Bayesian modelling

See AI/Math and Statistics/Monte Carlo methods and AI/Deep Learning/Probabilistic deep learning

Resources

https://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation
In Bayesian statistics, a maximum a posteriori probability(MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior distribution. The MAP can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data.It is closely related toFisher's method of maximum likelihood(ML) estimation, but employs an augmented optimization objective which incorporates a prior distribution(that quantifies the additional information available through prior knowledge of a related event) over the quantity one wants to estimate. MAP estimation can therefore be seen as a regularization of ML estimation.

https://en.wikipedia.org/wiki/Maximum_likelihood_estimation
Maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model given observations, by finding the parameter values that maximize the likelihood of making the observations given the parameters. MLE can be seen as a special case of the maximum a posteriori estimation (MAP) that assumes a uniform prior distribution of the parameters, or as a variant of the MAP that ignores the prior and which therefore is unregularized.