## R package truncnorm

Posted in Statistics with tags , , , , , on November 8, 2017 by xi'an

This week in Warwick, thanks to a (rather incomprehensible) X validated question, I came across the CRAN R package truncnorm, which provides the “density, distribution function, quantile function, random generation and expected value function for the truncated normal distribution”. The short description of the sampler states that the method follows the accept-reject solution of John Geweke (1991), which I reproduced [independently!] a few years later. I may have missed the right code, but checking on the Github depository associated with this package, I did not find in the C code a trace of our optimal solution via a translated exponential proposal, since the exponential proosal, when used, relies on a scale equal to the left truncation point, a in the above picture. Obviously, this does not make a major difference in the execution time (and the algorithm is still correct!).

## The winds of Winter [Bayesian prediction]

Posted in Books, Kids, R, Statistics, University life with tags , , , , , , , , , , on October 7, 2014 by xi'an

A surprising entry on arXiv this morning: Richard Vale (from Christchurch, NZ) has posted a paper about the characters appearing in the yet hypothetical next volume of George R.R. Martin’s Song of ice and fire series, The winds of Winter [not even put for pre-sale on amazon!]. Using the previous five books in the series and the frequency of occurrence of characters’ point of view [each chapter being told as from the point of view of one single character], Vale proceeds to model the number of occurrences in a given book by a truncated Poisson model,

$x_{it} \sim \mathcal{P}(\lambda_i)\text{ if }|t-\beta_i|<\tau_i$

in order to account for [most] characters dying at some point in the series. All parameters are endowed with prior distributions, including the terrible “large” hyperpriors familiar to BUGS users… Despite the code being written in R by the author. The modelling does not use anything but the frequencies of the previous books, so knowledge that characters like Eddard Stark had died is not exploited. (Nonetheless, the prediction gives zero chapter to this character in the coming volumes.) Interestingly, a character who seemingly died at the end of the last book is still given a 60% probability of having at least one chapter in  The winds of Winter [no spoiler here, but many in the paper itself!]. As pointed out by the author, the model as such does not allow for prediction of new-character chapters, which remains likely given Martin’s storytelling style! Vale still predicts 11 new-character chapters, which seems high if considering the series should be over in two more books [and an unpredictable number of years!].

As an aside, this paper makes use of the truncnorm R package, which I did not know and which is based on John Geweke’s accept-reject algorithm for truncated normals that I (independently) proposed a few years later.