Application Of Bayesian Theory In Model Selection

Constructing a model for the data collected is the basis of applied probability and statistics. The common method of constructing a model is assigning a model for the data arbitrarily and artificially, and then using the model to analyze the data. But this method has its limitation. That is, because of assigning a model arbitrarily and artificially, this method dose not take the character of data into account For the sake of easy-calculation, the uncertainty of model itself is ignored. All those cause the poor stability of result, and the result obtained through this method is apt to deviate from the true value. This paper mainly deals with the selection of model in data-analysis. It incorporates the Bayesian theory into the process of model selection. Various models have been considered on the basis of the prior information and the character of data. Because the whole model space is unknown, the model in the space is regarded as random variable, and each model has a prior probability. With the Total-probability formula and Bayesian formula, the author considers more models with the prior probability, so the uncertainty of model is solved. With the method of the Analytic Hierarchy Process, the difficulty of computation is decreased. The validity of the application of Bayesian theory in model selection is proved by an example. It demonstrates that the result obtained from this method is better than that from other methods. This result is more reasonable, more accurate and more persuadable.