self.minStartTime)
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                        theta_symbols_plt[j] = r'$R_{\textrm{glitch}}$'

            if type(nstds) is int and 'range' not in kwargs:
                _range = []
                for j, s in enumerate(samples_plt.T):
                    median = np.median(s)
                    std = np.std(s)
                    _range.append((median - nstds*std, median + nstds*std))
            else:
                _range = None

            fig_triangle = corner.corner(samples_plt,
                                         labels=theta_symbols_plt,
                                         fig=fig,
                                         bins=50,
                                         max_n_ticks=4,
                                         plot_contours=True,
                                         plot_datapoints=True,
                                         label_kwargs={'fontsize': 8},
                                         data_kwargs={'alpha': 0.1,
                                                      'ms': 0.5},
                                         range=_range,
                                         **kwargs)

            axes_list = fig_triangle.get_axes()
            axes = np.array(axes_list).reshape(self.ndim, self.ndim)
            plt.draw()
            for ax in axes[:, 0]:
                ax.yaxis.set_label_coords(-label_offset, 0.5)
            for ax in axes[-1, :]:
                ax.xaxis.set_label_coords(0.5, -label_offset)
            for ax in axes_list:
                ax.set_rasterized(True)
                ax.set_rasterization_zorder(-10)
            plt.tight_layout(h_pad=0.0, w_pad=0.0)
            fig.subplots_adjust(hspace=0.05, wspace=0.05)

            if add_prior:
                self.add_prior_to_corner(axes, samples_plt)

            fig_triangle.savefig('{}/{}_corner.png'.format(
                self.outdir, self.label), dpi=dpi)
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    def add_prior_to_corner(self, axes, samples):
        for i, key in enumerate(self.theta_keys):
            ax = axes[i][i]
            xlim = ax.get_xlim()
            s = samples[:, i]
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            prior = self.generic_lnprior(**self.theta_prior[key])
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            x = np.linspace(s.min(), s.max(), 100)
            ax2 = ax.twinx()
            ax2.get_yaxis().set_visible(False)
            ax2.plot(x, [prior(xi) for xi in x], '-r')
            ax.set_xlim(xlim)

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    def plot_prior_posterior(self, normal_stds=2):
        """ Plot the posterior in the context of the prior """
        fig, axes = plt.subplots(nrows=self.ndim, figsize=(8, 4*self.ndim))
        N = 1000
        from scipy.stats import gaussian_kde

        for i, (ax, key) in enumerate(zip(axes, self.theta_keys)):
            prior_dict = self.theta_prior[key]
            prior_func = self.generic_lnprior(**prior_dict)
            if prior_dict['type'] == 'unif':
                x = np.linspace(prior_dict['lower'], prior_dict['upper'], N)
                prior = prior_func(x)
                prior[0] = 0
                prior[-1] = 0
            elif prior_dict['type'] == 'norm':
                lower = prior_dict['loc'] - normal_stds * prior_dict['scale']
                upper = prior_dict['loc'] + normal_stds * prior_dict['scale']
                x = np.linspace(lower, upper, N)
                prior = prior_func(x)
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            elif prior_dict['type'] == 'halfnorm':
                lower = prior_dict['loc']
                upper = prior_dict['loc'] + normal_stds * prior_dict['scale']
                x = np.linspace(lower, upper, N)
                prior = [prior_func(xi) for xi in x]
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            elif prior_dict['type'] == 'neghalfnorm':
                upper = prior_dict['loc']
                lower = prior_dict['loc'] - normal_stds * prior_dict['scale']
                x = np.linspace(lower, upper, N)
                prior = [prior_func(xi) for xi in x]
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            else:
                raise ValueError('Not implemented for prior type {}'.format(
                    prior_dict['type']))
            priorln = ax.plot(x, prior, 'r', label='prior')
            ax.set_xlabel(self.theta_symbols[i])

            s = self.samples[:, i]
            while len(s) > 10**4:
                # random downsample to avoid slow calculation of kde
                s = np.random.choice(s, size=int(len(s)/2.))
            kde = gaussian_kde(s)
            ax2 = ax.twinx()
            postln = ax2.plot(x, kde.pdf(x), 'k', label='posterior')
            ax2.set_yticklabels([])
            ax.set_yticklabels([])

        lns = priorln + postln
        labs = [l.get_label() for l in lns]
        axes[0].legend(lns, labs, loc=1, framealpha=0.8)

        fig.savefig('{}/{}_prior_posterior.png'.format(
            self.outdir, self.label))

