# Bayesian data analysis in population ecology: motivations, methods, and benefits

• Special feature: Review
• Bayesian, Fisherian, error, and evidential statistical approaches for population ecology
• Published:

## Abstract

During the 20th century ecologists largely relied on the frequentist system of inference for the analysis of their data. However, in the past few decades ecologists have become increasingly interested in the use of Bayesian methods of data analysis. In this article I provide guidance to ecologists who would like to decide whether Bayesian methods can be used to improve their conclusions and predictions. I begin by providing a concise summary of Bayesian methods of analysis, including a comparison of differences between Bayesian and frequentist approaches to inference when using hierarchical models. Next I provide a list of problems where Bayesian methods of analysis may arguably be preferred over frequentist methods. These problems are usually encountered in analyses based on hierarchical models of data. I describe the essentials required for applying modern methods of Bayesian computation, and I use real-world examples to illustrate these methods. I conclude by summarizing what I perceive to be the main strengths and weaknesses of using Bayesian methods to solve ecological inference problems.

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## Notes

1. I use bracket notation (Gelfand and Smith 1990) to specify probability density functions; thus, [xy] denotes the joint density of random variables X and Y, [x | y] denotes the conditional density of X given $$Y=y$$, and [x] denotes the unconditional (marginal) density of X.

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## Acknowledgments

I thank Dr. Yukihiko Toquenaga for inviting me to present this article in a plenary symposium of the 30th Annual Meeting of the Society of Population Ecology in Tsukuba, Japan. I am also grateful to the Society and to the University of Tsukuba for providing funding for my travel expenses and publication costs. Chris Wikle and two anonymous referees kindly provided suggestions that improved an earlier draft of this article. Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

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Correspondence to Robert M. Dorazio.

This manuscript was submitted for the special feature based on a symposium in Tsukuba, Japan, held on 11 October 2014.

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Dorazio, R.M. Bayesian data analysis in population ecology: motivations, methods, and benefits. Popul Ecol 58, 31–44 (2016). https://doi.org/10.1007/s10144-015-0503-4