Loss Developments via Growth Curves and Stan

Last week I posted a biological example of fitting a non-linear growth curve with Stan/RStan. Today, I want to apply a similar approach to insurance data using ideas by David Clark [1] and James Guszcza [2]. Instead of predicting the growth of dugongs (sea cows), I would like to predict the growth of cumulative insurance loss payments over time, originated from different origin years. Loss payments of younger accident years are just like a new generation of dugongs, they will be small in size initially, grow as they get older, until the losses are fully settled.

Bayesian regression models using Stan in R

It seems the summer is coming to end in London, so I shall take a final look at my ice cream data that I have been playing around with to predict sales statistics based on temperature for the last couple of weeks [1], [2], [3]. Here I will use the new brms (GitHub, CRAN) package by Paul-Christian Bürkner to derive the 95% prediction credible interval for the four models I introduced in my first post about generalised linear models.

Visualising the predictive distribution of a log-transformed linear model

Last week I presented visualisations of theoretical distributions that predict ice cream sales statistics based on linear and generalised linear models, which I introduced in an earlier post. Theoretical distributionsToday I will take a closer look at the log-transformed linear model and use Stan/rstan, not only to model the sales statistics, but also to generate samples from the posterior predictive distribution. The posterior predictive distribution is what I am most interested in.

Notes from the Kölner R meeting, 26 June 2015

Last Friday the Cologne R user group came together for the 14th time. For the first time we met at Startplatz, a start-up incubator venue. The venue was excellent, not only did they provide us with a much larger room, but also with table-football and drinks. Many thanks to Kirill for organising all of this! Photo: Günter FaesWe had two excellent advanced talks. Both were very informative and well presented.

Hello Stan!

In my previous post I discussed how Longley-Cook, an actuary at an insurance company in the 1950’s, used Bayesian reasoning to estimate the probability for a mid-air collision of two planes. Here I will use the same model to get started with Stan/RStan, a probabilistic programming language for Bayesian inference. Last week my prior was given as a Beta distribution with parameters $\alpha=1, \beta=1$ and the likelihood was assumed to be a Bernoulli distribution with parameter $\theta$: $$\begin{aligned}