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    def plot_cumulative_max(self, **kwargs):
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        d, maxtwoF = self.get_max_twoF()
        for key, val in self.theta_prior.iteritems():
            if key not in d:
                d[key] = val
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        if hasattr(self, 'search') is False:
            self.inititate_search_object()
        if self.binary is False:
            self.search.plot_twoF_cumulative(
                self.label, self.outdir, F0=d['F0'], F1=d['F1'], F2=d['F2'],
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                Alpha=d['Alpha'], Delta=d['Delta'],
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                tstart=self.minStartTime, tend=self.maxStartTime,
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                **kwargs)
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        else:
            self.search.plot_twoF_cumulative(
                self.label, self.outdir, F0=d['F0'], F1=d['F1'], F2=d['F2'],
                Alpha=d['Alpha'], Delta=d['Delta'], asini=d['asini'],
                period=d['period'], ecc=d['ecc'], argp=d['argp'], tp=d['argp'],
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                tstart=self.minStartTime, tend=self.maxStartTime, **kwargs)
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    def generic_lnprior(self, **kwargs):
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        """ Return a lambda function of the pdf

        Parameters
        ----------
        kwargs: dict
            A dictionary containing 'type' of pdf and shape parameters

        """

        def logunif(x, a, b):
            above = x < b
            below = x > a
            if type(above) is not np.ndarray:
                if above and below:
                    return -np.log(b-a)
                else:
                    return -np.inf
            else:
                idxs = np.array([all(tup) for tup in zip(above, below)])
                p = np.zeros(len(x)) - np.inf
                p[idxs] = -np.log(b-a)
                return p

        def halfnorm(x, loc, scale):
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            if x < loc:
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                return -np.inf
            else:
                return -0.5*((x-loc)**2/scale**2+np.log(0.5*np.pi*scale**2))

        def cauchy(x, x0, gamma):
            return 1.0/(np.pi*gamma*(1+((x-x0)/gamma)**2))

        def exp(x, x0, gamma):
            if x > x0:
                return np.log(gamma) - gamma*(x - x0)
            else:
                return -np.inf

        if kwargs['type'] == 'unif':
            return lambda x: logunif(x, kwargs['lower'], kwargs['upper'])
        elif kwargs['type'] == 'halfnorm':
            return lambda x: halfnorm(x, kwargs['loc'], kwargs['scale'])
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        elif kwargs['type'] == 'neghalfnorm':
            return lambda x: halfnorm(-x, kwargs['loc'], kwargs['scale'])
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        elif kwargs['type'] == 'norm':
            return lambda x: -0.5*((x - kwargs['loc'])**2/kwargs['scale']**2
                                   + np.log(2*np.pi*kwargs['scale']**2))
        else:
            logging.info("kwargs:", kwargs)
            raise ValueError("Print unrecognise distribution")

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    def generate_rv(self, **kwargs):
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        dist_type = kwargs.pop('type')
        if dist_type == "unif":
            return np.random.uniform(low=kwargs['lower'], high=kwargs['upper'])
        if dist_type == "norm":
            return np.random.normal(loc=kwargs['loc'], scale=kwargs['scale'])
        if dist_type == "halfnorm":
            return np.abs(np.random.normal(loc=kwargs['loc'],
                                           scale=kwargs['scale']))
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        if dist_type == "neghalfnorm":
            return -1 * np.abs(np.random.normal(loc=kwargs['loc'],
                                                scale=kwargs['scale']))
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        if dist_type == "lognorm":
            return np.random.lognormal(
                mean=kwargs['loc'], sigma=kwargs['scale'])
        else:
            raise ValueError("dist_type {} unknown".format(dist_type))

