Elements of Bayesian StatisticsThe ingratiating title notwithstanding, this is in no standard sense a text but a monograph, based largely upon the authors' research over a period of years, and intended to be read by sophisticated students of theoretical statistics. No exercises attach to the nine chapters, nor are they interrup |
Contents
Basic Tools and Notation from Probability Theory | 1 |
Sufficiency and Ancillarity | 2 |
Trace of M on A | 3 |
ƒ¹B M | 6 |
MIR Measure positive | 13 |
Maximal Ancillarity | 139 |
Further Results | 187 |
Sequential Experiments | 241 |
Asymptotic Experiments | 283 |
ལྤ ཎྞཱ æ 3 3 སྐྱེ བ པ 8 8 བསྐྱ | 347 |
Invariant Experiments | 349 |
Invariance in Stochastic Processes | 403 |
76 | 441 |
| 463 | |
| 489 | |
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Common terms and phrases
admissible reductions analysis ancillarity ancillary statistic assumption B₁ Bayesian experiment Borel Chapter characterized Clearly concept conditional expectation conditional independence conditionally consider Corollary defined Definition denoted density dominated E-sufficient elementary Property example exists experiment Ɛ ƐAvs filtration finite Florens identified implies Lemma M₁ M₁ M2 M₂ M2 V M3 M3 V M4 M4 V M5 maximal ancillary measurable function measurable separability measurable space minimal splitting minimal sufficient parameter Mn)-transitive Mouchart mutual exogeneity mutually sufficient N₁ N₂ Note null sets o-field obtain parameter space posterior prior distribution prior probability probability measure probability space Proof Proposition regular respect result sample space sampling probabilities sampling process sampling theory Section sequence sequential statistical experiment stochastic process strong identification sub-o-field subsets sufficient statistic T₁ tail-sufficient Theorem transitivity trivial unreduced experiment