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396 INDEXRiley et al. (1999), 381, 386Robert (2007), 378, 380, 386Rommel et al. (2007), 380, 386Rubin (2005), 379, 386Savage (1962), 377, 386Schwarz (1978), 380, 386Shannon (1948), 379, 386Shannon (1956), 379, 386Silk et al. (2005), 381, 386Silver (2012), 377, 386Simpson (1951), 379, 386Sober (2008), 376, 386Spiegelhalter et al. (2002), 380, 386Stein (1955), 382, 386Stigler (1981), 379, 386Stone (1977), 380, 386eobald (2010), 377, 386Van Horn (2003), 377, 386Venn (1876), 376, 386Wald (1939), 380, 386Wald (1943), 380, 386Wald (1950), 380, 386Watanabe (2010), 380, 386Wittgenstein (1953), 375, 386Wolpert and Macready (1997), 377, 386AIC, 184Akaike weight, 199Akaike information criterion, 184barplot, 202Bayes factor, 190Bayes’ theorem, 38Bayesian information criterion, 169, 190Bayesian updating, 32beta distribution, 312bias-variance tradeoff, see also overfitting, 176burn-in, 252categorical variable, 154categorical variables, 124centering, 103, 105, 224, 225complete pooling, 337complete-case, 359Conditioning, 209confidence interval, 58consistent, 189credible interval, 58cross-validation, 184cumulative log-odds, 297cumulative logistic, 298data compression, 172data dredging, 205design formula, 161deviance, 168, 182deviance information criterion, 186, 190DIC, 186divergence, see also Kullback-Leibler divergence,180dotchart, 202dummy data, 66dummy variable, 155effective number of parameters, 191exchangeable, 88exponential family, 19, 81factor analysis, 153frequentist, 23gamma-Poisson, 320Gibbs sampling, 241Hamiltonian Monte Carlo, 244highest posterior density interval, 61imputation, 359information criteria, 27, 168, 184information entropy, 179information theory, 27, 82, 178Kullback-Leibler divergence, 180interaction, 210interactions, 124large world, 29likelihood, 35linear model, 98Linear regression, 77log-odds, 297logistic, 273logit, 273logit link, 273loss function, 63Markov chain Monte Carlo, 47maxent, 180maximum a posteriori, 44maximum entropy, 19, 82, 180maximum likelihood estimate, 46MCAR, 359Metropolis algorithm, 241Minimum Description Length, 174Model averaging, 196Model checking, 68Model comparison, 196model selection, 196modus tollens, 19multicollinearity, 145multilevel model, 25multiple comparison, 332multiple membership, 343multivariate regression, 123no pooling, 338
INDEX 397non-identifiability, 153Ockham’s razor, 167OLS, 160ordinary least squares, 160Overfitting, 170overfitting, 15, 27, 145, 168, 169pairs, 151parameters, 36partial pooling, 338penalized likelihood, 37percentile intervals, 59point estimate, 62polynomial regression, 115pooling, 336posterior distribution, 38posterior predictive distribution, 69prequential, 186principle components, 153prior, 36pseudoreplication, 332quadratic approximation, 43random slopes, 349regularizing, 37, 194regularizing prior, 168, 335ridge regression, 195sampling distribution, 23shrinkage, 335, 356Simpson’s paradox, 123small world, 29Stan, 237standard error, 46standardize, 116stargazing, 169stochastic, 84subjective Bayesian, 37trace plot, 250underfitting, 168, see also overfitting, 174variance-covariance, 96varying effects, 333varying slopes, 349WAIC, 186Watanabe-Akaike information criterion, 186weakly informative, 37widely applicable information criterion, 186
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Statistical RethinkingA BAYESIAN CO
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4 CONTENTS5.5. Ordinary least squar
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PrefaceMasons, when they start upon
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HOW TO USE THIS BOOK 9least a minor
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HOW TO USE THIS BOOK 11than initial
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1 e Golem of PragueIn the 16th cent
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16 1. THE GOLEM OF PRAGUEconverses
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1.2. WRECKING PRAGUE 19model P 1B ,
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1.2. WRECKING PRAGUE 21e dominant r
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1.3. THREE TOOLS FOR GOLEM ENGINEER
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2 Small Worlds and Large WorldsWhen
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2.1. PROBABILITY IS JUST COUNTING 3
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2.2. COLOMBO’S FIRST BAYESIAN MOD
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W L W W W L W L W2.2. COLOMBO’S F
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2.3. COMPONENTS OF THE MODEL 41not