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    def plot_walkers(self, sampler, symbols=None, alpha=0.4, color="k", temp=0,
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                     lw=0.1, nprod=0, add_det_stat_burnin=False,
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                     fig=None, axes=None, xoffset=0, plot_det_stat=True,
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                     context='classic', subtractions=None, labelpad=0.05):
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        """ Plot all the chains from a sampler """

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        if np.ndim(axes) > 1:
            axes = axes.flatten()

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        shape = sampler.chain.shape
        if len(shape) == 3:
            nwalkers, nsteps, ndim = shape
            chain = sampler.chain[:, :, :]
        if len(shape) == 4:
            ntemps, nwalkers, nsteps, ndim = shape
            if temp < ntemps:
                logging.info("Plotting temperature {} chains".format(temp))
            else:
                raise ValueError(("Requested temperature {} outside of"
                                  "available range").format(temp))
            chain = sampler.chain[temp, :, :, :]

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        if subtractions is None:
            subtractions = [0 for i in range(ndim)]
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        else:
            if len(subtractions) != self.ndim:
                raise ValueError('subtractions must be of length ndim')
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        with plt.style.context((context)):
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            plt.rcParams['text.usetex'] = True
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            if fig is None and axes is None:
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                fig = plt.figure(figsize=(4, 3.0*ndim))
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                ax = fig.add_subplot(ndim+1, 1, 1)
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                axes = [ax] + [fig.add_subplot(ndim+1, 1, i)
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                               for i in range(2, ndim+1)]
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            idxs = np.arange(chain.shape[1])
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            burnin_idx = chain.shape[1] - nprod
            if hasattr(self, 'convergence_idx'):
                convergence_idx = self.convergence_idx
            else:
                convergence_idx = burnin_idx
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            if ndim > 1:
                for i in range(ndim):
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                    axes[i].ticklabel_format(useOffset=False, axis='y')
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                    cs = chain[:, :, i].T
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                    if burnin_idx > 0:
                        axes[i].plot(xoffset+idxs[:convergence_idx],
                                     cs[:convergence_idx]-subtractions[i],
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                                     color="r", alpha=alpha,
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                                     lw=lw)
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                    axes[i].plot(xoffset+idxs[burnin_idx:],
                                 cs[burnin_idx:]-subtractions[i],
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                                 color="k", alpha=alpha, lw=lw)
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                    if symbols:
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                        if subtractions[i] == 0:
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                            axes[i].set_ylabel(symbols[i], labelpad=labelpad)
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                        else:
                            axes[i].set_ylabel(
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                                symbols[i]+'$-$'+symbols[i]+'$_0$',
                                labelpad=labelpad)
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                    if hasattr(self, 'convergence_diagnostic'):
                        ax = axes[i].twinx()
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                        c_x = np.array(self.convergence_diagnosticx)
                        c_y = np.array(self.convergence_diagnostic)
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                        break_idx = np.argmin(np.abs(c_x - burnin_idx))
                        ax.plot(c_x[:break_idx], c_y[:break_idx, i], '-b')
                        ax.plot(c_x[break_idx:], c_y[break_idx:, i], '-b')
                        ax.set_ylabel('PSRF')
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                        ax.ticklabel_format(useOffset=False)
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                        ax.set_ylim(1, self.convergence_plot_upper_lim)
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            else:
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                axes[0].ticklabel_format(useOffset=False, axis='y')
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                cs = chain[:, :, temp].T
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                if burnin_idx:
                    axes[0].plot(idxs[:burnin_idx], cs[:burnin_idx],
                                 color="r", alpha=alpha, lw=lw)
                axes[0].plot(idxs[burnin_idx:], cs[burnin_idx:], color="k",
                             alpha=alpha, lw=lw)
                if symbols:
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                    axes[0].set_ylabel(symbols[0], labelpad=labelpad)
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            if plot_det_stat:
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                if len(axes) == ndim:
                    axes.append(fig.add_subplot(ndim+1, 1, ndim+1))

