Abstract

In Bayesian inference, complete knowledge about a vector of model parameters, θ ∈ Θ, obtained by fitting a model ℳ y o b s ∈ Y , is contained in the posterior distribution. Here, prior beliefs about the model parameters, as expressed through the prior distribution, π(θ), are updated by observing data π ( θ | y o b s ) = p ( y o b s | θ ) π ( θ ) ∫ Θ p ( y o b s | θ ) π ( θ )   d θ , through the likelihood function p(y_obs |θ) of the model. Using Bayes’ theorem, the resulting posterior distribution: π ( θ | y o b s )   ≈   1 N ∑ i   =   1 N δ θ ( i )   ( θ ) ,