Baysian Estimation on Latent Structure Models for Mixed Measurement Level Data

本研究的目的如下。第一个是针对混合测量水平的多变量数据提出了潜在变量贝叶斯模型。本研究取得了以下成果：(1)开发了基于逻辑的符号程序设计语言PROLOG，实现了对基本统计对象(向量、矩阵、关系表和离散范畴)的操作。程序依赖于瑞典计算机科学研究所开发的SICStus Prolog对象系统。(2)提出了一种能够表示变量间拓扑关系的贝叶斯框架。该模型是Akaike(1980)公式的扩展。对贝叶斯网络及相关统计模型的研究现状进行了综述。一些定理在PROLOG上被实现为谓词。该程序确定了小于等于6^<th>阶的有向无环图的统计等价类，但对能够利用混合测量水平数据的先验信息的潜在变量模型的研究还没有完全完成。这就是即将出现的问题。

The purpose of the research was the followings. The first was proposing latent variable Baysian models for multivariate data with mixed measurement levels. And the second was developing a software that can represent and manipulate various prior information for those models.In this research, the followings were achieved.(1) Prolog (a logic based symbolic programming language) predicates for manipulating fundamental statistical objects (vectors, matrices, relational tables, and discrete categories) were developed. The program depends on SICStus Prolog Object System (developed by Swedish lnstitute of Computer Science).(2) A Baysian framework that can represent topological relations between variables was proposed. The model is an extension of Akaike's (1980) formulation. Also a program that manipulates the complex model structure was developed.(3) The researches on Baysian networks and related statistical models were reviewed. Some theorems were implemented as predicates on Prolog. Statistically equivalent classes of directed acyclic graphs less than or equal to 6^<th> order were determined by the program.Research on latent variable models that can use the prior information for mixed measurement level data was not fully achieved. This is the forthcoming problem.