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1 | (12) |
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1 | (1) |
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The subjectivist view of probability |
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2 | (1) |
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Bayesian Statistics in perspective |
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3 | (2) |
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An overview of Bayesian Theory |
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5 | (4) |
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5 | (1) |
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5 | (1) |
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6 | (1) |
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7 | (1) |
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7 | (1) |
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8 | (1) |
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8 | (1) |
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9 | (1) |
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9 | (4) |
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13 | (92) |
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13 | (3) |
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16 | (7) |
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16 | (2) |
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18 | (5) |
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Coherence and quantification |
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23 | (10) |
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Events, options and preferences |
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23 | (1) |
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23 | (5) |
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28 | (5) |
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Beliefs and probabilities |
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33 | (16) |
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Representation of beliefs |
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33 | (5) |
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Revision of beliefs and Bayes' theorem |
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38 | (7) |
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45 | (2) |
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Sequential revision of beliefs |
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47 | (2) |
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49 | (7) |
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Bounded sets of consequences |
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49 | (1) |
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Bounded decision problems |
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50 | (4) |
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General decision problems |
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54 | (2) |
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Sequential decision problems |
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56 | (11) |
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Complex decision problems |
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56 | (3) |
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59 | (4) |
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63 | (4) |
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Inference and information |
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67 | (14) |
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Reporting beliefs as a decision problem |
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67 | (2) |
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The utility of a probability distribution |
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69 | (6) |
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Approximation and discrepancy |
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75 | (2) |
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77 | (4) |
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Discussion and further references |
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81 | (24) |
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81 | (2) |
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Quantitative coherence theories |
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83 | (2) |
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85 | (7) |
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92 | (13) |
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105 | (60) |
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Generalised representation of beliefs |
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105 | (4) |
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105 | (1) |
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106 | (3) |
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Review of probability theory |
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109 | (32) |
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Random quantities and distributions |
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109 | (5) |
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Some particular univariate distributions |
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114 | (11) |
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Convergence and limit theorems |
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125 | (2) |
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Random vectors, Bayes' theorem |
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127 | (6) |
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Some particular multivariate distributions |
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133 | (8) |
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Generalised options and utilities |
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141 | (9) |
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Motivation and preliminaries |
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141 | (4) |
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145 | (2) |
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147 | (3) |
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Generalised information measures |
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150 | (10) |
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The general problem of reporting beliefs |
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150 | (1) |
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The utility of a general probability distribution |
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151 | (3) |
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Generalised approximation and discrepancy |
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154 | (3) |
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157 | (3) |
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Discussion and further references |
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160 | (5) |
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160 | (1) |
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161 | (4) |
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165 | (76) |
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165 | (2) |
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165 | (2) |
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Exchangeability and related concepts |
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167 | (5) |
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Dependence and independence |
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167 | (1) |
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Exchangeability and partial exchangeability |
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168 | (4) |
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Models via exchangeability |
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172 | (9) |
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The Bernoulli and binomial models |
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172 | (4) |
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176 | (1) |
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177 | (4) |
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181 | (9) |
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181 | (4) |
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The multivariate normal model |
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185 | (2) |
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187 | (2) |
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189 | (1) |
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Models via sufficient statistics |
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190 | (19) |
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190 | (1) |
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Predictive sufficiency and parametric sufficiency |
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191 | (6) |
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Sufficiency and the exponential family |
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197 | (10) |
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Information measures and the exponential family |
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207 | (2) |
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Models via partial exchangeability |
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209 | (17) |
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Models for extended data structures |
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209 | (2) |
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211 | (6) |
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217 | (2) |
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219 | (3) |
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222 | (4) |
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226 | (9) |
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Finite and infinite exchangeability |
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226 | (2) |
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Parametric and nonparametric models |
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228 | (1) |
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229 | (4) |
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233 | (1) |
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234 | (1) |
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Discussion and further references |
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235 | (6) |
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235 | (1) |
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Subjectivity and objectivity |
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236 | (1) |
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237 | (4) |
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241 | (136) |
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241 | (24) |
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Observables, beliefs and models |
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241 | (1) |
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The role of Bayes' theorem |
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242 | (1) |
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Predictive and parametric inference |
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243 | (4) |
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Sufficiency, ancillarity and stopping rules |
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247 | (8) |
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Decisions and inference summaries |
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255 | (8) |
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263 | (2) |
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265 | (20) |
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265 | (4) |
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Canonical conjugate analysis |
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269 | (10) |
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Approximations with conjugate families |
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279 | (6) |
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285 | (13) |
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286 | (1) |
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287 | (8) |
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Asymptotics under transformations |
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295 | (3) |
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298 | (41) |
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299 | (3) |
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One-dimensional reference distributions |
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302 | (14) |
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Restricted reference distributions |
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316 | (4) |
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320 | (13) |
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333 | (6) |
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339 | (17) |
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340 | (6) |
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346 | (2) |
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348 | (2) |
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Sampling-importance-resampling |
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350 | (3) |
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353 | (3) |
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Discussion and further references |
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356 | (21) |
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356 | (1) |
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357 | (10) |
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367 | (4) |
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Hierarchical and empirical Bayes |
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371 | (2) |
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Further methodological developments |
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373 | (1) |
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374 | (3) |
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377 | (50) |
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377 | (32) |
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377 | (6) |
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Perspectives on model comparison |
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383 | (3) |
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Model comparison as a decision problem |
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386 | (3) |
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Zero-one utilities and Bayes factors |
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389 | (6) |
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395 | (8) |
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Approximation by cross-validation |
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403 | (4) |
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407 | (2) |
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409 | (8) |
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Model rejection through model comparison |
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409 | (3) |
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Discrepancy measures for model rejection |
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412 | (1) |
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413 | (2) |
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415 | (2) |
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Discussion and further references |
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417 | (10) |
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417 | (1) |
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Modelling and remodelling |
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418 | (1) |
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418 | (9) |
A. SUMMARY OF BASIC FORMULAE |
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427 | (16) |
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Probability distributions |
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427 | (9) |
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436 | (7) |
B. NON-BAYESIAN THEORIES |
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443 | (46) |
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443 | (2) |
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445 | (15) |
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Classical decision theory |
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445 | (4) |
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449 | (5) |
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454 | (2) |
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Fiducial and related theories |
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456 | (4) |
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Stylised inference problems |
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460 | (18) |
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460 | (5) |
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465 | (4) |
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469 | (6) |
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475 | (3) |
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478 | (11) |
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Conditional and unconditional inference |
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478 | (1) |
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Nuisance parameters and marginalisation |
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479 | (3) |
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482 | (3) |
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485 | (1) |
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486 | (3) |
References |
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489 | (66) |
Subject Index |
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555 | (18) |
Author Index |
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573 | |