statisticalrethinkin..

ENDNOTES 387[217]96. From Nunn and Puga 2011. [218]97. Riley et al. 1999 [218]Chapter 898. Metropolis et al. (1953). e algorithm has been named aer the first author of this paper, however it’s notclear how each co-author participated in discovery and implementation of the algorithm. Among the other authorswere Edward Teller, most famous as the father of the hydrogen bomb, and Marshall Rosenbluth, a renownphysicist in his own right, as well as their wives Augusta and Arianna (respectively), who did much of the computerprogramming. Nicholas Metropolis lead the research group. ere work was in turn based on earlier workwith Stanislaw Ulam, Metropolis and Ulam (1949). [247]99. Hastings (1970) [247]100. Geman and Geman (1984) is the original. I recommend Casella and George (1992) as well. Note that Gibbssampling is named aer physicist and mathematician J. W. Gibbs, one of the founders of statistical physics. However,Gibbs died in the year 1903, long before even the Metropolis algorithm was invented. Instead the strategyis named aer Gibbs, both to honor him and in light of the algorithms connections to statistical physics. [247]101. Chapter 16 of Jaynes (2003). [250]102. Cite Gelman chapter in Handbook of MCMC. [258]Chapter 9Chapter 9103. Does Jaynes have a clear proof of this? Could cite Frank paper, but I think he just cites Jaynes. [274]104. Common intro text is Singer and Willett 2003. [275]Chapter 10105. No one knows precisely why this function has this name, but there are plausible guesses. e term appearsto originate with Verhulst’s 1838 paper on population growth, in which he called it logistique. At the time, theterm logarithm and logistic were sometimes used interchangeably. So perhaps Verhulst was stating nothingmore than this is a logarithmic curve. e term logit is a play on the term probit, which is itself an shortening ofprobability unit. Probit usually refers to the Gaussian quantile distribution. [279]106. Silk et al. (2005). [279]107. Kline and Boyd 2010. [294]Chapter 11108. Because these models are built on cumulative densities, rather than regular densities, they are sometimescalled cumulative link models. Remember, the “link” in a GLM refers to the function that connects the additivemodel to the outcome. So a “cumulative” link uses a cumulative density function, of log-odds in this case, to doso. [304]109. Cushman et al. 2006. [307]110. ere are notable exceptions. Find a good introductory citation. [318]111. R calls A shape1 and B shape2. See ?dbeta, for example. [320]112. e built-in R function dnbinom provides the same likelihoods, but under a different guise. Using dgampoisis pedagogically useful, but functionally equivalent to dnbinom. [328]