B d"@s>dZddlZddlmZddZddZd d d Zd d ZdS)z` This modules provides functions for estimating the marginal likelihood or evidence of a model. N) integratecCsbt|}t|}d}x*t|D]\}}|t|||7}q Wt|}||t|7}|S)aReturns the log evidence via the prior arithmetic mean estimator (AME). The logarithm form of AME is used. This is the most basic evidence estimator, and often requires O(billions) of samples from the prior. Parameters ---------- log_likelihood : 1d array of floats The log likelihood of the data sampled from the prior distribution. Returns ------- float : Estimation of the log of the evidence. g)lennumpymax enumerateexplog)log_likelihood num_sampleslogl_max log_evidencei_re/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/pycbc/inference/evidence.pyarithmetic_mean_estimators  rcCsrt|}td|}d}x.t|D]"\}}|td|||7}q$Wdt|}||7}|t|7}|S)aReturns the log evidence via posterior harmonic mean estimator (HME). The logarithm form of HME is used. This method is not recommended for general use. It is very slow to converge, formally, has infinite variance, and very error prone. Not recommended for general use. Parameters ---------- log_likelihood : 1d array of floats The log likelihood of the data sampled from the posterior distribution. Returns ------- float : Estimation of the log of the evidence. gg)rrrrrr)r r r r r rrrrharmonic_mean_estimator6srsimpsonscsdddg}||kr"td||ft|}||}|tt|tdftjdd}|dkr~t||}|dkrd}xhtt|dD]T|d|}d |d } t d} | t 8} || | 8}qW||7}n|dkrt j ||d d }t td} g} x|dkrx2t dD]"\} t j | |d d | <qWt| tttd}||fS)awReturns the log evidence of the model via thermodynamic integration. Also returns an estimated standard deviation for the log evidence. Current options are integration through the trapezoid rule, a first-order corrected trapezoid rule, and Simpson's rule. Parameters ---------- log_likelihood : 3d array of shape (betas, walker, iteration) The log likelihood for each temperature separated by temperature, walker, and iteration. betas : 1d array The inverse temperatures used in the MCMC. method : {"trapzoid", "trapezoid_corrected", "simpsons"}, optional. The numerical integration method to use for the thermodynamic integration. Choices include: "trapezoid", "trapezoid_corrected", "simpsons", for the trapezoid rule, the first-order correction to the trapezoid rule, and Simpson's rule. [Default = "simpsons"] Returns ------- log_evidence : float Estimation of the log of the evidence. mcmc_std : float The standard deviation of the log evidence estimate from Monte-Carlo spread. trapezoidtrapezoid_correctedrz$Method %s not supported. Expected %sr)Zaxis)rrgUUUUUU?g@last)Zevencsg|]}|qSrr).0x)r r rr sz-thermodynamic_integration..) ValueErrorrargsortreshaperflattenaverageZtrapzrangevarrZsimpszerosrappendZstdsqrtfloat)r betasmethodZ method_listorderZ average_loglr Zvar_correction delta_betaZ pre_fac_varZvar_diffZti_vecZ logl_per_samprmcmc_stdr)r r rthermodynamic_integrationXsL#       (    r+cCszt|ddd}||}||}t|t|t|df}tt|d}x|tt|dD]h}||||d}t||d}||}|||d|}tt t |}||||<qhWt |} | } d} xhtt|dD]T}||||d}|||d||} t | d} t | d} | | 7} qW| t t|dd} t | } | | fS)aReturns the log evidence of the model via stepping stone algorithm. Also returns an estimated standard deviation for the log evidence. Parameters ---------- log_likelihood : 3d array of shape (betas, walker, iteration) The log likelihood for each temperature separated by temperature, walker, and iteration. betas : 1d array The inverse temperatures used in the MCMC. Returns ------- log_evidence : float Estimation of the log of the evidence. mcmc_std : float The standard deviation of the log evidence estimate from Monte-Carlo spread. Nrrg?g@)rrrrrr"r rrrrsumr%r$)r r&r(Z log_rk_pbr r)Z max_logl_pbZval_1Zval_2Zlog_rkr r*Zpre_factvalrrrstepping_stone_algorithms4   r0)r)__doc__rZscipyrrrr+r0rrrrs  # i