Archive for joint posterior

Bayesian GANs [#2]

Posted in Books, pictures, R, Statistics with tags , , , , , , , , , , , , on June 27, 2018 by xi'an

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…

Statistical Inference

Posted in Books, Statistics, University life with tags , , , , , , , , , on November 16, 2010 by xi'an

Following the publication of several papers on the topic of integrated evidence (about competing models), Murray Aitkin has now published a book entitled Statistical Inference and I have now finished reading it. While I appreciate the effort made by Murray Aitkin to place his theory within a coherent Bayesian framework, I remain unconvinced of the said coherence, for reasons exposed below.

The main chapters of the book are Chapter 2 about the “Integrated Bayes/likelihood approach” and Chapter 4 about the “Unified analysis of finite populations”, Chapter 7 also containing a new proposal about “Goodness of fit and model diagnostics”. Chapter 1 is a nice introduction to frequentist, likelihood and Bayesian approaches to inference and the four remaining chapters are applications of Murray Aitkin‘s principles to various models.  The style of the book is quite pleasant although slightly discursive in what I (a Frenchman!) would qualify as an English style in that it is often relying on intuition to develop concepts. I also think that the argument of being close to the frequentist decision (aka the p-value) too often serves as a justification in the book (see, e.g., page 43 “the p-value has a direct interpretation as a posterior probability”). As an aside, Murray Aitkin is a strong believer in plotting cdfs rather than densities to provide information about a distribution and hence cdf plots abound throughout the book.  (I counted 82 pictures of them.) While the book contains a helpful array of examples and datasets, the captions of the (many) figures are too terse for my taste: The figures are certainly not self-contained and even with the help of the main text they do not always make complete sense. Continue reading