Module bayespputils

Workaround for missing astropy.table.Table.replace_column method, which was added in Astropy 1.1.

FIXME: remove this function when LALSuite depends on Astropy >= 1.1.

Workaround for missing astropy.table.Table.as_array method, which was added in Astropy 1.0.

FIXME: remove this function when LALSuite depends on Astropy >= 1.0.

input: posterior class instance, list of confidence levels, optional choice of inital parameter space, samples per box in kdtree note initial_boundingbox is [[lowerbound of each param][upper bound of each param]], if not specified will just take limits of samples fraction is proportion of samples used for making the tree structure. returns: confidence_intervals, sorted list of kd objects, initial_boundingbox, injInfo where injInfo is [bounding box injection is found within, samples in said box, weighting of box (in case of repeated samples),inj_confidence, inj_confidence_area]

Determine the 2-parameter Bayesian Confidence Intervals using a greedy binning algorithm.

Parameters:

• posterior - an instance of the Posterior class.
• greedy2Params - a dict - {param1Name:param1binSize,param2Name:param2binSize} .
• confidence_levels - A list of floats of the required confidence intervals [(0-1)].

Greedy bins the sky posterior samples into a grid on the sky constructed so that sky boxes have roughly equal size (determined by skyres).

Parameters:

• posterior - Posterior class instance containing ra and dec samples.
• skyres - Desired approximate size of sky pixel on one side.
• confidence_levels - List of desired confidence levels [(0-1)].

Plots a sky map from a healpix map, optionally including an
injected position.

:param hpmap: An array representing a healpix map (in nested
  ordering if ``nest = True``).

:param outdir: The output directory.

:param inj: If not ``None``, then ``[ra, dec]`` of the injection
  associated with the posterior map.

:param nest: Flag indicating the pixel ordering in healpix.

Utility function for converting mchirp,eta to component masses. The masses are defined so that m1>m2. The rvalue is a tuple (m1,m2).

Utility function for converting mchirp,q to component masses. The masses are defined so that m1>m2. The rvalue is a tuple (m1,m2).

Utility function for converting mchirp,q to eta. The rvalue is eta.

Calculate orbital angular momentum vector. Note: The units of Lmag are different than what used in lalsimulation. Mc must be called in units of Msun here.

Note that if one wants to build J=L+S1+S2 with L returned by this function, S1 and S2 must not get the Msun^2 factor.

Calculate the magnitude of the effective precessing spin following convention from Phys. Rev. D 91, 024043 -- arXiv:1408.1810 note: the paper uses naming convention where m1 < m2 (and similar for associated spin parameters) and q > 1

Calculate the redshift from the luminosity distance measurement using the Cosmology Calculator provided in LAL. By default assuming cosmological parameters from arXiv:1502.01589 - 'Planck 2015 results. XIII. Cosmological parameters' Using parameters from table 4, column 'TT+lowP+lensing+ext' This corresponds to Omega_M = 0.3065, Omega_Lambda = 0.6935, H_0 = 67.90 km s^-1 Mpc^-1 Returns an array of redshifts

Wrapper function for SimInspiralTransformPrecessingNewInitialConditions(). Vectorizes function for use in append_mapping() methods of the posterior class.

Plots a 1D histogram and (gaussian) kernel density estimate of the distribution of posterior samples for a given parameter.

Parameters:

• posterior - an instance of the Posterior class.
• plot1DParams - a dict; {paramName:Nbins}
• analyticPDF - an analytic probability distribution function describing the distribution.
• analyticCDF - an analytic cumulative distribution function describing the distribution.

round given angle in radians to integer hours, degrees, mins or secs accuracy can be 'hour'. 'deg', 'min', 'sec', 'all', all does nothing 'arcmin', 'arcsec'

Make a corner plot using the triangle module (See http://github.com/dfm/corner.py)

Parameters:

• posterior - The Posterior object
• levels - a list of confidence levels
• parnames - list of parameters to include

Plots a 2D kernel density estimate of the 2-parameter marginal posterior.

Parameters:

• posterior - an instance of the Posterior class.
• plot2DkdeParams - a dict {param1Name:Nparam1Bins,param2Name:Nparam2Bins}

Plots a 2D kernel density estimate of the 2-parameter marginal posterior.

