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Applied Bayesian modelling for ecologists and epidemiologists (ABME02)
24th October 2016 - 29th October 2016£630 - £1080
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 modelling & spatial point-process modelling. 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 modelling.
Research postgraduates, practicing academics and primary investigators in ecology and epidemiology and professionals in government and industry.
We offer two packages
• COURSE ONLY – Includes lunch and refreshments.
• ALL INCLUSIVE – Includes breakfast, lunch, dinner, refreshments, minibus to and from meeting point and accommodation. Accommodation is multiple occupancy (max 3 people) single sex en-suite rooms. Arrival Sunday 23rd October and departure Saturday 29th October PM.
To book ‘COURSE ONLY’ or ‘ALL INCLUSIVE’ pleases scroll to the bottom of this page.
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Cancellation policy: Cancellations are accepted up to 28 days before the course start date subject to a 25% cancellation fee. Cancellations later than this may be considered, contact firstname.lastname@example.org Failure to attend will result in the full cost of the course being charged. In the unfortunate event that PR~statistics must cancel this course due to unforeseen circumstances a full refund for the course will be credited. However PR~statistics cannot be held responsible for any travel fees, accommodation or other expenses incurred to you as a result of the cancellation.
Introductory lectures on the concepts and refreshers on R usage. Intermediate-level lectures interspersed with hands-on mini practicals and longer projects. Round-table discussions about the analysis requirements of attendees (option for them to bring their own data). Data sets for computer practicals will be provided by the instructors, but participants are welcome to bring their own data.
Assumed quantitative knowledge
A good understanding of statistical concepts. Specifically, statistical significance and hypothesis testing and the basic ideas of probability and likelihood.
Assumed computer background
At entry you should make sure that you have a working knowledge of: Basic R usage (command-line interactive, generation of graphs); Manipulation of data-frames in R; Regression modelling (linear, generalised linear & mixed effects models). In addition, you should have had some exposure to: Programming structures (loops, conditional statements).
Equipment and software requirements
A laptop/personal computer with a working version or R, RStudio and JAGS installed. R, RStudio and JAGS are supported by both PC and MAC and can be downloaded for free by following these links.
Further information on interfacing JAGS and R using the runjags package can be found from the following website: http://runjags.sourceforge.net/.
It is essential that you come with all necessary software and packages already installed (you will be sent a list of packages prior to the course) internet access may not always be available.
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Meet at the Tullie Inn, Balloch at approximately 18:30 before being taken by minibus to SCENE (Download directions PDF)
Monday 24th – Classes from 09:00 to 17:00
Module 1: Revision of likelihoods using full likelihood profiles and an introduction to the theory of Bayesian statistics. Probability and likelihood. Conditional, joint and total probability, independence, Baye’s law. Probability distributions. Uniform, Bernoulli, Binomial, Poisson, Gamma, Beta and Normal distributions – their range, parameters and common uses of Likelihood and parameter estimation by maximum likelihood. Numerical likelihood profiles and 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.
Tuesday 25th – Classes from 09:00 to 17:00
Module 2: An introduction to the workings of MCMC, and the potential dangers of MCMC inference. Participants will program their own (basic) MCMC sampler to illustrate the concepts and fully understand the strengths and weaknesses of the general approach. The day will end with an introduction to the bugs language.
Introduction to MCMC. The curse of dimensionality & the advantages of MCMC sampling to determine a posterior distribution. Monte Carlo integration, standard 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 and Monte Carlo error. The concept of a stationary distribution and burnin. Requirement for convergence diagnostics, and 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.
Wednesday 26th – Classes from 09:00 to 17:00
Module 3: Common models for which jags/bugs would be used in practice, with examples given for different types of model code. All aspects of writing, running, assessing and interpreting these models will be extensively discussed so that participants are able and confident to run similar models on their own. There will be a particularly heavy focus on practical sessions during this day. The day will finish with a discussion of how to assess the fit of mcmc models using the deviance information criterion (dic) and other methods. 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. Most commonly used methods Rationale and use for fixed threshold, ABGD, K/theta, PTP, GMYC with computer practicals. Other methods, Haplowebs, bGMYC, etc. with computer practicals.
Thursday 27th – Classes from 09:00 to 17:00
Module 4: The flexibility of MCMC, and precautions required for using MCMC to model commonly encountered datasets. An introduction to conjugate priors and the potential benefits of exploiting gibbs sampling will be given. More complex types of models such as hierarchical models, latent class models, mixture models and state space models will be introduced and discussed. The practical sessions will follow on from day 3.
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.
Friday 28th – Classes from 09:00 to 17:00
Module 5: Additional practical guidance for the use of Bayesian methods in practice, and finish with a brief overview of more advanced Bayesian tools such as Integrated Nested Laplace Approximation (INLA) and stan.
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 INLA compared to BUGS. Strengths and weaknesses of stan compared to BUGS.
Saturday 29th – Classes from 09:00 to 14:00
Module 6: Additional practical guidance for the use of Bayesian methods in practice, and finish with a brief overview of more advanced Bayesian tools such as INLA and stan. 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 INLA compared to BUGS. Strengths and weaknesses of stan compared to BUGS.