Model selection

Model selection is the task of selecting a mathematical model from a set of potential models, given evidence. There are many model selection methods, including Akaike information criterion (AIC), Bayesian information criteria (BIC), Deviance information criterion (DIC), various Linear regression methods, Minimum description length (MDL), Minimum Message Length (MML), and many more.

A standard example of model selection is that of curve fitting, where, given a set of points and other background knowledge (e.g. points are a result of i.i.d. samples), we must select a function that describes the best curve. What is meant by best is controversial. Often this is expressed as being a matter of finding the proper tradeoff between goodness of fit (in the chi-square sense) and complexity (in terms of number of free parameters), or Bias (statistics) and variance.