Abstract
Several paradigms provide a basis for statistical inference; the two most dominant are the frequentist (sometimes called classical, traditional, or Neyman– Pearsonian) and Bayesian. The term Bayesian refers to Reverend Thomas Bayes (Fig. 8.1), a nonconformist minister interested in mathematics whose posthumously published essay (Bayes, 1763) is fundamental for this kind of inference. According to the Bayesian paradigm, the unobservable parameters in a statistical model are treated as random. Before data are collected, a prior distribution is elicited to quantify our knowledge about the parameter. This knowledge comes from expert opinion, theoretical considerations, or previous similar experiments. When data are available, the prior distribution is updated to the posterior distribution. This is a conditional distribution that incorporates the observed data. The transition from the prior to the posterior is possible via Bayes’ theorem.
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Vidakovic, B. (2011). Bayesian Approach to Inference. In: Statistics for Bioengineering Sciences. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0394-4_8
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