Changes

In order to compare hypothesis [[Bayesian model selection]] is often used. This is when each hypothesis you want to test is assigned a prior probability, and then the likelihood of the data given each hypothesis being test is calculated. You can then us Bayes equation to determine the relative probabilities that each hypothesis is correct. This method is almost always testing relative probabilites since to calculate an absolute probability would require knowing every possible hypothesis. Usually this is not possible, but sometimes the subset is finite enough it can be tested.  

In order to compare hypothesis [[Bayesian model selection]] is often used. This is when each hypothesis you want to test is assigned a prior probability, and then the likelihood of the data given each hypothesis being test is calculated. You can then us Bayes equation to determine the relative probabilities that each hypothesis is correct. This method is almost always testing relative probabilites since to calculate an absolute probability would require knowing every possible hypothesis. Usually this is not possible, but sometimes the subset is finite enough it can be tested.  

Because of the large number of calculations needed for model selection Bayesian approaches have only became practical and popular with the advent of computers. But even with the most modern computers available many Bayesian models remain computational intractable. Recent developments in applying [[Monte Carlo method | Markov chain Monte Carlo methods]] to these problems have lead to promising results.

Because of the large number of calculations needed for model selection Bayesian approaches have only became practical and popular with the advent of computers. But even with the most modern computers available many Bayesian models remain computational intractable. Recent developments in applying [[Monte Carlo method | Markov chain Monte Carlo methods]] to these problems have led to promising results.

==Non-parametric and Bootstrapping methods==

==Non-parametric and Bootstrapping methods==