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.

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.

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 distributions Today 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.

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 Faes We had two excellent advanced talks.

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 \(\theta\): \[\begin{aligned} \theta & \sim \mbox{Beta}(1, 1)\\ y_i & \sim \mbox{Bernoulli}(\theta), \;\forall i \in N \end{aligned}\]For the previous five years no mid-air collision were observed, \(x=\{0, 0, 0, 0, 0\}\).

© Markus Gesmann 2011 - 2024 CC BY-NC-SA 3.0 · Powered by the Academic theme for Hugo.