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Introduction to Bayesian Estimation and Copula Models of Dependence
book

Introduction to Bayesian Estimation and Copula Models of Dependence

by Arkady Shemyakin, Alexander Kniazev
March 2017
Beginner to intermediate content levelBeginner to intermediate
352 pages
9h 18m
English
Wiley
Content preview from Introduction to Bayesian Estimation and Copula Models of Dependence

5 Statistical Dependence Structures

5.1 Introduction

In this chapter we will briefly survey common statistical tools for modeling dependence between two or more random variables. In order to explain the problem in its most general form, let us consider a dataset consisting of n pairs (xi, yi), where xi and yi represent values of two random variables X and Y corresponding to the ith case (observation). A classical example introduced by Gary Alt, a famous black bear expert [1], contains measurements of length (X, measured in inches) and weight (Y, measured in pounds) of a sample of 143 black bears taken in the state of Pennsylvania. Figure 5.1 shows the scatterplot of this dataset.

Graph showing the plotting which is done for weight versus length of black bears in Pennsylvania and it is like weight increases along with length.

Figure 5.1 Black bears in Pennsylvania.

Another example deals with a joint survival or joint mortality problem. We consider data on the length of human life, studying married couples, where X represents the wife's age at death, and Y represents the husband's. Figure 5.2 shows the scatterplot for about 11,000 pairs of spouses observed for a period of 5 years introduced in [7]. Evidently, not all of the observed died by the end of the period, so the actual number of points on the graph is much smaller than 11,000.

Graph showing the joint mortality data which is indicating the ages at death and it is plotted on graph as many dark spots which finally looks like a big black hole.

Figure 5.2 Joint mortality data.

Why can X and Y in these two examples be considered ...

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Publisher Resources

ISBN: 9781118959015Purchase book