(This article was originally published at R – Xi'an's Og, and syndicated at StatsBlogs.)
As an illustration of the lack of convergence of the Gibbs sampler applied to the two “conditionals” defined in the Bayesian GANs paper discussed yesterday, I took the simplest possible example of a Normal mean generative model (one parameter) with a logistic discriminator (one parameter) and implemented the scheme (during an ISBA 2018 session). With flat priors on both parameters. And a Normal random walk as Metropolis-Hastings proposal. As expected, since there is no stationary distribution associated with the Markov chain, simulated chains do not exhibit a stationary pattern,
And they eventually reach an overflow error or a trapping state as the log-likelihood gets approximately to zero (red curve).
Too bad I missed the talk by Shakir Mohammed yesterday, being stuck on the Edinburgh by-pass at rush hour!, as I would have loved to hear his views about this rather essential issue…
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