Conditional Specification of Statistical ModelsThe concept of conditional specification of distributions is not new but, except in normal families, it has not been well developed in the literature. Computational difficulties undoubtedly hindered or discouraged developments in this direction. However, such roadblocks are of dimished importance today. Questions of compatibility of conditional and marginal specifications of distributions are of fundamental importance in modeling scenarios. Models with conditionals in exponential families are particularly tractable and provide useful models in a broad variety of settings. |
Contents
Concepts and Theorems | 1 |
1 | 40 |
Introduction | 53 |
Exponential Families | 75 |
5 | 82 |
7 | 88 |
Other Conditionally Specified Families | 102 |
Improper and Nonstandard Models | 133 |
12 | 275 |
Bayesian Analysis Using Conditionally | 293 |
14 | 337 |
5 | 344 |
Paella 353 | 352 |
1 | 354 |
Introduction | 371 |
B Notation Used in This Book | 383 |
1 | 146 |
8 | 169 |
2 | 175 |
Compatibility in Three Dimensions | 176 |
Estimation in Conditionally Specified Models | 197 |
Marginal and Conditional Specification in General | 229 |
11 | 255 |
| 391 | |
175 | 393 |
| 404 | |
| 405 | |
| 411 | |
Other editions - View all
Conditional Specification of Statistical Models Barry C. Arnold,Enrique Castillo,Jose M. Sarabia Limited preview - 2007 |
Conditional Specification of Statistical Models Barry C. Arnold,Enrique Castillo,Jose M. Sarabia No preview available - 1999 |
Conditional Specification of Statistical Models Barry Arnold,Enrique Castillo,Jose M. Sarabia No preview available - 2013 |
Common terms and phrases
algorithm analogous Arnold and Strauss assume Bayesian bivariate distributions bivariate normal distribution Chapter characterize classical bivariate normal compatible conditional densities conditional moments conditional probability conditional specification conditional survival functions conditionally conjugate conditionally specified models conditionals distribution conditionals in exponential conditionals model conjugate prior conjugate prior family Consider correlation corresponding cross-product ratio defined denote determine discussed example exponential conditionals exponential families family of conditional family of priors functional equation fx(x gamma distribution Gibbs sampler given Gumbel hyperparameters integrable involves joint density joint distribution k-dimensional likelihood estimates linear marginal densities marginal likelihood matrix maximum likelihood method multivariate nonnegative normal conditionals distribution normalizing constant obtain parametric family Pareto conditionals Pareto distribution prior beliefs pseudolikelihood random variable random vector regression function sample Sarabia Section simulation solution solve Statistics Suppose survival functions Theorem tion unique Weibull X₁