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Consistency of Bayesian Linear Model Selection With a Growing Number of Parameters
| Content Provider | Semantic Scholar |
|---|---|
| Author | Shang, Zuofeng Clayton, Murray K. |
| Copyright Year | 2011 |
| Abstract | Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which provide a stochastic search of informative variables, have gained popularity. In this paper, we will study the asymptotic properties related to Bayesian model selection when the model dimension p is growing with the sample size n. We consider p ≤ n and provide sufficient conditions under which: (1) with large probability, the posterior probability of the true model (from which samples are drawn) uniformly dominates the posterior probability of any incorrect models; and (2) with large probability, the posterior probability of the true model converges to one. Both (1) and (2) guarantee that the true model will be selected under a Bayesian framework. We also demonstrate several situations when (1) holds but (2) fails, which illustrates the difference between these two properties. Simulated examples are provided to illustrate the main results. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.stat.wisc.edu/~shang/PMC.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Bayes factor Bayesian network Feature selection Gain Genetic Selection Information Linear model Model selection Stochastic optimization |
| Content Type | Text |
| Resource Type | Article |