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                lnl = sampler.lnlikelihood[temp, :, :]
                if burnin_idx and add_det_stat_burnin:
                    burn_in_vals = lnl[:, :burnin_idx].flatten()
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                    try:
                        axes[-1].hist(burn_in_vals[~np.isnan(burn_in_vals)],
                                      bins=50, histtype='step', color='r')
                    except ValueError:
                        logging.info('Det. Stat. hist failed, most likely all '
                                     'values where the same')
                        pass
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                else:
                    burn_in_vals = []
                prod_vals = lnl[:, burnin_idx:].flatten()
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                try:
                    axes[-1].hist(prod_vals[~np.isnan(prod_vals)], bins=50,
                                  histtype='step', color='k')
                except ValueError:
                    logging.info('Det. Stat. hist failed, most likely all '
                                 'values where the same')
                    pass
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                if self.BSGL:
                    axes[-1].set_xlabel(r'$\mathcal{B}_\mathrm{S/GL}$')
                else:
                    axes[-1].set_xlabel(r'$\widetilde{2\mathcal{F}}$')
                axes[-1].set_ylabel(r'$\textrm{Counts}$')
                combined_vals = np.append(burn_in_vals, prod_vals)
                if len(combined_vals) > 0:
                    minv = np.min(combined_vals)
                    maxv = np.max(combined_vals)
                    Range = abs(maxv-minv)
                    axes[-1].set_xlim(minv-0.1*Range, maxv+0.1*Range)

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                xfmt = matplotlib.ticker.ScalarFormatter()
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                xfmt.set_powerlimits((-4, 4))
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                axes[-1].xaxis.set_major_formatter(xfmt)

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            axes[-2].set_xlabel(r'$\textrm{Number of steps}$', labelpad=0.2)
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        return fig, axes

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    def apply_corrections_to_p0(self, p0):
        """ Apply any correction to the initial p0 values """
        return p0

    def generate_scattered_p0(self, p):
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        """ Generate a set of p0s scattered about p """
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        p0 = [[p + self.scatter_val * p * np.random.randn(self.ndim)
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               for i in xrange(self.nwalkers)]
              for j in xrange(self.ntemps)]
        return p0

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    def generate_initial_p0(self):
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        """ Generate a set of init vals for the walkers """

        if type(self.theta_initial) == dict:
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            logging.info('Generate initial values from initial dictionary')
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            if hasattr(self, 'nglitch') and self.nglitch > 1:
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                raise ValueError('Initial dict not implemented for nglitch>1')
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            p0 = [[[self.generate_rv(**self.theta_initial[key])
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                    for key in self.theta_keys]
                   for i in range(self.nwalkers)]
                  for j in range(self.ntemps)]
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        elif type(self.theta_initial) == list:
            logging.info('Generate initial values from list of theta_initial')
            p0 = [[[self.generate_rv(**val)
                    for val in self.theta_initial]
                   for i in range(self.nwalkers)]
                  for j in range(self.ntemps)]
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        elif self.theta_initial is None:
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            logging.info('Generate initial values from prior dictionary')
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            p0 = [[[self.generate_rv(**self.theta_prior[key])
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                    for key in self.theta_keys]
                   for i in range(self.nwalkers)]
                  for j in range(self.ntemps)]
        elif len(self.theta_initial) == self.ndim:
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            p0 = self.generate_scattered_p0(self.theta_initial)
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        else:
            raise ValueError('theta_initial not understood')

        return p0

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    def get_new_p0(self, sampler):
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        """ Returns new initial positions for walkers are burn0 stage

        This returns new positions for all walkers by scattering points about
        the maximum posterior with scale `scatter_val`.

