Bayesian method of modelling stems from the Bayes theorem and derived using conditional probabilities. Its advantage lies in its ability to include prior knowledge of unknown parameters to ascertain their uncertainties. Thus, the prior parameters are updated by the data likelihood to obtain the posteriors. The challenge of Bayesian modelling has been the integration of the denominator which always resulted into improper integrals. This actually prolonged its wide applications. With the advent of high performance computers, solution to such integrals are easily solved using Markov chain Monte Carlo simulations. The advent robust approximation methods through integrated nested Laplace approximations (INLA) has even made parameter estimation faster; thus making Bayesian methods interesting and better. Unlike frequentist approaches, Bayesian methods can present estimates of parameters as densities from which their uncertainties and credible intervals can be estimated. They have now found wide applications in divers areas like environmental modelling, climate modeling, agriculture, epidemiology and many other domains that requires modeling.
Explain the advantage of Bayesian methods over frequentist methods
Understand different estimation methods for Bayesian models
Completed (GI-N2K)