Parameters:

• posterior - an instance of the Posterior class.
• plot2DkdeParams - a dict {param1Name:Nparam1Bins,param2Name:Nparam2Bins}

Returns a 2D histogram and edges for the two parameters passed in greedy2Params, plus the actual discrete confidence levels
imposed by the finite number of samples.
   H,xedges,yedges,Hlasts = histogram2D(posterior,greedy2Params,confidence_levels)
@param posterior: Posterior instance
@param greedy2Params: a dict ;{param1Name:param1binSize,param2Name:param2binSize}
@param confidence_levels: a list of the required confidence levels to plot on the contour map.

@param posteriors_by_name A dictionary of posterior objects indexed by name

Parameters:

• greedy2Params - a dict ;{param1Name:param1binSize,param2Name:param2binSize}
• confidence_levels - a list of the required confidence levels to plot on the contour map.

Plots the confidence level contours as determined by the 2-parameter greedy binning algorithm.

Parameters:

• posteriors_by_name - A dict containing Posterior instances referenced by some id.
• greedy2Params - a dict ;{param1Name:param1binSize,param2Name:param2binSize}
• confidence_levels - a list of the required confidence levels to plot on the contour map.
• colors_by_name - A dict of colors cross-referenced to the above Posterior ids.
• legend - Argument for legend placement or None for no legend ('right', 'upper left', 'center' etc)

Histograms of the ranked pixels produced by the 2-parameter greedy binning algorithm colured by their confidence level.

Parameters:

• toppoints - Nx2 array of 2-parameter posterior samples.
• posterior - an instance of the Posterior class.
• greedy2Params - a dict ;{param1Name:param1binSize,param2Name:param2binSize}

Determine the 1-parameter Bayesian Confidence Interval using a greedy binning algorithm.

Parameters:

• posterior - an instance of the posterior class.
• greedy1Param - a dict; {paramName:paramBinSize}.
• confidence_levels - A list of floats of the required confidence intervals [(0-1)].

Calculates the smallest contigious 1-parameter confidence interval for a set of given confidence levels.

Parameters:

• posterior - an instance of the Posterior class.
• contInt1Params - a dict {paramName:paramBinSize}.
• confidence_levels - Required confidence intervals.

Returns an estimate of the autocorrelation function of a given series. Returns only the positive-lag portion of the ACF, normalized so that the zero-th element is 1.

Attempts to find a self-consistent estimate of the autocorrelation length of a given series.

If C(tau) is the autocorrelation function (normalized so C(0) = 1, for example from the autocorrelation procedure in this module), then the autocorrelation length is the smallest s such that

1 + 2*C(1) + 2*C(2) + ... + 2*C(M*s) < s

In words: the autocorrelation length is the shortest length so that the sum of the autocorrelation function is smaller than that length over a window of M times that length.

The maximum window length is restricted to be len(series)/K as a safety precaution against relying on data near the extreme of the lags in the ACF, where there is a lot of noise. Note that this implies that the series must be at least M*K*s samples long in order to get a reliable estimate of the ACL.

If no such s can be found, raises ACLError; in this case it is likely that the series is too short relative to its true autocorrelation length to obtain a consistent ACL estimate.

Parse a VO Table RESOURCE containing nested sampling output and return a VOTable TABLE element with posterior samples in it. This can be added to an existing tree by the user. Nlive will be read from the nsresource, unless specified

Returns a tuple (relative_change, fractional_uncertainty, percentile_uncertainty) giving the uncertainty in confidence intervals from multiple posteriors.

The uncertainty in the confidence intervals is the difference in length between the widest interval, formed from the smallest to largest values among all the cl_bounds, and the narrowest interval, formed from the largest-small and smallest-large values among all the cl_bounds. Note that neither the smallest nor the largest confidence intervals necessarily correspond to one of the cl_bounds.

The relative change relates the confidence interval uncertainty to the expected value of the parameter, the fractional uncertainty relates this length to the length of the confidence level from the combined posteriors, and the percentile uncertainty gives the change in percentile over the combined posterior between the smallest and largest confidence intervals.

@param cl The confidence level (between 0 and 1).

@param cl_bounds A list of (low, high) pairs giving the confidence interval associated with each posterior.

@param posteriors A list of PosteriorOneDPDF objects giving the posteriors.

Return location of lower or upper confidence levels
Args:
    x: List of samples.
    cl: Confidence level to return the bound of.
    lower: If ``True``, return the lower bound, otherwise return the upper bound.

