  # Bayesian Statistics

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## Bayesian Statistics

Bayesian Statistics are a specific subset within the wider range of statistics. The definition of Bayesian Statistics is essentially that of evidence being expressed in what is known as Bayesian probabilities, which are probability calculations derived from the statistics, and are based on ‘degrees of belief’. These calculations take in to account previous knowledge of events as well as accumulated experiences.

Bayesian Statistics are based on Bayes’ theorem (also known as Bayes’ rule or Bayes’ Law), named after Thomas Bayes, whose work in the 18th Century showed how to update beliefs based on new evidence. This theorem is a way to calculate the probability of something happening when faced with one or multiple pieces of evidence. Bayes’ Theorem is important as it allows researchers to base calculations on probabilities rather than exact counts, while it is often the case that there is no access to the counts, but researchers may know the probabilities.

Bayesian Statistics can often determine results that would initially seem counterintuitive to an initial understanding.

Many regular statistical techniques have their own unique Bayesian version. For example Bayesian inference, this is a type of statistical inference. Other examples would be the Bayesian design of experiments, Bayesian linear regression and approximate Bayesian computation. Bayesian inference uses Bayes’ theorem to update the probability of a certain hypotheses happening as new evidence is acquired. Bayesian linear regression is an alternative approach to bivariate regression, using Bayesian Inference

Bayesian Statistics are used in Market Research, but, in recent years have also started to become popular in other fields such as Law and Medicine. A commonly stated example of the uses of Bayesian Statistics in the field of Law is for predicting the likelihood that a suspect committed a crime given that his or her fingerprints are found at the scene.

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