Bayesianism
Overview
Bayesianism is an approach to statistics and machine learning that uses
Bayes Rule
to help estimate unknown model parameters.
In standard (frequentist) statistics, model parameters are generally fixed, even if unknown.
In a Bayes model, model parameters ({% \vec{\theta} %}) are themselves random variables.
Given a sampled dataset D, Bayes rule implies
{% \mathbb{P}(\vec{\theta}|D) = \frac{\mathbb{P} (D|\vec{\theta}) \mathbb{P}(\vec{\theta})}{\sum_{i=1}^n \mathbb{P}(D|\vec{\theta}_i) \mathbb{P}(\vec{\theta}_i)} %}
That is, if it is known how the probability of the given sampled dataset D relates to a set of given parameters
{% \vec{\theta}_i %}, and it is known the prior probability {% \mathbb{P}(\vec{\theta}_i) %}, then the probability
of any given set of parameters is known.
Topics
