| dc.description | As MCMC (Markov Chain Monte Carlo) theory was set up, Bayes
Theory could be employed in the application, because by using MCMC,
it is possible for us to summarize the posterior distribution of the unknown
parameter. In the process of computing the posterior, choosing
the right prior is important. In recent years, the intrinsic prior draws
more and more attentions of the statisticians because the use of intrinsic
priors for model selection has proven to provide sensible prior for a
wide variety of model selection problem, especially in the nested model
scenario. For the univariate normal test, it is relatively easier to get
the intrinsic prior and to check the property of it, such as proper or
improper, or the type of the distribution. However, for the multivariate
normal test, it is not an easy job. Then, how to get the intrinsic prior
under di erent hypotheses for multivariate normal tests; Is it proper
or improper? And is there any relationship between the intrinsic prior
and the di erence dimension of the unknown parameters of the two
models. The goal of my thesis is to study these problems. The thesis is organized as follows: in Chapter II, we recall basic theory
which we will need for our discussion; in Chapter III, we carry out
our arguments and prove main theorems; in Chapter IV, we summarize
the results and give the conclusions; in the appendix, we list some basic
probability and statistics concepts and theorems in favor of readers; at
the end, an index of frequently used concepts are included. | |
