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Sep 29, 2024
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NRES 779 - Bayesian Hierarchical Modeling in Natural Resources (3 units)
This course will focus on gaining insight on natural processes, qualified by uncertainty, using statistics, mathematics, and empirical data in the Bayesian framework. We discuss basic principles of probability and distribution theory, review maximum likelihood estimation, and extend these principles to Bayesian statistics. We will cover MCMC algorithms for fitting Bayesian models. Students will be able to apply Bayesian methods to a broad array of disciplines and research questions.
Recommended Preparation: MATH 330 ; STAT 446 or STAT 461 or STAT 646 or STAT 661 or NRES 746 .
Grading Basis: Graded
Units of Lecture: 2
Units of Laboratory/Studio: 1
Offered: Every Spring
Student Learning Outcomes
Upon completion of this course, students will be able to:
1. learn the basic principles of probability and statistical distributions needed to link deterministic models to data and apply these to a number of real data sets.
2. explain maximum likelihood methods for estimating parameters in ecological models.
3. explain key principles of Bayesian statistics. Understand the relationship between inference accomplished by maximum likelihood and by applying Bayes theorem.
4. diagram, write, and implement hierarchical models appropriate for diverse problems in ecological and natural resource science.
5. explain how Markov chain Monte Carlo (MCMC) methods can be used to approximate marginal pos- terior distributions. Write MCMC algorithms and computer code in R implementing MCMC methods for simple Bayesian models.
6. use software for implementing MCMC methods (i.e., JAGS, R packages) to approximate marginal posterior distributions of parameters, latent variables, and derived quantities of interest. Be able to evaluate convergence.
7. apply procedures for model checking and model selection in the Bayesian framework.
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