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2.3. COMPONENTS OF THE MODEL 43You
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2.3. COMPONENTS OF THE MODEL 45e ma
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2.4. MAKING THE MODEL GO 47other pr
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2.4. MAKING THE MODEL GO 495 points
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2.4. MAKING THE MODEL GO 51just the
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2.4. MAKING THE MODEL GO 53between
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2.6. PRACTICE 55Medium.2.6.5. m1. R
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2.6. PRACTICE 57implied by the equa
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3 Sampling the ImaginaryLots of boo
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3. SAMPLING THE IMAGINARY 61a probl
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3.2. SAMPLING TO SUMMARIZE 63plot(
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3.2. SAMPLING TO SUMMARIZE 65Densit
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3.2. SAMPLING TO SUMMARIZE 67In con
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3.2. SAMPLING TO SUMMARIZE 69Densit
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3.3. SAMPLING TO SIMULATE PREDICTIO
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3.5. PRACTICE 793.5. PracticeEasy.
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3.5. PRACTICE 813.5.17. Predict sec
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84 4. LINEAR MODELSFIGURE 4.1. e Pt
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86 4. LINEAR MODELSexperiment with
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88 4. LINEAR MODELS4.1.4.2. Epistem
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90 4. LINEAR MODELSe approach above
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92 4. LINEAR MODELS'data.frame': 54
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94 4. LINEAR MODELSe point isn’t
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96 4. LINEAR MODELShave the samples
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98 4. LINEAR MODELSere’s no troub
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100 4. LINEAR MODELS)Note the comma
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102 4. LINEAR MODELSpreviously obse
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104 4. LINEAR MODELS4.4. Adding a p
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106 4. LINEAR MODELS(1) What is the
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108 4. LINEAR MODELSdata(Howell1)d
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110 4. LINEAR MODELSRethinking: Wha
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112 4. LINEAR MODELSheight140 150 1
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116 4. LINEAR MODELSYou end up with
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118 4. LINEAR MODELS(1) Use link to
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122 4. LINEAR MODELSRethinking: Lin
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126 4. LINEAR MODELS4.7.1. e1. In t
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5 Multivariate Linear ModelsOne of
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5.1. SPURIOUS ASSOCIATION 131Divorc
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5.1. SPURIOUS ASSOCIATION 133But me
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5.1. SPURIOUS ASSOCIATION 135abmbas
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5.1. SPURIOUS ASSOCIATION 137this i
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5.1. SPURIOUS ASSOCIATION 139slower
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5.1. SPURIOUS ASSOCIATION 141Median
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5.1. SPURIOUS ASSOCIATION 143(a)(b)
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5.2. MASKED RELATIONSHIP 145N
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5.2. MASKED RELATIONSHIP 147a ~ dno
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5.2. MASKED RELATIONSHIP 149dcc$log
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5.3. WHEN ADDING VARIABLES HURTS 15
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5.4. CATEGORICAL VARIABLES 161$ wei
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5.4. CATEGORICAL VARIABLES 1635.4.2
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5.4. CATEGORICAL VARIABLES 165# sam
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168 5. MULTIVARIATE LINEAR MODELS5.
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170 5. MULTIVARIATE LINEAR MODELS5.
