**I**n continuation of my earlier post on Bayesian GANs, which resort to strongly incompatible conditionals, I read a 2015 paper of Chen and Ip that I had missed. (Published in the Journal of Statistical Computation and Simulation which I first confused with JCGS and which I do not know at all. Actually, when looking at its editorial board, I recognised only one name.) But the study therein is quite disappointing and not helping as it considers Markov chains on finite state spaces, meaning that the transition distributions are matrices, meaning also that convergence is ensured if these matrices have no null probability term. And while the paper is motivated by realistic situations where incompatible conditionals can reasonably appear, the paper only produces illustrations on two and three states Markov chains. Not that helpful, in the end… The game is still afoot!

## Archive for Bayesian GANs

## Gibbs for incompatible kids

Posted in Books, Statistics, University life with tags Bayesian GANs, convergence of Gibbs samplers, GANs, Gibbs for Kids, Gibbs sampling, irreducibility, JCGS, Markov chains, MCMC algorithms, Monte Carlo Statistical Methods, stationarity on September 27, 2018 by xi'an## Bayesian GANs [#2]

Posted in Books, pictures, R, Statistics with tags ABC in Edinburgh, Bayesian GANs, compatible conditional distributions, Edinburgh, GANs, generative adversarial networks, ISBA 2018, joint posterior, MCMC convergence, Metropolis-within-Gibbs algorithm, Monte Carlo Statistical Methods, normal model, University of Edinburgh on June 27, 2018 by xi'an**A**s 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…