Probability Theory and Some Useful Probability Distributions
Effective Bayesian inference requires familiarity with probability distributions. In fact, as will be seen in subsequent chapters, the most important choices in Bayesian inference usually involve the choices of distributions to represent the state of know
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oduction to Bayesian Methods in Ecology and Natural Resources
Introduction to Bayesian Methods in Ecology and Natural Resources
Edwin J. Green Andrew O. Finley William E. Strawderman •
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Introduction to Bayesian Methods in Ecology and Natural Resources
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Edwin J. Green Department of Ecology Evolution and Natural Resources Cook College, Rutgers University New Brunswick, NJ, USA
Andrew O. Finley Department Forestry & Geography Michigan State University East Lansing, MI, USA
William E. Strawderman Department of Statistics Rutgers University Piscataway, NJ, USA
ISBN 978-3-030-60749-4 ISBN 978-3-030-60750-0 https://doi.org/10.1007/978-3-030-60750-0
(eBook)
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To Rosemary, Jimmy, Tara, Anthony, Marla, EJ, Mandy, Jane, and Amelia Sarah, Ava, Oliver, Callum, James, Linda, and Gail Rob, Myla, Bill, Jinny, Heather, Jim, Kay, Matt, Will, Tom, Evan, Emma, AJ, and Lily In memory of Susan
Contents
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1 2 3 4 6 9
2 Probability Theory and Some Useful Probability Distributions . . 2.1 Discrete and Continuous Random Variables . . . . . . . . . . . . . 2.2 Expectation, Mean, Standard Deviation, and Variance . . . . . . 2.3 Unconditional, Conditional, Marginal, and Joint Distributions 2.4 Likelihood Functions and Random Samples . . . . . . . . . . . . . 2.5 Some Useful Discrete Probability Distributions . . . . . . . . . . . 2.5.1 Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Multinomial Distribution . . . . . . . . . . . . . . . . . . . . . 2.5.3 Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Some Useful Cont
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