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 , , .
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 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.
Two weeks ago I discussed various linear and generalised linear models in R using ice cream sales statistics. The data showed not surprisingly that more ice cream was sold at higher temperatures.
icecream <- data.frame(
temp=c(11.9, 14.2, 15.2, 16.4, 17.2, 18.1, 18.5, 19.4, 22.1, 22.6, 23.4, 25.1),
units=c(185L, 215L, 332L, 325L, 408L, 421L, 406L, 412L, 522L, 445L, 544L, 614L)
)I used a linear model, a log-transformed linear model, a Poisson and Binomial generalised linear model to predict sales within and outside the range of data available.
Linear models are the bread and butter of statistics, but there is a lot more to it than taking a ruler and drawing a line through a couple of points.
Some time ago Rasmus Bååth published an insightful blog article about how such models could be described from a distribution centric point of view, instead of the classic error terms convention.
I think the distribution centric view makes generalised linear models (GLM) much easier to understand as well.
This is the third post about Christofides’ paper on Regression models based on log-incremental payments . The first post covered the fundamentals of Christofides’ reserving model in sections A - F, the second focused on a more realistic example and model reduction of sections G - K. Today’s post will wrap up the paper with sections L - M and discuss data normalisation and claims inflation. I will use the same triangle of incremental claims data as introduced in my previous post.
Following on from last week’s post I will continue to go through the paper Regression models based on log-incremental payments by Stavros Christofides . In the previous post I introduced the model from the first 15 pages up to section F. Today I will progress with sections G to K which illustrate the model with a more realistic incremental claims payments triangle from a UK Motor Non-Comprehensive account:# Page D5.17
A recent post on the PirateGrunt blog on claims reserving inspired me to look into the paper Regression models based on log-incremental payments by Stavros Christofides , published as part of the Claims Reserving Manual (Version 2) of the Institute of Actuaries.
The paper is available together with a spread sheet model, illustrating the calculations. It is very much based on ideas by Barnett and Zehnwirth, see  for a reference.