Plot calibration posterior estimates for a spline model in log space.
Args:
    logf: The (log) location of spline control points.
    ys: List of posterior draws of function at control points ``logf``
    nx: Number of points to evaluate spline at for plotting.
    level: Credible level to fill in.
    color: Color to plot with.
    label: Label for plot.
    xform: Function to transform the spline into plotted values.

logParams

Value:

['logl', 'loglh1', 'loglh2', 'logll1', 'loglv1', 'deltalogl', 'deltalo glh1', 'deltalogll1', 'deltaloglv1', 'logw', 'logprior', 'logpost', 'n ulllogl', 'chain_log_evidence', 'chain_delta_log_evidence', 'chain_log _noise_evidence', 'chain_log_bayes_factor']

relativePhaseParams

Value:

[a+ b+ '_relative_phase' for a, b in combinations(['h1', 'l1', 'v1'], 2)]

snrParams

Value:

['snr', 'optimal_snr', 'matched_filter_snr']+ ['%s_optimal_snr' %(i) f or i in ['h1', 'l1', 'v1']]+ ['%s_cplx_snr_amp' %(i) for i in ['h1', ' l1', 'v1']]+ ['%s_cplx_snr_arg' %(i) for i in ['h1', 'l1', 'v1']]+ rel ativePhaseParams

calPhaseParams

Value:

['calpha_%s' %(ifo) for ifo in ['h1', 'l1', 'v1']]

massParams

Value:

['m1', 'm2', 'chirpmass', 'mchirp', 'mc', 'eta', 'q', 'massratio', 'as ym_massratio', 'mtotal', 'mf']

spinParamsPrec

Value:

['a1', 'a2', 'phi1', 'theta1', 'phi2', 'theta2', 'costilt1', 'costilt2 ', 'costheta_jn', 'cosbeta', 'tilt1', 'tilt2', 'phi_jl', 'theta_jn', ' phi12', 'af']

spinParamsEff

Value:

['chi', 'effectivespin', 'chi_eff', 'chi_tot', 'chi_p']

cosmoParam

Value:

['m1_source', 'm2_source', 'mtotal_source', 'mc_source', 'redshift', ' mf_source']

ppEParams

Value:

['ppEalpha', 'ppElowera', 'ppEupperA', 'ppEbeta', 'ppElowerb', 'ppEupp erB', 'alphaPPE', 'aPPE', 'betaPPE', 'bPPE']

tigerParams

Value:

['dchi%i' %(i) for i in range(8)]+ ['dchi%il' %(i) for i in [5, 6]]+ [ 'dxi%d' %(i+ 1) for i in range(6)]+ ['dalpha%i' %(i+ 1) for i in range (5)]+ ['dbeta%i' %(i+ 1) for i in range(3)]+ ['dsigma%i' %(i+ 1) for i in range(4)]

tidalParams

Value:

['lambda1', 'lambda2', 'lam_tilde', 'dlam_tilde', 'lambdat', 'dlambdat ']

strongFieldParams

Value:

ppEParams+ tigerParams+ bransDickeParams+ massiveGravitonParams+ tidal Params+ energyParams

statsParams

Value:

['logprior', 'logl', 'deltalogl', 'deltaloglh1', 'deltalogll1', 'delta loglv1', 'deltaloglh2', 'deltaloglg1']

calibParams

Value:

['calpha_l1', 'calpha_h1', 'calpha_v1', 'calamp_l1', 'calamp_h1', 'cal amp_v1']

greedyBinSizes

Value:

{'mc': 0.025, 'm1': 0.1, 'm2': 0.1, 'mass1': 0.1, 'mass2': 0.1, 'mtota l': 0.1, 'mc_source': 0.025, 'm1_source': 0.1, 'm2_source': 0.1, 'mtot al_source': 0.1, 'eta': 0.001, 'q': 0.01, 'asym_massratio': 0.01, 'iot a': 0.01, 'cosiota': 0.02, 'time': 1e-4, 'time_mean': 1e-4, 'distance' : 1.0, 'dist': 1.0, 'redshift': 0.01, 'mchirp': 0.025, 'chirpmass': 0. 025, 'spin1': 0.04, 'spin2': 0.04, 'a1z': 0.04, 'a2z': 0.04, 'a1': 0.0 2, 'a2': 0.02, 'phi1': 0.05, 'phi2': 0.05, 'theta1': 0.05, 'theta2': 0 .05, 'ra': 0.05, 'dec': 0.05, 'chi': 0.05, 'chi_eff': 0.05, 'chi_tot': ...