Editing Statistics (section)

=== Bayesian Statistics ===
{{main|Bayesian Statistics}}
An alternative paradigm to the popular [[frequentist inference|frequentist]] paradigm is to use [[Bayes' theorem]] to update the [[prior probability]] of the hypotheses in consideration based on the [[likelihood function|relative likelihood]] of the evidence gathered to obtain a [[posterior probability]]. Bayesian methods have been aided by the increase in available computing power to compute the [[posterior probability]] using numerical approximation techniques like [[Markov Chain Monte Carlo]]. 

For statistically modelling purposes, Bayesian models tend to be [[Bayesian hierarchical modeling|hierarchical]], for example, one could model each [[Youtube]] channel as having video views distributed as a normal distribution with channel dependent mean and variance <math> \mathcal{N}(\mu_i, \sigma_i) </math>, while modeling the channel means as themselves coming from a normal distribution representing the distribution of average video view counts per channel, and the variances as coming from another distribution. 

The concept of using [[likelihood_function#Likelihood_ratio|likelihood ratio]] can also be prominently seen in [[likelihood ratios in diagnostic testing|medical diagnostic testing]].