Session 1- 01:15:00 – What Is Bayesian Statistics?
Introduction to Bayesian vs. frequentist probability; Bayes’ theorem and its components (prior, likelihood, posterior), the role of belief updating and uncertainty quantification in ecological modelling.
Session 2 – 01:15:00 – Priors, Posteriors, and Credible Intervals
Understanding different types of priors, posterior distributions and credible intervals; interpreting Bayesian results with ecological examples.
Session 3 – 01:15:00 – MCMC and the Bayesian Modelling Workflow
Introduction to MCMC algorithms, convergence diagnostics (traceplots, R-hat), overview of the Bayesian modelling cycle and iterative workflow.
Session 4 – 01:15:00 – Introduction to brms
Overview of the brms package; Stan as backend; model formula syntax, specifying families and priors; fitting basic models with brm().
Session 5 – 01:15:00 – Bayesian GLMs for Ecologists
Fitting Poisson, Gaussian, and logistic models in brms; posterior summaries and interpretation; visualising fitted effects and posterior uncertainty.
Session 6 – 01:15:00 – Visualising and Summarising Models
Using bayesplot, ggplot2, and tidybayes to explore posterior distributions and posterior predictions.
Session 7 – 01:15:00 – Why Multilevel Models?
Introducing Pseudo-replication and non-independence in ecological data; random intercepts and partial pooling; visualising multilevel model structure.
Session 8 – 01:15:00 – Fitting Random Intercepts in brms
Syntax for random effects in brms; interpreting group-level effects and variance components; extracting and plotting random intercepts.
Session 9 – 01:15:00 – Model Diagnostics for Multilevel Models
Examining traceplots, convergence checks, posterior predictive checks by group; assessing fit and structure of random intercept models.
Session 10 – 01:15:00 – Random Slopes and Slope and Intercept Models
Motivation for random slopes, syntax and interpretation, understanding and visualising intercept-slope correlations.
Session 11 – 01:15:00 – Crossed vs. Nested Random Effects
Conceptual and practical distinctions between nested and crossed designs; specifying models in brms; ecological use cases and implications.
Session 12 – 01:15:00 – Centring and Scaling Predictors
Grand mean vs. group mean centring; standardisation for model convergence and interpretation; coding and plotting strategies.
Session 13 – 01:15:00 – Count Models: Poisson, Negative Binomial, and Zero-Inflated
Modelling count data in ecology; overdispersion and zero inflation; comparing Poisson and NB models; fitting ZIP/ZINB models in brms.
Session 14 – 01:15:00 – Binary and Proportional Data
Bernoulli and binomial models; grouped trials and proportion data; predicting and visualising probabilities; accounting for random effects.
Session 15 – 01:15:00 – Posterior Predictive Checks for GLMMs
Assessing model fit; using bayes_R2(), LOO cross-validation, and residual plots to evaluate model performance.
Session 16 – 01:15:00 – Time as a Predictor or Grouping Variable
Modelling time trends in repeated measures; fixed and random slopes for time; visualising site- or individual-level changes over time.
Session 17 – 01:15:00 – Temporal Autocorrelation in brms
Autoregressive models with cor_ar(); diagnosing residual structure; fitting and interpreting temporal autocorrelation parameters.
Session 18 – 01:15:00 – Case Study: Bird Counts Over Years
Worked example of multilevel temporal modelling with autocorrelation; evaluating model improvement; ecological interpretation of trends.
Session 19 – 01:15:00 – Spatial Dependence in Ecological Models
Why spatial structure matters; detecting spatial autocorrelation; overview of spatial options in brms (Gaussian Process and CAR).
Session 20 – 01:15:00 – Gaussian Process Models in brms
Fitting continuous spatial models using gp(); understanding spatial range and smoothness parameters; visualising fitted surfaces.
Session 21 – 01:15:00 – CAR Models and Spatial Case Study
Fitting discrete spatial models with car(); setting up adjacency matrices; interpreting spatial random effects on maps; full case study.
Session 22 – 01:15:00 – Choosing Priors for Ecological Models
Setting meaningful priors for intercepts, slopes, and random effects; linking priors to ecological knowledge; interpreting on the link scale.
Session 23 – 01:15:00 – Prior Predictive Simulation
Simulating from the prior with sample_prior = “only”; identifying unrealistic priors; adjusting and refining priors based on biological plausibility.
Session 24 – 01:15:00 – Sensitivity to Priors
Assessing robustness of posterior results to different prior choices; comparing models; interpreting and reporting sensitivity in ecological applications.
Session 25 – 01:15:00 – Multivariate Outcomes in Ecology
Motivation for modelling multiple responses; syntax for multivariate models with mvbf(); estimating and interpreting residual correlations.
Session 26 – 01:15:00 – Joint Species Distribution Models
Using multivariate GLMs to model species co-occurrence; extracting correlation matrices; limitations and ecological interpretation of species distribution models in brms.
Session 27 – 01:15:00 – Ecological Case Study
Modelling multiple species across sites; fitting and interpreting a multivariate logistic model; plotting site-level predictions and species correlations.
Session 28 – 01:15:00 – Interpreting and Plotting Posteriors
Summarising model results using fixef(), ranef(), and posterior intervals; visualising effects with tidybayes, bayesplot, and ggplot2.
Session 29 – 01:15:00 – Predictions and Posterior Simulation
Using fitted(), posterior_predict(), and posterior_epred() to generate predictions.
Session 30 – 01:15:00 – Final Summary and Best Practices
Review of full Bayesian workflow; reporting model structure and diagnostics; practical tips for reproducibility, transparency, and extensions (e.g. causal models, mixture models).
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