        """
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        temp_idx = 0
        pF = sampler.chain[temp_idx, :, :, :]
        lnl = sampler.lnlikelihood[temp_idx, :, :]
        lnp = sampler.lnprobability[temp_idx, :, :]
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        # General warnings about the state of lnp
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        if np.any(np.isnan(lnp)):
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            logging.warning(
                "Of {} lnprobs {} are nan".format(
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                    np.shape(lnp), np.sum(np.isnan(lnp))))
        if np.any(np.isposinf(lnp)):
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            logging.warning(
                "Of {} lnprobs {} are +np.inf".format(
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                    np.shape(lnp), np.sum(np.isposinf(lnp))))
        if np.any(np.isneginf(lnp)):
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            logging.warning(
                "Of {} lnprobs {} are -np.inf".format(
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                    np.shape(lnp), np.sum(np.isneginf(lnp))))
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        lnp_finite = copy.copy(lnp)
        lnp_finite[np.isinf(lnp)] = np.nan
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        idx = np.unravel_index(np.nanargmax(lnp_finite), lnp_finite.shape)
        p = pF[idx]
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        p0 = self.generate_scattered_p0(p)
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        self.search.BSGL = False
        twoF = self.logl(p, self.search)
        self.search.BSGL = self.BSGL

        logging.info(('Gen. new p0 from pos {} which had det. stat.={:2.1f},'
                      ' twoF={:2.1f} and lnp={:2.1f}')
                     .format(idx[1], lnl[idx], twoF, lnp_finite[idx]))

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        return p0

    def get_save_data_dictionary(self):
        d = dict(nsteps=self.nsteps, nwalkers=self.nwalkers,
                 ntemps=self.ntemps, theta_keys=self.theta_keys,
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                 theta_prior=self.theta_prior, scatter_val=self.scatter_val,
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                 log10temperature_min=self.log10temperature_min,
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                 BSGL=self.BSGL)
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        return d

    def save_data(self, sampler, samples, lnprobs, lnlikes):
        d = self.get_save_data_dictionary()
        d['sampler'] = sampler
        d['samples'] = samples
        d['lnprobs'] = lnprobs
        d['lnlikes'] = lnlikes

        if os.path.isfile(self.pickle_path):
            logging.info('Saving backup of {} as {}.old'.format(
                self.pickle_path, self.pickle_path))
            os.rename(self.pickle_path, self.pickle_path+".old")
        with open(self.pickle_path, "wb") as File:
            pickle.dump(d, File)

    def get_saved_data(self):
        with open(self.pickle_path, "r") as File:
            d = pickle.load(File)
        return d

    def check_old_data_is_okay_to_use(self):
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        if args.use_old_data:
            logging.info("Forcing use of old data")
            return True

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        if os.path.isfile(self.pickle_path) is False:
            logging.info('No pickled data found')
            return False

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        if self.sftfilepath is not None:
            oldest_sft = min([os.path.getmtime(f) for f in
                              self.get_list_of_matching_sfts()])
            if os.path.getmtime(self.pickle_path) < oldest_sft:
                logging.info('Pickled data outdates sft files')
                return False
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        old_d = self.get_saved_data().copy()
        new_d = self.get_save_data_dictionary().copy()

        old_d.pop('samples')
        old_d.pop('sampler')
        old_d.pop('lnprobs')
        old_d.pop('lnlikes')

        mod_keys = []
        for key in new_d.keys():
            if key in old_d:
                if new_d[key] != old_d[key]:
                    mod_keys.append((key, old_d[key], new_d[key]))
            else:
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                raise ValueError('Keys {} not in old dictionary'.format(key))
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        if len(mod_keys) == 0:
            return True
        else:
            logging.warning("Saved data differs from requested")
            logging.info("Differences found in following keys:")
            for key in mod_keys:
                if len(key) == 3:
                    if np.isscalar(key[1]) or key[0] == 'nsteps':
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                        logging.info("    {} : {} -> {}".format(*key))
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                    else:
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                        logging.info("    " + key[0])
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                else:
                    logging.info(key)
            return False

    def get_max_twoF(self, threshold=0.05):
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        """ Returns the max likelihood sample and the corresponding 2F value
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        Note: the sample is returned as a dictionary along with an estimate of
        the standard deviation calculated from the std of all samples with a
        twoF within `threshold` (relative) to the max twoF

        """
        if any(np.isposinf(self.lnlikes)):
            logging.info('twoF values contain positive infinite values')
        if any(np.isneginf(self.lnlikes)):
            logging.info('twoF values contain negative infinite values')
        if any(np.isnan(self.lnlikes)):
            logging.info('twoF values contain nan')
        idxs = np.isfinite(self.lnlikes)
        jmax = np.nanargmax(self.lnlikes[idxs])
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        maxlogl = self.lnlikes[jmax]
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        d = OrderedDict()
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        if self.BSGL:
            if hasattr(self, 'search') is False:
                self.inititate_search_object()
            p = self.samples[jmax]
            self.search.BSGL = False
            maxtwoF = self.logl(p, self.search)
            self.search.BSGL = self.BSGL
        else:
            maxtwoF = maxlogl

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        repeats = []
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        for i, k in enumerate(self.theta_keys):
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            if k in d and k not in repeats:
                d[k+'_0'] = d[k]  # relabel the old key
                d.pop(k)
                repeats.append(k)
            if k in repeats:
                k = k + '_0'
                count = 1
                while k in d:
                    k = k.replace('_{}'.format(count-1), '_{}'.format(count))
                    count += 1
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            d[k] = self.samples[jmax][i]
        return d, maxtwoF

    def get_median_stds(self):
        """ Returns a dict of the median and std of all production samples """
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        d = OrderedDict()
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        repeats = []
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        for s, k in zip(self.samples.T, self.theta_keys):
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            if k in d and k not in repeats:
                d[k+'_0'] = d[k]  # relabel the old key
                d[k+'_0_std'] = d[k+'_std']
                d.pop(k)
                d.pop(k+'_std')
                repeats.append(k)
            if k in repeats:
                k = k + '_0'
                count = 1
                while k in d:
                    k = k.replace('_{}'.format(count-1), '_{}'.format(count))
                    count += 1

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            d[k] = np.median(s)
            d[k+'_std'] = np.std(s)
        return d

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    def check_if_samples_are_railing(self, threshold=0.01):
        return_flag = False
        for s, k in zip(self.samples.T, self.theta_keys):
            prior = self.theta_prior[k]
            if prior['type'] == 'unif':
                prior_range = prior['upper'] - prior['lower']
                edges = []
                fracs = []
                for l in ['lower', 'upper']:
                    bools = np.abs(s - prior[l])/prior_range < threshold
                    if np.any(bools):
                        edges.append(l)
                        fracs.append(str(100*float(np.sum(bools))/len(bools)))
                if len(edges) > 0:
                    logging.warning(
                        '{}% of the {} posterior is railing on the {} edges'
                        .format('% & '.join(fracs), k, ' & '.join(edges)))
                    return_flag = True
        return return_flag

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    def write_par(self, method='med'):
        """ Writes a .par of the best-fit params with an estimated std """
        logging.info('Writing {}/{}.par using the {} method'.format(
            self.outdir, self.label, method))
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        median_std_d = self.get_median_stds()
        max_twoF_d, max_twoF = self.get_max_twoF()

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        logging.info('Writing par file with max twoF = {}'.format(max_twoF))
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        filename = '{}/{}.par'.format(self.outdir, self.label)
        with open(filename, 'w+') as f:
            f.write('MaxtwoF = {}\n'.format(max_twoF))
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            f.write('tref = {}\n'.format(self.tref))
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            if hasattr(self, 'theta0_index'):
                f.write('theta0_index = {}\n'.format(self.theta0_idx))
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            if method == 'med':
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                for key, val in median_std_d.iteritems():
                    f.write('{} = {:1.16e}\n'.format(key, val))
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            if method == 'twoFmax':
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                for key, val in max_twoF_d.iteritems():
                    f.write('{} = {:1.16e}\n'.format(key, val))

