Introduction to Bayesian Hierarchical Modelling

– a pre-conference hands-on session

Ullrika Sahlin and Paul Caplat, Centre of Environmental and Climate Reserach

Bayesian modelling allows addressing complex problems with flexible model structure arranged in a nested or hierarchical way (hence the name BHM). We will demonstrate Bayesian updating using MCMC sampling in two commonly used open source software. For the sake of simplicity and generality we will introduce BHM using simple examples, increasing complexity (i.e. hierarchical nature) of the models step by step. Bayesian modelling allows addressing complex problems with flexible model structure arranged in a nested or hierarchical way (hence the name BHM).

We hope that the attendants will leave the workshop able to further explore the fun and usefulness of BHM.

Participants were asked to bring their own laptop. It was also possible to attend by looking over the shoulder of someone else.

The modelling will be performed in R with pre-made code that we put up on the conference website prior to the workshop. We recommended installing the programs before the workshop. We are running the examples in two types of software. Which one you choose is up to you, both have their advantages and they look very similar in the R-coding.

The examples we will go through are the following:

Bayesian updating: •The chance to get heads up in a tossing experiment using a Binomial model. •Bayesian linear regression and the influence of priors having little or lots of data.

Hierarchical modelling: •Bayesian linear modelling with a random effect. •Bayesian calibration of a process based model of population dynamics over time. •Bayesian calibration of the population dynamics model considering the error in observations using a Binomial model.