Trainings

Tutorial 1 • Getting Started

Introduction to Bayesian Inference

Learn the fundamentals: Bayes' theorem, conjugate priors, MCMC sampling, and why INLA is fast. Fit your first Poisson model with pyINLA using the Game of Thrones counting example.

Bayes' theorem and posterior distributions
Conjugate analysis (Poisson-Gamma)
Metropolis-Hastings MCMC
pyINLA model fitting and posterior transformation

Conjugate vs MCMC vs pyINLA

Tutorial 2 • Core Concepts

Regression and Generalized Linear Models

Fit linear regression and Poisson GLMs, compare models with DIC/WAIC/CPO, and work with posterior marginals and sampling.

Linear regression with pyINLA
Poisson GLM with offsets
Model comparison: DIC, WAIC, CPO
Marginal utilities and posterior sampling

Tutorial 3 • Random Effects

Mixed Effects Models

Add random effects to your models: IID for overdispersion, time series (RW1, AR1), constraints, and generic structures.

IID random effects for overdispersion
Time series: RW1 and AR1 models
Constraints on random effects
Generic models: Z and custom precision

Tutorial 4 • Hierarchical

Multilevel Models

Students in classrooms, patients in hospitals: real data has layers. Learn to model nested and crossed random effects.

Crossed effects: Penicillin experiment
Longitudinal data: Sleep deprivation study
Three-level nesting: Lab quality control
Logistic multilevel: Election 1988
Poisson multilevel and overdispersion: NYC Stops

Tutorial 5 • Prior Specification

Priors

Choose and customize prior distributions: built-in priors, expression-based custom priors, Penalized Complexity (PC) priors, sensitivity analysis, and model scaling.

Built-in priors: loggamma, Gaussian, flat, PC
Custom priors with expression: syntax
Penalized Complexity (PC) priors
Sensitivity analysis across prior choices
Scaling intrinsic random effects (RW1, RW2, Besag)

Tutorial 6 • Spatial

Spatial Models

Areal data, geostatistics, and point patterns: model spatial autocorrelation with lattice models, SPDE, and adjacency structures.

Regular lattice: RW2D and Matern2D models
Irregular lattice: Besag, BYM, and Leroux models
Geostatistics: SPDE with Matern covariance
Point patterns: Log-Gaussian Cox processes
Model comparison across spatial specifications

Tutorial 7 • Temporal

Temporal Models

Model time series and spatio-temporal data: AR(1), RW1, forecasting with NAs, and Kronecker products for space-time interaction.

AR(1) and RW1 for climate reconstruction
Poisson time series: earthquake counts
Forecasting with the NA trick
Spatio-temporal: Besag x AR1 Kronecker models
Informative priors and model comparison

Tutorial 8 • Non-parametric

Smoothing

Estimate flexible, data-driven curves with penalized splines: RW1/RW2 random walks, binned covariates, and 1D SPDE for non-parametric regression.

Polynomial regression as a baseline
Penalized splines: RW1 and RW2 models
Binned covariates for computational efficiency
Non-Gaussian smoothing: binomial dose-response
1D SPDE with Matern covariance

Tutorial 9 • Time-to-Event

Survival Models

Model censored time-to-event data: exponential, Weibull, lognormal, Cox proportional hazards, and frailty models for clustered survival.

Exponential, Weibull, and lognormal survival
Cox proportional hazards with baseline hazard
Accelerated failure time interpretation
Frailty models: random effects for clustered data
Model comparison across survival specifications

Tutorial 10 • Advanced

Advanced Features

Unlock the full power of pyINLA: predictor matrices, linear combinations, multiple likelihoods, shared terms (copy and replicate), and linear constraints.

Predictor matrices (A-matrix) for custom designs
Linear combinations of latent effects
Multiple likelihoods: joint Gaussian + Poisson models
Copy and replicate for shared terms
Linear constraints (sum-to-zero and beyond)

Tutorial 11 • Missing Data

Missing Data

Handle missing observations: predict missing responses automatically, impute missing covariates with plug-in values, and propagate uncertainty with multiple imputation and INLA within MCMC.

Missingness mechanisms: MCAR, MAR, MNAR
Predicting missing responses (the NA trick)
Plug-in imputation for missing covariates
Multiple imputation with Rubin's rules
INLA within MCMC for complex imputation

Tutorial 12 • Mixtures

Mixture Models

Fit finite mixture models: handle known groups with multiple likelihoods, estimate unknown group assignments with INLA within MCMC, select the number of components, and fit cure rate survival models.

Gaussian mixtures with known group assignments
INLA within MCMC for unknown allocations
Model selection via marginal likelihoods
Cure rate models (weibullcure family)
Label switching and identifiability

Tutorial 13 • Count Data

Zero-inflated and Hurdle Models

Handle excess zeros common in count data: zero-inflated Poisson and negative binomial models, hurdle models, and strategies for choosing among them.

Zero-inflation vs. overdispersion: diagnosis and remedies
Zero-inflated Poisson (ZIP) and ZINB models
Hurdle Poisson and hurdle negative binomial
Two-part models with different covariates per component
Model comparison via DIC, WAIC, and marginal likelihood

Tutorial 14 • Longitudinal + Survival

Joint Models

Simultaneously model a longitudinal biomarker trajectory and a time-to-event outcome, linked through shared latent effects. Accounts for informative dropout and measurement error.

Motivating example: CD4 counts and AIDS progression
Longitudinal sub-model: linear mixed effects with INLA
Survival sub-model: Cox hazard with shared random effect
Association structures: current value, current slope, cumulative
Dynamic predictions and discrimination metrics