# Bayesian Inference

In statistics, Bayesian inference is a method of inference in which Bayes' rule is used to update the probability estimate for a hypothesis as additional evidence is learned. Bayesian updating is an important technique throughout statistics, and especially in mathematical statistics: Exhibiting a Bayesian derivation for a statistical method automatically ensures that the method works as well as any competing method, for some cases. Bayesian updating is especially important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a range of fields including science, engineering, medicine, and law.

In the philosophy of decision theory, Bayesian inference is closely related to discussions of subjective probability, often called "Bayesian probability." Bayesian probability provides a rational method for updating beliefs; however, non-Bayesian updating rules are compatible with rationality, according to philosophers Ian Hacking and Bas van Fraassen.

### Other articles related to "bayesian inference, bayesian, inference":

Bayesian Inference In Phylogeny
... Bayesian inference in phylogeny generates a posterior distribution for a parameter, composed of a phylogenetic tree and a model of evolution, based on the ... The Bayesian approach has become more popular due to advances in computational machinery, especially, Markov chain Monte Carlo algorithms ... Bayesian inference has a number of applications in molecular phylogenetics, for example, estimation of species phylogeny and species divergence times ...
Bayesian Inference - History
... Main article History of statistics#Bayesian statistics The term Bayesian refers to Thomas Bayes (1702–1761), who proved a special case of what is now called Bayes' theorem ... Early Bayesian inference, which used uniform priors following Laplace's principle of insufficient reason, was called "inverse probability" (because it ... directions, giving rise to objective and subjective currents in Bayesian practice ...
List Of Phylogenetics Software
... neighbor-joining, maximum parsimony (also simply referred to as parsimony), UPGMA, Bayesian phylogenetic inference, maximum likelihood and distance matrix methods ... Workflow platform dedicated to phylogenetic and general bioinformatic analysis Inference of phylogenetic trees using Distance, Maximum Likelihood, Maximum Parsimony, Bayesian methods and related workflows ... Makarenkov BAli-Phy Simultaneous Bayesian inference of alignment and phylogeny Bayesian inference, alignment as well as tree search ...
Coalescent Theory - Software
... BEAST - Bayesian MCMC inference package with a wide range of coalescent models including the use of temporally sampled sequences ... of disease genes using coalescent theory based on an Bayesian MCMC framework ... Migrate - Maximum likelihood and Bayesian inference of migration rates under the n-coalescent ...
Frequentist Inference - Basis
... To a large extent, frequentist inference has been associated with the frequency interpretation of probability, specifically that any given experiment can be considered as one of an ... In this view, the frequentist inference approach to drawing conclusions from data is effectively to require that the correct conclusion should be drawn with a given (high ... Similarly, Bayesian inference has often been thought of as almost equivalent to the Bayesian interpretation of probability and thus that the essential difference ...

### Famous quotes containing the word inference:

I have heard that whoever loves is in no condition old. I have heard that whenever the name of man is spoken, the doctrine of immortality is announced; it cleaves to his constitution. The mode of it baffles our wit, and no whisper comes to us from the other side. But the inference from the working of intellect, hiving knowledge, hiving skill,—at the end of life just ready to be born,—affirms the inspirations of affection and of the moral sentiment.
Ralph Waldo Emerson (1803–1882)