*N. Thompson Hobbs and Mevin B. Hooten*

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691159287
- eISBN:
- 9781400866557
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159287.003.0005
- Subject:
- Biology, Ecology

This chapter lays out the basic principles of Bayesian inference, building on the concepts of probability developed in Chapter 3. It seeks to use the rules of probability to show how Bayes' theorem ...
More

This chapter lays out the basic principles of Bayesian inference, building on the concepts of probability developed in Chapter 3. It seeks to use the rules of probability to show how Bayes' theorem works, by making use of the conditional rule of probability and the law of total probability. The chapter begins with the central, underpinning tenet of the Bayesian view: the world can be divided into quantities that are observed and quantities that are unobserved. Unobserved quantities include parameters in models, latent states predicted by models, missing data, effect sizes, future states, and data before they are observed. We wish to learn about these quantities using observations. The Bayesian framework for achieving that understanding is applied in exactly the same way regardless of the specifics of the research problem at hand or the nature of the unobserved quantities.Less

This chapter lays out the basic principles of Bayesian inference, building on the concepts of probability developed in Chapter 3. It seeks to use the rules of probability to show how Bayes' theorem works, by making use of the conditional rule of probability and the law of total probability. The chapter begins with the central, underpinning tenet of the Bayesian view: the world can be divided into quantities that are observed and quantities that are unobserved. Unobserved quantities include parameters in models, latent states predicted by models, missing data, effect sizes, future states, and data before they are observed. We wish to learn about these quantities using observations. The Bayesian framework for achieving that understanding is applied in exactly the same way regardless of the specifics of the research problem at hand or the nature of the unobserved quantities.

*N. Thompson Hobbs and Mevin B. Hooten*

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691159287
- eISBN:
- 9781400866557
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159287.003.0008
- Subject:
- Biology, Ecology

This chapter shows how to make inferences using MCMC samples. Here, the process of inference begins on the assumption that a single model is being analyzed. The objective is to estimate parameters, ...
More

This chapter shows how to make inferences using MCMC samples. Here, the process of inference begins on the assumption that a single model is being analyzed. The objective is to estimate parameters, latent states, and derived quantities based on that model and the data. These estimates are conditioned on the single model being analyzed. The chapter also returns to an example advanced in the first chapter, to illustrate choices on specific distributions needed to implement the model, to show how informative priors can be useful, and to illustrate some of the inferential procedures described in this chapter—posterior predictive checks, marginal posterior distributions, estimates of derived quantities, and forecasting.Less

This chapter shows how to make inferences using MCMC samples. Here, the process of inference begins on the assumption that a single model is being analyzed. The objective is to estimate parameters, latent states, and derived quantities based on that model and the data. These estimates are conditioned on the single model being analyzed. The chapter also returns to an example advanced in the first chapter, to illustrate choices on specific distributions needed to implement the model, to show how informative priors can be useful, and to illustrate some of the inferential procedures described in this chapter—posterior predictive checks, marginal posterior distributions, estimates of derived quantities, and forecasting.