On Bayesian Geometry

Bayesian inference is based on the fact that we often don't know the underlying distribution of data, so we need to build a model and then iteratively adjust it as we get more data. In parametric Bayesian inference you start with picking a general form of the probability distribution f(x;θ) defined by parameters θ. A good example of the distribution could be a Normal distribution with two parameters μ and σ 2. The probability of the data under a hypothetical distribution, assuming independent data examples, is: This function is called likelihood function. The parameter θ is itself a random variable, and its probability distribution can be found using Bayes' theorem: Here p(θ) is called posterior distribution, π(θ) is prior distribution and expresses our beliefs about parameter θ before we see any data. The term in the denominator is called evidence and represents probability of data.