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6 Model Selection, Comparison, and
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6.1. THE PROBLEM WITH PARAMETERS 17
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6.2. INFORMATION THEORY AND MODEL P
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6.3. AKAIKE INFORMATION CRITERION 1
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6.4. DEVIANCE INFORMATION CRITERION
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6.5. USING AIC 203helps guard again
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6.5. USING AIC 205compare( m6.11 ,
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6.5. USING AIC 207e attitude this b
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6.5. USING AIC 209kcal.per.g0.5 0.7
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6.7. PRACTICE 211Consider by analog
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6.7. PRACTICE 2136.7.3. e deviance
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216 7. INTERACTIONSFIGURE 7.1. TOP:
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218 7. INTERACTIONSlog(rgdppc_2000)
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220 7. INTERACTIONSird, we may want
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222 7. INTERACTIONSlog GDP year 200
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226 7. INTERACTIONSInteraction mode
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228 7. INTERACTIONSthis model and t
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232 7. INTERACTIONSe main effect li
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234 7. INTERACTIONSbs -38.91 34.94s
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236 7. INTERACTIONSe primary reason
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238 7. INTERACTIONSNow for the plot
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240 7. INTERACTIONS7.4. Higher-orde
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8 Markov Chain Monte Carlo Estimati
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8.1. GOOD KING MARKOV AND HIS ISLAN
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8.2. MARKOV CHAIN MONTE CARLO 247fo
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8.2. MARKOV CHAIN MONTE CARLO 249No
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8.3. EASY HMC: MAP2STAN 251We’re
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8.3. EASY HMC: MAP2STAN 253$ cont_a
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8.3. EASY HMC: MAP2STAN 255mcmcpair
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8.3. EASY HMC: MAP2STAN 257FIGURE 8
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8.4. CARE AND FEEDING OF YOUR MARKO
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8.6. PRACTICE 265And since the chai
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268 9. BIG ENTROPY AND THE GENERALI
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270 9. BIG ENTROPY AND THE GENERALI
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10 Distance and DurationA curious t
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10.2. GAMMA 275can be quite complic
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278 11. COUNTING AND CLASSIFICATION
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304 12. MONSTERS AND MIXTUREShere?
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306 12. MONSTERS AND MIXTURESdensit
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308 12. MONSTERS AND MIXTURESfootbr
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310 12. MONSTERS AND MIXTURESWhy di
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312 12. MONSTERS AND MIXTURESm11.3
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314 12. MONSTERS AND MIXTURESResult
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316 12. MONSTERS AND MIXTURESanswer
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318 12. MONSTERS AND MIXTURESDensit
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320 12. MONSTERS AND MIXTURESBut we
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322 12. MONSTERS AND MIXTURESdisper
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324 12. MONSTERS AND MIXTURESe resu
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326 12. MONSTERS AND MIXTURESDensit
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328 12. MONSTERS AND MIXTURESR code
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330 12. MONSTERS AND MIXTURESPoisso
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332 12. MONSTERS AND MIXTURESthe ga
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334 12. MONSTERS AND MIXTURESdata=d
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336 12. MONSTERS AND MIXTURESma2 ~
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338 13. MULTILEVEL MODELSrepeat obs
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340 13. MULTILEVEL MODELSSo how do
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342 13. MULTILEVEL MODELSprobabilit
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344 13. MULTILEVEL MODELSa conseque
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Page 360 and 361: 360 15. MISSING DATA AND OTHER OPPO
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Page 382 and 383: 382 ENDNOTES12. For an autopsy of t
Page 384 and 385: 384 ENDNOTES45. Fisher (1925), in C
Page 386 and 387: 386 ENDNOTES77. See two famous edit
Page 388 and 389: 388 ENDNOTES113. Hurlbert (1984) is
Page 390 and 391: 390 BibliographyFrank, S. A. (2011)
Page 392 and 393: 392 BibliographyProulx, S. R. and A
Page 395: IndexAkaike (1973), 380, 383Akaike
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