Introduction to Bayesian Modeling in Ecology

Bayesian methods for analyzing data are now widely used in ecology and wildlife management. The Bayesian approach involves specifying the “prior” distribution, which represents the uncertainty about the model parameters before we collect the data, and the likelihood, which represents the plausibility of different parameters values based solely on the data. These are combined via Bayes’ Rule to obtain the “posterior” distribution for the parameters, which represents the uncertainty about the parameters after we have analyzed the data. Using the Bayesian approach gives you more flexibility in the type of models that you can fit, compared to the classical frequentist approach, as the model is typically specified in the same way that you would write it down mathematically. Once you have become familiar with fitting a Bayesian model in R, you will appreciate the extra flexibility and the more intuitive way in which the results can be presented.

Learn at your your own pace with or without instructor support (see Online Course Format Chart below for details).

Summer: June 2 - August 24, 2025 (Early bird ends May 4th)

Fall: September 2 – November 23, 2025 (Early bird ends August 3rd)

*Early bird saves $75

Experience with the basics of probability, statistical methods (e.g., Introduction to Ecological Statistics and Modeling & Generalized Linear, Additive, and Mixed Models), and using R to fit statistical models.

TOPICS

• Why use the Bayesian approach to data analysis?

• Motivating examples

• Prior distribution and Likelihood

• Bayes’ Rule and the posterior distribution

• Exercises with solutions on using Bayes’ Rule

• Introduction to Markov chain Monte Carlo methods for implementing Bayes’ Rule

• Introduction to rjags, an R package for fitting Bayesian models

• Bayesian normal linear models

• Exercises with solutions on Bayesian normal linear models

• Bayesian generalized linear models

• Exercises with solutions on Bayesian generalized linear models

• Bayesian hierarchical models

• Exercises with solutions on Bayesian hierarchical models

• Bayesian model checking and comparison

• Overview of R packages for Bayesian data analysis

• Bayesian vs frequentist approaches to data analysis

LEARNING OUTCOMES

• Be able to describe the advantages and disadvantages of the Bayesian approach

• Understand the basic theory underlying the Bayesian approach

• Know how to fit normal and generalized linear hierarchical models in R using “rjags”

• Understand how to check lack-of-fit of a Bayesian model, and how to compare Bayesian models

• Clearly describe the results you obtain after fitting a Bayesian model

• Have a good overview of R packages for Bayesian data analysis

FORMAT:

• 3 months of access to course materials as you work at your own pace 

CONTINUING EDUCATION:

• 16 CEUs with The Wildlife Society

• 4 CEUs in Category I(a): Scientific Education and Training with the Ecological Society of America

• Go to our Continuing Education Page for more details

FORMAT:

• 3 months of access to course materials as you work at your own pace 

• Get instructor support for the 3-month term via email, discussion threads, group meetings, and one-on-one appointments

• After working through the course materials, set up an optional 1-hr meeting with the instructor to discuss your own personal project from work or school

CONTINUING EDUCATION:

• 16 CEUs with The Wildlife Society

• 4 CEUs in Category I(a): Scientific Education and Training with the Ecological Society of America

• Go to our Continuing Education Page for more details

CERTIFICATIONS:

• Earn 1 credit toward certification as an Ecologist (at any level) with Ecological Society of America

• Earn 1 credit toward certification as an Associate/Certified Wildlife Biologist® (at any level) with The Wildlife Society

FORMAT:

• 12 months of access to course materials as you work at your own pace 

• Get instructor support for the 3-month term via email, discussion threads, group meetings, and one-on-one appointments

• After working through the course materials, set up an optional 1-hr meeting with the instructor to discuss your own personal project from work or school

CONTINUING EDUCATION:

• 16 CEUs with The Wildlife Society

• 4 CEUs in Category I(a): Scientific Education and Training with the Ecological Society of America

• Go to our Continuing Education Page for more details

CERTIFICATIONS:

• Earn 1 credit toward certification as an Ecologist (at any level) with Ecological Society of America

• Earn 1 credit toward certification as an Associate/Certified Wildlife Biologist® (at any level) with The Wildlife Society

• Earn 1 credit towards a professional certificate in Applied Quantitative Ecology with CWS

ACADEMIC CREDIT:

• Earn 1 academic credit (go to our Academic Credit Page for details)

• Earn an additional 1-2 academic credits with an Applied Project