Article

Bayesian Statistics

Alexander LoPilato and Mo Wang

in Management

ISBN: 9780199846740
Published online July 2016 | | DOI: http://dx.doi.org/10.1093/obo/9780199846740-0102
Bayesian Statistics

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Bayesian statistics refer to a general method of estimating statistical models. In contrast to classic or frequentist statistics, Bayesian statistics, also referred to as Bayesian methods, view the population parameter as a random variable instead of a fixed value. Bayesian methods are used to combine the information obtained from the observed data and the specified statistical model—in the form of the likelihood function—with the researchers’ prior beliefs about the effects under investigation (in the form of the prior distribution) to estimate a posterior distribution for each effect. The posterior distribution is a probability distribution that describes the uncertainty surrounding an effect. Because the posterior distribution is a combination of the likelihood function and the prior distribution, it can be changed by obtaining more data or changing the prior distribution to reflect different degrees of certainty about the effect. However, as the sample size increases, the results obtained from Bayesian methods converge to those obtained from frequentist methods. Bayesian methods are named after Reverend Thomas Bayes, who derived the Bayesian theorem. Using conditional probabilities, this theorem equates a model’s posterior distribution, which is a probability distribution for the model parameters conditional on the observed data, to the product of its likelihood function, which is informed only by the observed data, and the prior distribution, which is informed by a researcher’s prior beliefs about possible parameter values. The product is then rescaled or normalized by dividing it by the marginal probability of the observed data. Given this mathematical formulation, we can appreciate how the posterior distribution can be changed either by obtaining more data or by changing the prior distribution to reflect different degrees of certainty about the effect. However, as more data are collected and sample sizes increase, the “likelihood swamps the prior,” and results obtained from Bayesian methods converge to those obtained from frequentist methods. The advantage of Bayesian methods remains, however, because one still gets use language referring to the most probable parameters given the data.

Article.  7296 words. 

Subjects: Business and Management

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