Applied Bayesian modeling for ecologists and epidemiologists (statistics course)
This 6 day course will be held at SCENE (Scottish Centre for Ecology and the Natural Environment), Glasgow, United Kingdom from August 26th – 31st October 2015
The course is being delivered by Dr. Matt Denwood (University of Copenhagen) and Prof. Jason Matthiopoulos (University of Glasgow)
This application-driven course will provide a founding in the basic theory & practice of Bayesian statistics, with a focus on MCMC modeling for ecological & epidemiological problems. Starting from a refresher on probability & likelihood, the course will take students all the way to cutting-edge applications such as state-space population modeling & spatial point-process modeling. By the end of the week, you should have a basic understanding of how common MCMC samplers work and how to program them, and have practical experience with the BUGS language for common ecological and epidemiological models. The experience gained will be a sufficient foundation enabling you to understand current papers using Bayesian methods, carry out simple Bayesian analyses on your own data and springboard into more elaborate applications such as dynamical, spatial and hierarchical modeling.
Course timetable:
Day 1: Revision of likelihoods
Probability & likelihood
• Conditional, joint & total probability, independence, Baye’s law
• Probability distributions
• Uniform, Bernoulli, Binomial, Poisson, Gamma, Beta & Normal distributions – their range, parameters & common uses
• Likelihood & parameter estimation by maximum likelihood
• Numerical likelihood profiles & maximum likelihood
Introduction to Bayesian statistics
• Relationship between prior, likelihood & posterior distributions
• Summarising a posterior distribution; The philosophical differences between frequentist & Bayesian statistics, & the practical implications of these
• Applying Bayes’ theorem to discrete & continuous data for common data types given different priors
• Building a posterior profile for a given dataset, & compare the effect of different priors for the same data
Day 2: MCMC
Introduction to MCMC
• The curse of dimensionality & the advantages of MCMC sampling to determine a posterior distribution
• Monte Carlo integration, st&ard error, & summarising samples from posterior distributions in R
• Writing a Metropolis algorithm & generating a posterior distribution for a simple problem using MCMC
Markov chains, autocorrelation & convergence;
• Definition of a Markov chain
• Autocorrelation, effective sample size & Monte Carlo error
• The concept of a stationary distribution & burnin;
• Requirement for convergence diagnostics, & common statistics for assessing convergence
• Adapting an existing Metropolis algorithm to use two chains, & assessing the effect of the sampling distribution on the autocorrelation
Introduction to BUGS & running simple models in JAGS
• Introduction to the BUGS language & how a BUGS model is translated to an MCMC sampler during compilation
• The difference between deterministic & stochastic nodes, & the contribution of priors & the likelihood
• Running, extending & interpreting the output of simple JAGS models from within R using the runjags interface
Day 3: Common models for JAGS and BUGS
Using JAGS for common problems in biology
• Understanding and generating code for basic generalised linear mixed models in JAGS
• Syntax for quadratic terms and interaction terms in JAGS
Essential fitting tips and model selection
• The need for minimal cross-correlation and independence between parameters and how to design a model with these properties
• The practical methods and implications of minimizing Monte Carlo error and autocorrelation, including thinning
• Interpreting the DIC for nested models, and understanding the limitations of how this is calculated
• Other methods of model selection and where these might be more useful than DIC
Day 4: The flexibility of MCMC
General guidance for model specification
• The flexibility of the BUGS language and MCMC methods
• The difference between informative and diffuse priors
• Conjugate priors and how they can be used
• Gibbs sampling
State space models
• Hierarchical and state space models
• Latent class and mixture models
• Conceptual application to animal movement
• Hands-on application to population biology
• Conceptual application to epidemiology
Day 5: Practical guidance for Bayesian methods in practise
Additional Bayesian methods
• Understand the usefulness of conjugate priors for robust analysis of proportions (Binomial and Multinomial data)
• Be aware of some methods of prior elicitation
Advanced Bayesian tools
• Strengths and weaknesses of Integrated Nested Laplace Approximation (INLA) compared to BUGS
• Strengths and weaknesses of Stan compared to BUGS
Day 6: Round table discussion and problem solving with final Q and A
Final day
The final day will consist of round table discussions, the class will be split in to smaller groups to discuss set topics/problems. This will include participants own data where possible. After an early lunch there will be a general question and answer time until approx. 2pm as a whole group before transport to Balloch train station.
Cost is £585 for the 6 days including lunches and refreshments or £765 for an all-inclusive option which includes the addition of accommodation, breakfast, lunch, dinner and refreshments.
For further details or questions or to register please email [log in to unmask] or visit www.prstatistics.co.uk
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Additional upcoming courses; STABLE ISOTOPE MIXING MODELS USING SIAR, SIBER AND MIXSIAR; GENETIC DATA ANAYSIS USING R; BIOINFORMATICS FOR GENETICISTS AND BIOLOGISTS; SPATIAL ANALYSIS OF ECOLOGICAL DATA USING R; ADVANCING IN R.
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