2015Princeton University Press eBooksRequires access

Likelihood

N. Thompson Hobbs, Mevin B. Hooten

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Abstract

This chapter is an overview of likelihood and maximum likelihood. Likelihood forms the fundamental link between models and data in the Bayesian framework. In addition, maximum likelihood is a widely used alternative to Bayesian methods for estimating parameters in ecological models. Though is possible to learn Bayesian modeling with a bare-bones treatment of likelihood, the chapter emphasizes the importance of this concept in Bayesian analysis. A significant aspect of likelihood within the Bayesian framework can be found in the similarities and differences between Bayesian analysis and analysis based on maximum likelihood. In addition, the chapter also considers the relationship between a probability distribution and a likelihood function.

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What this paper is about

This chapter is an overview of likelihood and maximum likelihood. Likelihood forms the fundamental link between models and data in the Bayesian framework. In addition, maximum likelihood is a widely used alternative to Bayesian methods for estimating parameters in ecological models. Though is possible to learn Bayesian modeling with a bare-bones treatment of likelihood, the chapter emphasizes the importance of this concept in Bayesian analysis. A significant aspect of likelihood within the Bayesian framework can be found in the similarities and differences between Bayesian analysis and analysis based on maximum likelihood. In addition, the chapter also considers the relationship between a probability distribution and a likelihood function.

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Available abstract

This chapter is an overview of likelihood and maximum likelihood. Likelihood forms the fundamental link between models and data in the Bayesian framework. In addition, maximum likelihood is a widely used alternative to Bayesian methods for estimating parameters in ecological models. Though is possible to learn Bayesian modeling with a bare-bones treatment of likelihood, the chapter emphasizes the importance of this concept in Bayesian analysis. A significant aspect of likelihood within the Bayesian framework can be found in the similarities and differences between Bayesian analysis and analysis based on maximum likelihood. In addition, the chapter also considers the relationship between a probability distribution and a likelihood function.

Key concepts: Likelihood function, Marginal likelihood, Bayesian probability, Maximum likelihood, Bayes factor, Likelihood principle, Variable-order Bayesian network, Restricted maximum likelihood

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