This article illustrates how ordinary differential equations and multivariate observations can be modelled and fitted with the brms package (Bürkner (2017)) in R1.
As an example I will use the well known Lotka-Volterra model (Lotka (1925), Volterra (1926)) that describes the predator-prey behaviour of lynxes and hares. Bob Carpenter published a detailed tutorial to implement and analyse this model in Stan and so did Richard McElreath in Statistical Rethinking 2nd Edition (McElreath (2020)).

Over the last year I worked with Jake Morris on a research paper for the Casualty Actuarial Society. We are delighted to see it published:
Gesmann, M., and Morris, J. “Hierarchical Compartmental Reserving Models.” Casualty Actuarial Society, CAS Research Papers, 19 Aug. 2020, https://www.casact.org/research/research-papers/Compartmental-Reserving-Models-GesmannMorris0820.pdf
The paper demonstrates how one can describe the dynamics of claims processes with differential equations and probability distributions. All of this is set into a Bayesian framework that allows us to combine judgement and historical data into a consistent framework.

At the Insurance Data Science conference, both Eric Novik and Paul-Christian Bürkner emphasised in their talks the value of thinking about the data generating process when building Bayesian statistical models. It is also a key step in Michael Betancourt’s Principled Bayesian Workflow.
In this post, I will discuss in more detail how to set priors, and review the prior and posterior parameter distributions, but also the prior predictive distributions with brms (Bürkner (2017)).

Ahead of the Stan Workshop on Tuesday, here is another example of using brms (Bürkner (2017)) for claims reserving. This time I will use a model inspired by the 2012 paper A Bayesian Nonlinear Model for Forecasting Insurance Loss Payments (Zhang, Dukic, and Guszcza (2012)), which can be seen as a follow-up to Jim Guszcza’s Hierarchical Growth Curve Model (Guszcza (2008)).
I discussed Jim’s model in an earlier post using Stan.

How do you build a model from first principles? Here is a step by step guide.
Following on from last week’s post on Principled Bayesian Workflow I want to reflect on how to motivate a model.
The purpose of most models is to understand change, and yet, considering what doesn’t change and should be kept constant can be equally important.
I will go through a couple of models in this post to illustrate this idea.

This is a follow-up post on hierarchical compartmental reserving models using PK/PD models. It will show how differential equations can be used with Stan/ brms and how correlation for the same group level terms can be modelled.
PK/ PD is usually short for pharmacokinetic/ pharmacodynamic models, but as Eric Novik of Generable pointed out to me, it could also be short for Payment Kinetics/ Payment Dynamics Models in the insurance context.

Last Friday the Cologne R user group came together for the 17th time. This time, we were in for a special treatment, with two talks by psychologists!
But, there was nothing to fear, we were in safe hands, and for the first time, we met at the new Microsoft office in Cologne.
Lecture room at Microsoft, Cologne First up was Meik Michalke from the University of Düsseldorf presenting the RKWard project.

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.

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