Bayesian view of uncertainty
The classical or frequentist statistics typically take the view that any physical process-generating data containing noise can be modeled by a stochastic model with fixed values of parameters. The parameter values are learned from the observed data through procedures such as maximum likelihood estimate. The essential idea is to search in the parameter space to find the parameter values that maximize the probability of observing the data seen so far. Neither the uncertainty in the estimation of model parameters from data, nor the uncertainty in the model itself that explains the phenomena under study, is dealt with in a formal way. The Bayesian approach, on the other hand, treats all sources of uncertainty using probabilities. Therefore, neither the model to explain an observed dataset nor its parameters are fixed, but they are treated as uncertain variables. Bayesian inference provides a framework to learn the entire distribution of model parameters, not just...
