Martyn Plummer

JAGS is a program for Bayesian Graphical modelling which aims for compatibility with Classic BUGS. The program could eventually be developed as an R package. This article explains the motivations for this program, briefly describes the architecture and then discusses some ideas for a vectorized form of the BUGS language.

[1st paragraph] At first sight, Bayesian inference with Markov Chain Monte Carlo (MCMC) appears to be straightforward. The user defines a full probability model, perhaps using one of the programs discussed in this issue; an underlying sampling engine takes the model definition and returns a sequence of dependent samples from the posterior distribution of the model parameters, given the supplied data. The user can derive any summary of the posterior distribution from this sample. For example, to calculate a 95% credible interval for a parameter α, it suffices to take 1000 MCMC iterations of α and sort them so that α<sub>1</sub><α<sub>2</sub><...<α<sub>1000</sub>. The credible interval estimate is then (α<sub>25</sub>, α<sub>975</sub>). However, there is a price to be paid for this simplicity. Unlike most numerical methods used in statistical inference, MCMC does not give a clear indication of whether it has converged. The underlying Markov chain theory only guarantees that the distribution of the output will converge to the posterior in the limit as the number of iterations increases to infinity. The user is generally ignorant about how quickly convergence occurs, and therefore has to fall back on post hoc testing of the sampled output. By convention, the sample is divided into two parts: a “burn in” period during which all samples are discarded, and the remainder of the run in which the chain is considered to have converged sufficiently close to the limiting distribution to be used. Two questions then arise: 1. How long should the burn in period be? 2. How many samples are required to accurately estimate posterior quantities of interest? The <b>coda</b> package for R contains a set of functions designed to help the user answer these questions. Some of these convergence diagnostics are simple graphical ways of summarizing the data. Others are formal statistical tests.

HPV is the cause of almost all cervical cancer and is responsible for a substantial fraction of other anogenital cancers and oropharyngeal cancers. Understanding the HPV-attributable cancer burden can boost programs of HPV vaccination and HPV-based cervical screening. Attributable fractions (AFs) and the relative contributions of different HPV types were derived from published studies reporting on the prevalence of transforming HPV infection in cancer tissue. Maps of age-standardized incidence rates of HPV-attributable cancers by country from GLOBOCAN 2012 data are shown separately for the cervix, other anogenital tract and head and neck cancers. The relative contribution of HPV16/18 and HPV6/11/16/18/31/33/45/52/58 was also estimated. 4.5% of all cancers worldwide (630,000 new cancer cases per year) are attributable to HPV: 8.6% in women and 0.8% in men. AF in women ranges from <3% in Australia/New Zealand and the USA to >20% in India and sub-Saharan Africa. Cervix accounts for 83% of HPV-attributable cancer, two-thirds of which occur in less developed countries. Other HPV-attributable anogenital cancer includes 8,500 vulva; 12,000 vagina; 35,000 anus (half occurring in men) and 13,000 penis. In the head and neck, HPV-attributable cancers represent 38,000 cases of which 21,000 are oropharyngeal cancers occurring in more developed countries. The relative contributions of HPV16/18 and HPV6/11/16/18/31/33/45/52/58 are 73% and 90%, respectively. Universal access to vaccination is the key to avoiding most cases of HPV-attributable cancer. The preponderant burden of HPV16/18 and the possibility of cross-protection emphasize the importance of the introduction of more affordable vaccines in less developed countries.