Abstract
This chapter introduces and describes, at a high level, the topic of Bayesian inference. The overall motivation and background for a formal method of logical inference using probability is discussed. Key terms used to describe the Bayesian inference approach are also defined.
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Notes
- 1.
Also referred to synonymously as a “stochastic model,” “probabilistic model,” or “likelihood function.”
- 2.
A Bernoulli trial is an experiment whose outcomes can be assigned to one of two possible states (e.g., success/failure, heads/tails, yes/no), and mapped to two values, such as 0 and 1. A Bernoulli process is obtained by repeating the same Bernoulli trial, where each trial is independent of the others. If the outcome given for the value “1” has probability p, it can be shown that the summation of n Bernoulli trials is binomially distributed ~ binomial (p, n).
References
Siu NO, Kelly DL (1998) Bayesian parameter estimation in probabilistic risk assessment. Reliab Eng Syst Saf 62:89–116
Bayes T (1763) An essay towards solving a problem in the doctrine of chances. Philos Trans R Soc 53:370–418
Laplace PS (1814) A philosophical essay on probabilities. Dover Publications, New York (reprint 1996)
Stigler SM (1986) The history of statistics: the measurement of uncertainty before 1900. Belknap Press, Cambridge
de Finetti B (1974) Theory of probability. Wiley, New York
Winkler RL (1972) An introduction to Bayesian inference and decision. Holt, Rinehart, and Winston, New York
Apostolakis GE (1994) A commentary on model uncertainty. In: Mosleh A, Siu N, Smidts C, Lui C (eds) Proceedings of workshop I in advanced topics in risks and reliability analysis, model uncertainty: its characterization and quantification. NUREG/CP-0138, U.S. Nuclear Regulatory Commission, Washington
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Kelly, D., Smith, C. (2011). Introduction and Motivation. In: Bayesian Inference for Probabilistic Risk Assessment. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-1-84996-187-5_1
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DOI: https://doi.org/10.1007/978-1-84996-187-5_1
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