Abstract
Statistical models called graphical chain models correspond to special types of graphs which included both symmetric and casual relation between variables. A conditional Gaussian (CG) distribution is defined by a joint Gaussian distribution of the continuous variables given discrete variables and by positive probabilities for each level combination of the discrete variables. In CG distribution, a variable pair is conditionally independent given remaining variables if and only if all interaction terms containing this variable pair are zero. In this study, we present CG chain models and CG interactions.
Keywords
Conditional Gaussian distributions Conditional Gaussian interactions Chain Graph Conditional Gaussian regression
References
- Lauritzen S.L. Graphical Models. Elarendon Press, New York, (1996).
- Erbaş S.O., Bayrak H .. Grafiksel Zincir Modeller, İstatistik Sempozyumu 2000, 273-284, (2000).
- Lauritzen S.L and Richardson T.S., Chain Graph Models and Their Casual Interpretation, Department of Mathematical Science, Aalborg University, Research Report R-01-2003,(2001)
- Lauritzen S.L. and Jensen F., Stable Local Computation with Condinational Gaussian Distribution, Department of Mathematical Science, Aalborg University, Research Report R-99-2014, (1999)
- Lauritzen, S.L and Wermuth, N. Graphical Models for Associations Between Variables, Some of Which are Qualitative and Some Quantative. Annals of Statistics, 17,31 -57, (1989).
- Wermuth, N. and Lauritzen, S.L. On Substantive Research Hypotheses, Conditonal Independence Graphs and Graphical Chain Models (with discussion). Journal of Royal Statistical Society, Series B, 52, 72, (1990).
- Cox, D.R. “Interaction" Int. Statist. Rev., 52, 1-31, (1984).
Abstract
Grafiksel zincir modeller diye adlandırılan istatistiksel modeller, değişkenler arasında hem simetrik hem de nedensel ilişki içeren grafiklerin özel bir tipidir. Koşullu Gauss Dağılımı(CG) kesikli değişkenler verilmişken sürekli değişkenlerin bileşik Gauss dağılımı ve kesikli değişkenlerin her bir seviye kombinasyonunun pozitif olasılıkları ile tanımlanır. Bir CG dağılımında bir değişken çiftinin geri kalan değişkenler verilmişken koşullu bağımsız olabilmesi için gerek ve yeter koşul bu değişken çiftini ifade eden tüm etkileşim terimlerinin sıfır olmasıdır. Bu çalışmada koşullu Gauss etkileşimleri ve koşullu Gauss Zincir model tanıtılacaktır.
References
- Lauritzen S.L. Graphical Models. Elarendon Press, New York, (1996).
- Erbaş S.O., Bayrak H .. Grafiksel Zincir Modeller, İstatistik Sempozyumu 2000, 273-284, (2000).
- Lauritzen S.L and Richardson T.S., Chain Graph Models and Their Casual Interpretation, Department of Mathematical Science, Aalborg University, Research Report R-01-2003,(2001)
- Lauritzen S.L. and Jensen F., Stable Local Computation with Condinational Gaussian Distribution, Department of Mathematical Science, Aalborg University, Research Report R-99-2014, (1999)
- Lauritzen, S.L and Wermuth, N. Graphical Models for Associations Between Variables, Some of Which are Qualitative and Some Quantative. Annals of Statistics, 17,31 -57, (1989).
- Wermuth, N. and Lauritzen, S.L. On Substantive Research Hypotheses, Conditonal Independence Graphs and Graphical Chain Models (with discussion). Journal of Royal Statistical Society, Series B, 52, 72, (1990).
- Cox, D.R. “Interaction" Int. Statist. Rev., 52, 1-31, (1984).
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Statistical Theory |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | December 15, 2003 |
| Published in Issue | Year 2003 Volume: 2 Issue: 3 |
