Course flyer
This is an online course via Zoom
Dates and times: 7 - 11 September 2026. 14.00 - 20.00 (UK time)
This course provides an applied introduction to Bayesian time series analysis using generalised additive models (GAMs) and latent temporal structures implemented in inlabru.
The course focuses on modelling temporal dependence through smooth functions and random walk processes, with particular emphasis on RW2 models. We begin by revisiting regression and mixed-effects models and then introduce GAM-based approaches for analysing univariate time series. From there, the course progresses to hierarchical and multivariate time series models, allowing for shared and group-specific temporal trends across multiple animals, tagged individuals, sites, species, or monitoring devices.
A wide range of data types is covered, including continuous data, count data, presence–absence data, proportional data, and zero- and one-inflated (ordered) Beta data, using appropriate likelihoods such as Gaussian, Poisson, negative binomial, Bernoulli, Gamma, Tweedie, and Beta. Participants will learn how to incorporate covariates, seasonal and cyclic effects, long-term trends, random effects, and common latent temporal drivers.
Throughout the course, emphasis is placed on practical implementation in R, model interpretation, and model validation, including the use of posterior simulation and diagnostic tools such as DHARMa. All concepts are illustrated using real ecological and environmental case studies, including data from tagged animals, camera traps, and long-term monitoring programmes.
Course content
Module 1
- General introduction
- Revision exercise: linear regression.
- Revision exercise: linear mixed-effects models.
- Theory presentation on Bayesian statistics and INLA.
- Exercise showing how to fit a linear regression model in inlabru.
- Exercise showing how to fit a linear mixed-effects model in inlabru.
Module 2
- Theory presentation on time series analysis, generalised additive models, and how to fit these models in inlabru.
- Exercise showing how to fit a simple GAM in inlabru.
- Exercise showing how to fit a GAM with multiple covariates in inlabru.
- Exercise showing how to fit a univariate time series in inlabru.
- Exercise showing how to fit a univariate time series with multiple covariates in inlabru.
Module 3
- Exercise showing how to analyse time series of count data.
- Exercise showing how to analyse time series of absence/presence data.
- Theory presentation on hierarchical time series analysis (first encounter with multiple time series).
- Two exercises showing how to analyse multivariate time series.
Module 4
- Theory presentation on using multiple likelihoods in inlabru.
- Three exercises showing how to analyse multivariate time series.
Module 5
- A series of case studies in which we analyse multivariate time series (e.g. data from tagged animals, or data from multiple cameras, sites, or species).
- Keywords in these case studies: count data; proportional data (e.g. time budgeting); presence–absence; seasonality; long-term trends; covariate effects; common latent drivers; random effects; irregularly spaced time series; model validation; posterior simulation; DHARMa; cyclic patterns; prior specification.
This is an applied but advanced course, with a strong emphasis on practical implementation and interpretation of models in R. It assumes prior training in regression modelling and mixed-effects models and is not suitable for beginners. Participants who are not already comfortable with these techniques are strongly advised to attend an introductory regression or mixed-effects/GLM course before enrolling.
For terms and conditions, see: