Research On Two Problems In Multivariate Statistical Analysis

Statistical distribution is an important means to describe the characteristics and regular of random variable. Multivariate statistical analysis method is coll ection of a class of multivariate statistical data processing methods based on m ultivariate statistical distribution. It is an important branch of statistics have ric h the theory results and methods for many applications. In this article, we will study two parts. The first part is discriminant analysis in Bayesian decision the ory, and the second part is applied research of Canonical correlation analysis method.Discriminant analysis of bayesian decision theory: Statistical pattern recognition method is based on statistical probability of sample eigenvalues. This paper apply Bayesian decision theory, statistical theory to explore ways to do a series of works. Bayesian decision theory with its characteristics of smallest classification error probability have been widely used. According to the original Bayesian formula, scholars have deduced Bayesian discriminant function and decision-face of multivariate normal probability model, and through experiments to verify and analyze the derived conclusions. But under other statistical distribution analysis result is still unknown. Research data show that for many years, In practice, not all the distribution of sample data obey the multivariate normal distribution. When data presentation rush characteristics, on the probability density distribution picture, on the tail end of the show more serious. Multivariate normal distribution is unable to meet this situation. When we use the multivariate normal distribution to describe the long tail characteristics of the sample data. Abnormal points of sample data will inevitably affect the covariance matrix and estimates of the mean, so that the discriminant result appeared deviation, and will affect the robustness of the multivariate normal distribution. However, multivariate t distribution than the multivariate normal distribution has better robustness. In multivariate t distribution, we can adjust the size of the degrees of freedom parameter, and reduce the abnormal points in the data to affect the results of the study. In this paper, the first part is that multivariate t distribution probability density function as a basis for classification designed, according to the multivariate t distribution probability model to extract sample collection and analysis sample, with a strong practical significance. This article divided into six situations from a different expression of the covariance structure and the degree of freedom is equal and unequal. Discussed discriminant function expression in the multivariate t density model. For these six cases, we were again from prior probability equal and unequal to further discuss the case. Ultimately, we can deduce the expression of discriminant function of two multivariate t density model under each case. With the expression of discriminant function, we can get its decisions surface equation, and draw decisions graphics.Canonical correlation analysis in the application research in tobacco field: Canonical correlation analysis is an important research topic in multivariate statistical analysis. With the idea of Principal component analysis, and with a few comprehensive variables to reflect the nature of the linear correlation of the two sets of variables. Correlation analysis and forecasting analysis in many areas it has been widely used. In this paper, after study the theory of canonical correlation analysis, and applied to tobacco instance analysis. 35 main chemicals in tabacco and 10 sensory coziness indexes were analyzed by the canonical correlation analysis method. The results show that the chemical composition of flue-cured tobacco in some indicators for sensory comfort in some of the indicators have a significant impact. So in flue-cured tobacco production, processing, research emphasis can be placed on these indicators have a significant effect, thus improving the sensory comfort tobacco. Further illustrates the research the value of the canonical correlation analysis.