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(This article was first published on <strong><a href="https://xianblog.wordpress.com/2018/06/27/bayesian-gans-2/"> R – Xi'an's Og</a></strong>, and kindly contributed to <a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers)</a> </div>
<p><strong><img data-orig-file="https://xianblog.files.wordpress.com/2018/06/burgh061877-e1529907699259.jpg" data-orig-size="1440,772" data-medium-file="https://xianblog.files.wordpress.com/2018/06/burgh061877-e1529907699259.jpg?w=438&amp;h=235&amp;fit=438%2C235&amp;resize=438%2C235" data-attachment-id="36452" data-image-meta="{" data-image-description="" src="https://xianblog.files.wordpress.com/2018/06/burgh061877-e1529907699259.jpg?w=438&h=235&fit=438%2C235&resize=438%2C235" data-permalink="https://xianblog.wordpress.com/2018/06/27/bayesian-gans-2/olympus-digital-camera-469/" data-large-file="https://xianblog.files.wordpress.com/2018/06/burgh061877-e1529907699259.jpg?w=450" alt="" data-image-title="" sizes="(max-width: 438px) 100vw, 438px" width="438" data-comments-opened="1" class="wp-image-36452" data-recalc-dims="1" height="235">A</strong>s an illustration of the lack of convergence of the Gibbs sampler applied to the two “conditionals” defined in <a rel="nofollow" href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0ahUKEwiklfmapeTbAhVCrRQKHVyLCrYQwqsBCD8wAQ&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D24A8tWs6aug&usg=AOvVaw18PDeBErvFU-msuKHQ9zY1" target="_blank">the Bayesian GANs paper</a> <a rel="nofollow" href="https://xianblog.wordpress.com/2018/06/26/bayesian-gan-gan-style/" target="_blank">discussed yesterday</a>, 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 <a rel="nofollow" href="https://xianblog.wordpress.com/2018/04/26/isba-2018-provisional-program-is-now-on/" target="_blank">ISBA 2018</a> 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,<img data-orig-file="https://xianblog.files.wordpress.com/2018/06/bayesgan.jpeg" data-orig-size="573,236" data-medium-file="https://xianblog.files.wordpress.com/2018/06/bayesgan.jpeg?w=373&amp;h=154&amp;fit=373%2C154&amp;resize=373%2C154" data-attachment-id="36450" data-image-meta="{" data-image-description="" src="https://xianblog.files.wordpress.com/2018/06/bayesgan.jpeg?w=373&h=154&fit=373%2C154&resize=373%2C154" data-permalink="https://xianblog.wordpress.com/2018/06/27/bayesian-gans-2/bayesgan/" data-large-file="https://xianblog.files.wordpress.com/2018/06/bayesgan.jpeg?w=450" alt="" data-image-title="bayesgan" title="(u.l.) mean (u.r.) logistic (l.l.) product (l.r.) log-likelihood" sizes="(max-width: 373px) 100vw, 373px" width="373" data-comments-opened="1" class="wp-image-36450" data-recalc-dims="1" height="154"></p>
<p>And they eventually reach an overflow error or a trapping state as the log-likelihood gets approximately to zero (red curve).<img data-orig-file="https://xianblog.files.wordpress.com/2018/06/baygan.jpeg" data-orig-size="573,236" data-medium-file="https://xianblog.files.wordpress.com/2018/06/baygan.jpeg?w=370&amp;h=153&amp;fit=370%2C153&amp;resize=370%2C153" data-attachment-id="36451" data-image-meta="{" data-image-description="" src="https://xianblog.files.wordpress.com/2018/06/baygan.jpeg?w=370&h=153&fit=370%2C153&resize=370%2C153" data-permalink="https://xianblog.wordpress.com/2018/06/27/bayesian-gans-2/baygan/" data-large-file="https://xianblog.files.wordpress.com/2018/06/baygan.jpeg?w=450" alt="" data-image-title="baygan" title="(u.l.) mean (u.r.) logistic (l.l.) product (l.r.) log-likelihood" sizes="(max-width: 370px) 100vw, 370px" width="370" data-comments-opened="1" class="wp-image-36451" data-recalc-dims="1" height="153"></p>
<p>Too bad I missed <a rel="nofollow" href="http://xsbrg0.m.attendify.com/app/sessions/9VU49ovfh9N6mhVjRL/details" target="_blank">the talk by Shakir Mohammed</a> 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…</p>
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