History
The term Bayesian refers to Thomas Bayes (1702–1761), who proved a special case of what is now called Bayes' theorem in a paper titled "An Essay towards solving a Problem in the Doctrine of Chances". In that special case, the prior and posterior distributions were Beta distributions and the data came from Bernoulli trials. It was Pierre-Simon Laplace (1749–1827) who introduced a general version of the theorem and used it to approach problems in celestial mechanics, medical statistics, reliability, and jurisprudence. Early Bayesian inference, which used uniform priors following Laplace's principle of insufficient reason, was called "inverse probability" (because it infers backwards from observations to parameters, or from effects to causes). After the 1920s, "inverse probability" was largely supplanted by a collection of methods that came to be called frequentist statistics.
In the 20th century, the ideas of Laplace were further developed in two different directions, giving rise to objective and subjective currents in Bayesian practice. In the objectivist stream, the statistical analysis depends on only the model assumed and the data analysed. No subjective decisions need to be involved. In contrast, "subjectivist" statisticians deny the possibility of fully objective analysis for the general case.
In the 1980s, there was a dramatic growth in research and applications of Bayesian methods, mostly attributed to the discovery of Markov chain Monte Carlo methods, which removed many of the computational problems, and an increasing interest in nonstandard, complex applications. Despite the growth of Bayesian research, most undergraduate teaching is still based on frequentist statistics. Nonetheless, Bayesian methods are widely accepted and used, such as in the fields of machine learning and talent analytics.
Read more about this topic: Bayesian Probability
Famous quotes containing the word history:
“There is one great fact, characteristic of this our nineteenth century, a fact which no party dares deny. On the one hand, there have started into life industrial and scientific forces which no epoch of former human history had ever suspected. On the other hand, there exist symptoms of decay, far surpassing the horrors recorded of the latter times of the Roman empire. In our days everything seems pregnant with its contrary.”
—Karl Marx (1818–1883)
“The true theater of history is therefore the temperate zone.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“No one is ahead of his time, it is only that the particular variety of creating his time is the one that his contemporaries who are also creating their own time refuse to accept.... For a very long time everybody refuses and then almost without a pause almost everybody accepts. In the history of the refused in the arts and literature the rapidity of the change is always startling.”
—Gertrude Stein (1874–1946)