snowdrop.src.numeric.bayes package

Submodules

snowdrop.src.numeric.bayes.mcmc module

Created on Fri Apr 5 13:09:34 2019

Curently implemented for linear models only.

@author: A.Goumilevski

snowdrop.src.numeric.bayes.mcmc.func_likelihood(p, *args)[source]

Custom function defining log of likelihood.

snowdrop.src.numeric.bayes.mcmc.func_prior(p, *args)[source]

Custom function defining log of prior probability.

snowdrop.src.numeric.bayes.mcmc.gelman_rubin(chain)[source]

The Gelman-Rubin Test.

snowdrop.src.numeric.bayes.mcmc.likelihood_logp(parameters, stds)[source]

Function defining log of likelihood.

snowdrop.src.numeric.bayes.mcmc.logp(p, *args)[source]

Custom function defining log of posterioir probability.

snowdrop.src.numeric.bayes.mcmc.prior_logp(p)[source]

Function defining log of prior probability.

snowdrop.src.numeric.bayes.mcmc.sample(model, n, obs, Qm, Hm, y0, method='emcee', parameters=None, steady_state=None, burn=10, Ndraws=310, Niter=200, ind_non_missing=None, Parallel=False, resetParameters=True, debug=True, save=False)[source]

Draw model parameters samples by using MCMC sampler.

The variants of MC2 sampler are:

  • Affine Invariant Markov Chain Monte Carlo (MCMC) Ensemble sampler (emcee package).
  • Markov Chain Monte Carlo (MCMC) sampler includes different Metropolis based sampling techniques:
    • Metropolis-Hastings (MH): Primary sampling method.

    • Adaptive-Metropolis (AM): Adapts covariance matrix at specified intervals.

    • Delayed-Rejection (DR): Delays rejection by sampling from a narrower distribution. Capable of n-stage delayed rejection.

    • Delayed Rejection Adaptive Metropolis (DRAM): DR + AM

    Please see https://pymcmcstat.readthedocs.io/_/downloads/en/latest/pdf/

  • Markov Chain Monte Carlo (MCMC) sampler with “particles” package

    Please see https://pypi.org/project/particles , https://github.com/nchopin/particles ,

    Nicolas, Chopin and Omiros, Papaspiliopoulos, 2020, “An Introduction to Sequential Monte Carlo”, Springer Series in Statistics.

Parameters:
param model:

Model object.

type model:

Model.

param n:

Number of endogenous variables.

type n:

int.

param obs:

Measurement data.

type obs:

numpy.array.

param Qm:

Covariance matrix of errors of endogenous variables.

type Qm:

numpy.array.

param Hm:

Covariance matrix of errors of measurement variables.

type Hm:

numpy.array.

param y0:

Starting values of endogenous variables.

type y0:

list.

param method:

Sampler algorithm.

type method:

str.

param parameters:

List of model parameters.

type parameters:

list.

param steady_state:

List of steady states.

type steady_state:

list.

param burn:

Number of samples to discard.

type burn:

int.

param Ndraws:

Number of draws.

type Ndraws:

int.

param Niter:

Number of iterations.

type Niter:

int.

param ind_non_missing:

indices of non-missing observations.

type ind_non_missing:

list.

param Parallel:

If True runs parallel parameters sampling.

type Parallel:

bool.

param resetParameters:

If True resets parameters to the samples mean values.

type resetParameters:

bool

param debug:

If True print chain statistics information for pymcmcstat method.

type debug:

bool.

Module contents