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392 BibliographyProulx, S. R. and Adler, F. R. (2010). e standard of neutrality: still flapping in the breeze? Journalof Evolutionary Biology, 23:1339–1350.Rao, C. R. (1997). Statistics and Truth: Putting Chance To Work. World Scientific Publishing.Rice, K. (2010). A decision-theoretic formulation of Fisher’s approach to testing. e AmericanStatistician, 64(4):345–349.Riley, S. J., DeGloria, S. D., and Elliot, R. (1999). A terrain ruggedness index that quantifies topographicheterogeneity. Intermountain Journal of Sciences, 5:23–27.Robert, C. P. (2007). e Bayesian Choice: from decision-theoretic foundations to computational implementation.Springer Texts in Statistics. Springer, 2nd edition.Rommel, S. A., Costidis, A. M., Pitchford, T. D., Lightsey, J. D., Snyder, R. H., and Haubold,E. M. (2007). Forensic methods for characterizing watercra from watercra-induced woundson the Florida manatee (TRICHECHUS MANATUS LATIROSTRIS). Marine Mammal Science,23(1):110–132.Rubin, D. B. (2005). Causal inference using potential outcomes: Design, modeling, decisions. Journalof the American Statistical Association, 100(469):322–331.Savage, L. J. (1962). e Foundations of Statistical Inference. Methuen.Schwarz, G. E. (1978). Estimating the dimension of a model. Annals of Statistics, 6:461–464.Shannon, C. E. (1948). A mathematical theory of communication. e Bell System Technical Journal,27:379–423.Shannon, C. E. (1956). e bandwagon. IRE Transactions: on Information eory, 2:3.Silk, J. B., Brosnan, S. F., Vonk, J., Henrich, J., Povinelli, D. J., Richardson, A. S., Lambeth, S. P., Mascaro,J., and Schapiro, S. J. (2005). Chimpanzees are indifferent to the welfare of unrelated groupmembers. Nature, 437:1357–1359.Silver, N. (2012). e Signal and the Noise: Why So Many Predictions Fail—but Some Don’t. PenguinPress, New York.Simpson, E. H. (1951). e interpretation of interaction in contingency tables. Journal of the RoyalStatistical Society, Series B, 13:238–241.Sober, E. (2008). Evidence and Evolution: e logic behind the science. Cambridge University Press,Cambridge.Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and va der Linde, A. (2002). Bayesian measures of modelcomplexity and fit. Journal of the Royal Statistical Society B, 64:583–639.Stein, C. (1955). Inadmissibility of the usual estimator for the mean of a multivatiate normal distribution.In Proceedings of the ird Berkeley Symposium of Mathematical Statistics and Probability,volume 1, pages 197–206, Berkeley. University of California Press.Stigler, S. M. (1981). Gauss and the invention of least squares. e Annals of Statistics, 9(3):465–474.Stone, M. (1977). An asymptotic equivalence of choice of model by cross-validation and Akaike’scriterion. Journal of the Royal Statistical Society B, 39(1):44–47.eobald, D. L. (2010). A formal test of the theory of universal common ancestry. Nature, 465:219–222.Van Horn, K. S. (2003). Constructing a logic of plausible inference: a guide to Cox’s theorem. InternationalJournal of Approximate Reasoning, 34:3–24.Venn, J. (1876). e Logic of Chance. Macmillan and co, New York, 2nd edition.Wald, A. (1939). Contributions to the theory of statistical estimation and testing hypotheses. Annalsof Mathematical Statistics, 10(4):299–326.Wald, A. (1943). A method of estimating plane vulnerability based on damage of survivors. Technicalreport, Statistical Research Group, Columbia University.Wald, A. (1950). Statistical Decision Functions. J. Wiley, New York.Watanabe, S. (2010). Asymptotic equivalence of bayes cross validation and widely applicable informationcriterion in singular learning theory. Journal of Machine Learning Research, 11:3571–3594.Wittgenstein, L. (1953). Philosophical Investigations.
Bibliography 393Wolpert, D. and Macready, W. (1997). No free lunch theorems for optimization. IEEE Transactionson Evolutionary Computation, page 67.
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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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Page 353 and 354: 14 Multilevel Models II: Slopes14.1
Page 355 and 356: 14.1. EVERYTHING CAN VARY AND PROBA
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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 395 and 396: IndexAkaike (1973), 380, 383Akaike
Page 397: INDEX 397non-identifiability, 153Oc
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