    def print_summary(self):
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        max_twoFd, max_twoF = self.get_max_twoF()
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        median_std_d = self.get_median_stds()
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        logging.info('Summary:')
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        if hasattr(self, 'theta0_idx'):
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            logging.info('theta0 index: {}'.format(self.theta0_idx))
        logging.info('Max twoF: {} with parameters:'.format(max_twoF))
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        for k in np.sort(max_twoFd.keys()):
            print('  {:10s} = {:1.9e}'.format(k, max_twoFd[k]))
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        logging.info('Median +/- std for production values')
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        for k in np.sort(median_std_d.keys()):
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            if 'std' not in k:
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                logging.info('  {:10s} = {:1.9e} +/- {:1.9e}'.format(
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                    k, median_std_d[k], median_std_d[k+'_std']))
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        logging.info('\n')
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    def CF_twoFmax(self, theta, twoFmax, ntrials):
        Fmax = twoFmax/2.0
        return (np.exp(1j*theta*twoFmax)*ntrials/2.0
                * Fmax*np.exp(-Fmax)*(1-(1+Fmax)*np.exp(-Fmax))**(ntrials-1))

    def pdf_twoFhat(self, twoFhat, nglitch, ntrials, twoFmax=100, dtwoF=0.1):
        if np.ndim(ntrials) == 0:
            ntrials = np.zeros(nglitch+1) + ntrials
        twoFmax_int = np.arange(0, twoFmax, dtwoF)
        theta_int = np.arange(-1/dtwoF, 1./dtwoF, 1./twoFmax)
        CF_twoFmax_theta = np.array(
            [[np.trapz(self.CF_twoFmax(t, twoFmax_int, ntrial), twoFmax_int)
              for t in theta_int]
             for ntrial in ntrials])
        CF_twoFhat_theta = np.prod(CF_twoFmax_theta, axis=0)
        pdf = (1/(2*np.pi)) * np.array(
            [np.trapz(np.exp(-1j*theta_int*twoFhat_val)
             * CF_twoFhat_theta, theta_int) for twoFhat_val in twoFhat])
        return pdf.real

    def p_val_twoFhat(self, twoFhat, ntrials, twoFhatmax=500, Npoints=1000):
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        """ Caluculate the p-value for the given twoFhat in Gaussian noise
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        Parameters
        ----------
        twoFhat: float
            The observed twoFhat value
        ntrials: int, array of len Nglitch+1
            The number of trials for each glitch+1
        """
        twoFhats = np.linspace(twoFhat, twoFhatmax, Npoints)
        pdf = self.pdf_twoFhat(twoFhats, self.nglitch, ntrials)
        return np.trapz(pdf, twoFhats)

    def get_p_value(self, delta_F0, time_trials=0):
        """ Get's the p-value for the maximum twoFhat value """
        d, max_twoF = self.get_max_twoF()
        if self.nglitch == 1:
            tglitches = [d['tglitch']]
        else:
            tglitches = [d['tglitch_{}'.format(i)] for i in range(self.nglitch)]
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        tboundaries = [self.minStartTime] + tglitches + [self.maxStartTime]
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        deltaTs = np.diff(tboundaries)
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        ntrials = [time_trials + delta_F0 * dT for dT in deltaTs]
        p_val = self.p_val_twoFhat(max_twoF, ntrials)
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        print('p-value = {}'.format(p_val))
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        return p_val

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    def get_evidence(self):
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        fburnin = float(self.nsteps[-2])/np.sum(self.nsteps[-2:])
        lnev, lnev_err = self.sampler.thermodynamic_integration_log_evidence(
            fburnin=fburnin)

        log10evidence = lnev/np.log(10)
        log10evidence_err = lnev_err/np.log(10)
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        return log10evidence, log10evidence_err

    def compute_evidence_long(self):
        """ Computes the evidence/marginal likelihood for the model """
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        betas = self.betas
        alllnlikes = self.sampler.lnlikelihood[:, :, self.nsteps[-2]:]
        mean_lnlikes = np.mean(np.mean(alllnlikes, axis=1), axis=1)

        mean_lnlikes = mean_lnlikes[::-1]
        betas = betas[::-1]

        fig, (ax1, ax2) = plt.subplots(nrows=2, figsize=(6, 8))

