This package implements a few utilities for debugging MCMC samplers, which includes

• Geweke test
  • See the references [1,2] or this blog for details
• Central limit theorem test

See the notebook for an example.

The example notebook covers most of the usages. Some details on the model definition via DynamicPPL is explained below.

MCMCDebugging.jl allows using DynamicPPL.jl to define test models. In the example notebook, the test model is defined as

@model function BetaBinomial(θ=missing, x=missing)
    θ ~ Beta(2, 3)
    x ~ Binomial(3, θ)
    return θ, x
end

There are a few requirements from MCMCDebugging.jl to use the defined model.

1. The model should take θ and x as inputs (in order) and optionally being missing.

• So that the model can be used to generate the marginal sampler as e.g. BetaBinomial() and conditional sampler as e.g. BetaBinomial(θ)

2. The model should return the parameter θ and the data x as a tuple.

With these two points, MCMCDebugging.jl can generate several functions used by lower-level APIs.

1. rand_marginal(): drawing θ and x as a tuple
2. rand_x_given(θ): drawing x conditioned on θ
3. logjoint(θ, x): computing the log-joint probability of θ and x

1 and 2 are used to perform the Geweke test and 3 is used to make the Q-Q plot.

Defining the Geweke test

cfg = GewekeTest(n_samples::Int)

where n_samples is the number of samples used for testing.

Performing the Geweke test

res = perform(cfg::GewekeTest, rand_marginal, rand_x_given, rand_θ_given; g=nothing, progress=true)

where

• rand_marginal() draws θ and x as a tuple
• rand_x_given(θ) draws x conditioned on θ
• rand_θ_given(x) draws θ conditioned on x
• g(θ, x) is the test function

Making the Q-Q plot

plot(res::GewekeTestResult, logjoint)

where

• logjoint(θ, x) computes the log-joint probability of θ and x

In case models are defined by DynamicPPL.jl, you can use

plot(res::GewekeTestResult, model)

For example, plot(res, BetaBinomial()). Note we have to pass an instantiated model (i.e. BetaBinomial()) here, for now, to make Julia correctly dispatch the plot recipe.

[1] Geweke J. Getting it right: Joint distribution tests of posterior simulators. Journal of the American Statistical Association. 2004 Sep 1;99(467):799-804.

[2] Grosse RB, Duvenaud DK. Testing mcmc code. arXiv preprint arXiv:1412.5218. 2014 Dec 16.