Baysian Estimation on Latent Structure Models for Mixed Measurement Level Data

混合测量水平数据潜在结构模型的贝叶斯估计

• 批准号: 07680318
• 负责人: OTSU Tatsuo
• 金额: $ 0.7万
• 依托单位: HOKKAIDO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07680318/
• 关键词: Bays estimation; symbolic manipulation; meta data; model exploration; local regression; graphical models; ベイズ推定; 平滑化; 共分散構造分析; 同値モデル; 潜在構造; 記号処理言語

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.

研究的目的如下。第一个是针对具有混合测量水平的多元数据提出潜变量贝叶斯模型。第二个是开发一个可以表示和操作这些模型的各种先验信息的软件。在这项研究中，取得了以下成果。（1）Prolog（一种基于逻辑的符号编程语言）谓词，用于操作基本统计对象（向量、矩阵） 、关系表和离散类别）被开发出来。该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) 公式的延伸。并开发了操作复杂模型结构的程序。(3)综述了贝叶斯网络及相关统计模型的研究进展。一些定理作为 Prolog 上的谓词来实现。小于或等于6^<th>阶的有向无环图的统计等价类由程序确定。对于可以使用混合测量水平数据的先验信息的潜变量模型的研究尚未完全实现。这是即将面临的问题。

项目成果

大津起夫: "Rrologによる線形モデル探索の実現" 日本分類学会 研究報告予稿集. 12. 17-24 (1995)

Kio Otsu：“使用 Rrolog 实现线性模型搜索”日本分类学会研究报告论文集。12. 17-24 (1995)。

大津起夫: "Prologによる線形モデルの表現と操作" Hokkaido Behavioral Science Report M(S). 24. 1-18 (1996)

Kio Otsu：“使用 Prolog 的线性模型的表示和操作”北海道行为科学报告 M(S)。 24. 1-18 (1996)。

大津 起夫: "パスモデルにおける識別可能性の自動判定に向けて" 統計数理研究所共同研究レポート. 100. 29-40 (1997)

Kio Otsu：“走向路径模型中可识别性的自动确定”统计数学研究所联合研究报告。100. 29-40 (1997)。

Tastuo OTSU: "Toward the automatics detection of the identifiability of path models" ISM Cooperative Research Report. 100. 29-40 (1997)

Tastuo OTSU：“走向路径模型可识别性的自动检测”ISM 合作研究报告。

Tatsuo Otsu: "Horseshoe Problems in Dimension Reduction with Categorical Data" Hokkaido Behavioral Science Report Series M. 28. 1-26 (1996)

大津达雄：“分类数据降维中的马蹄问题”北海道行为科学报告系列 M.28.1-26（1996）