        if any(np.isinf(mean_lnlikes)):
            print("WARNING mean_lnlikes contains inf: recalculating without"
                  " the {} infs".format(len(betas[np.isinf(mean_lnlikes)])))
            idxs = np.isinf(mean_lnlikes)
            mean_lnlikes = mean_lnlikes[~idxs]
            betas = betas[~idxs]
            log10evidence = np.trapz(mean_lnlikes, betas)/np.log(10)
            z1 = np.trapz(mean_lnlikes, betas)
            z2 = np.trapz(mean_lnlikes[::-1][::2][::-1],
                          betas[::-1][::2][::-1])
            log10evidence_err = np.abs(z1 - z2) / np.log(10)

        ax1.semilogx(betas, mean_lnlikes, "-o")
        ax1.set_xlabel(r"$\beta$")
        ax1.set_ylabel(r"$\langle \log(\mathcal{L}) \rangle$")
        print("log10 evidence for {} = {} +/- {}".format(
              self.label, log10evidence, log10evidence_err))
        min_betas = []
        evidence = []
        for i in range(len(betas)/2):
            min_betas.append(betas[i])
            lnZ = np.trapz(mean_lnlikes[i:], betas[i:])
            evidence.append(lnZ/np.log(10))

        ax2.semilogx(min_betas, evidence, "-o")
        ax2.set_ylabel(r"$\int_{\beta_{\textrm{Min}}}^{\beta=1}" +
                       r"\langle \log(\mathcal{L})\rangle d\beta$", size=16)
        ax2.set_xlabel(r"$\beta_{\textrm{min}}$")
        plt.tight_layout()
        fig.savefig("{}/{}_beta_lnl.png".format(self.outdir, self.label))

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class MCMCGlitchSearch(MCMCSearch):
    """ MCMC search using the SemiCoherentGlitchSearch """
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    @helper_functions.initializer
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    def __init__(self, label, outdir, sftfilepath, theta_prior, tref,
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                 minStartTime, maxStartTime, nglitch=1, nsteps=[100, 100],
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                 nwalkers=100, ntemps=1, log10temperature_min=-5,
                 theta_initial=None, scatter_val=1e-10, dtglitchmin=1*86400,
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                 theta0_idx=0, detectors=None, BSGL=False, minCoverFreq=None,
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                 maxCoverFreq=None, earth_ephem=None, sun_ephem=None):
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        """
        Parameters
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        ----------
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        label, outdir: str
            A label and directory to read/write data from/to
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        sftfilepath: str
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            File patern to match SFTs
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        theta_prior: dict
            Dictionary of priors and fixed values for the search parameters.
            For each parameters (key of the dict), if it is to be held fixed
            the value should be the constant float, if it is be searched, the
            value should be a dictionary of the prior.
        theta_initial: dict, array, (None)
            Either a dictionary of distribution about which to distribute the
            initial walkers about, an array (from which the walkers will be
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            scattered by scatter_val), or None in which case the prior is used.
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        scatter_val, float or ndim array
            Size of scatter to use about the initialisation step, if given as
            an array it must be of length ndim and the order is given by
            theta_keys
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        nglitch: int
            The number of glitches to allow
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        tref, minStartTime, maxStartTime: int
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            GPS seconds of the reference time, start time and end time
        nsteps: list (m,)
            List specifying the number of steps to take, the last two entries
            give the nburn and nprod of the 'production' run, all entries
            before are for iterative initialisation steps (usually just one)
            e.g. [1000, 1000, 500].
        dtglitchmin: int
            The minimum duration (in seconds) of a segment between two glitches
            or a glitch and the start/end of the data
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        nwalkers, ntemps: int,
            The number of walkers and temperates to use in the parallel
            tempered PTSampler.
        log10temperature_min float < 0
            The  log_10(tmin) value, the set of betas passed to PTSampler are
            generated from np.logspace(0, log10temperature_min, ntemps).
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        theta0_idx, int
            Index (zero-based) of which segment the theta refers to - uyseful
            if providing a tight prior on theta to allow the signal to jump
            too theta (and not just from)
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        detectors: str
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            Two character reference to the data to use, specify None for no
            contraint.
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