Bayes

When working with distance measures between distributions, singularities can pose a significant challenge. This happens when one of the distributions is degenerate, concentrating all its probability mass on a single point. In this post we discussed the comparison of a Gamma distribution (representing a complex model) with a singular Gamma distribution (representing a base model) in the context of constructing a penalized complexity (PC) prior for the overdispersion parameter $\phi$ in a Bayesian negative binomial regression. In said post, I stated that the distance measure of interest for constructing the PC prior is ...

Negative Binomial as Poisson Mixture I have recently found it useful having the negative binomial (NB) distribution represented as a continuous mixture distribution. This makes it straightforward to understand how the NB distribution relates to the Poisson distribution (how the Poisson assumptions can be relaxed to allow for overdispersion in count data regression). Also, the Bayesian Poisson-Gamma mixture model is nice to illustrate the concept of penalized complexity priors. ...