\relax \citation{ElsnerBossak2001} \citation{Epstein1985} \@writefile{toc}{\contentsline {chapter}{\numberline {12}Bayesian Models}{332}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \newlabel{chap:bayesianmodels}{{12}{332}} \@writefile{toc}{\contentsline {section}{\numberline {12.1}Long-Range Outlook}{332}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.1.1}Poisson-gamma conjugate}{332}} \citation{TibshiraniLeisch2007} \@writefile{toc}{\contentsline {subsection}{\numberline {12.1.2}Prior parameters}{333}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.1.3}Posterior density}{335}} \@writefile{lof}{\contentsline {figure}{\numberline {12.1}{\ignorespaces Gamma densities for the landfall rate.}}{336}} \newlabel{fig:prior:like:post:gamma}{{12.1}{336}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.1.4}Predictive distribution}{336}} \@writefile{lof}{\contentsline {figure}{\numberline {12.2}{\ignorespaces Predictive probabilities. (a) 10 years and (b) 10, 20, and 30 years.}}{337}} \newlabel{fig:posteriorprobs}{{12.2}{337}} \@writefile{toc}{\contentsline {section}{\numberline {12.2}Seasonal Model}{338}} \citation{Plummer2011} \@writefile{lof}{\contentsline {figure}{\numberline {12.3}{\ignorespaces Posterior samples for the (a) SST ($\beta _1$) and (b) SOI ($\beta _2$) parameters.}}{340}} \newlabel{fig:sstsoihist}{{12.3}{340}} \@writefile{lof}{\contentsline {figure}{\numberline {12.4}{\ignorespaces Modeled annual hurricane rates.}}{341}} \newlabel{fig:annualrates}{{12.4}{341}} \citation{RafteryEtAl2005} \citation{JaggerElsner2010} \@writefile{lof}{\contentsline {figure}{\numberline {12.5}{\ignorespaces Extra variation in hurricane rates.}}{342}} \newlabel{fig:extravariation}{{12.5}{342}} \@writefile{toc}{\contentsline {section}{\numberline {12.3}Consensus Model}{342}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.3.1}Bayesian model averaging}{343}} \citation{HoetingEtAl1999} \citation{MadiganRaftery1994} \citation{RafteryZheng2003} \citation{HoetingEtAl1999} \citation{Raftery1996} \citation{RafteryZheng2003} \@writefile{toc}{\contentsline {subsection}{\numberline {12.3.2}Data plots}{345}} \citation{RafteryEtAl2009} \@writefile{lof}{\contentsline {figure}{\numberline {12.6}{\ignorespaces Covariates by month. (a) SST, (b) NAO, (c) SOI, and (d) sunspot number.}}{346}} \newlabel{fig:covariatesplot}{{12.6}{346}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.3.3}Model selection}{346}} \@writefile{lot}{\contentsline {table}{\numberline {12.1}{\ignorespaces Selected models from a BMA procedure.}}{348}} \newlabel{tab:selectedmodels}{{12.1}{348}} \@writefile{lof}{\contentsline {figure}{\numberline {12.7}{\ignorespaces Covariates by model number.}}{349}} \newlabel{fig:imageplotmodels}{{12.7}{349}} \citation{ElsnerJagger2008} \citation{ElsnerEtAl2010} \citation{Kodera2002} \citation{OgiEtAl2003} \@writefile{lof}{\contentsline {figure}{\numberline {12.8}{\ignorespaces Covariates by model number. (a) Actual and (b--d) permuted series.}}{351}} \newlabel{fig:bmarandom}{{12.8}{351}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.3.4}Consensus hindcasts}{351}} \citation{JaggerElsner2010} \citation{CressieWikle2011} \@writefile{lof}{\contentsline {figure}{\numberline {12.9}{\ignorespaces Forecasts from the consensus model.}}{353}} \newlabel{fig:compareyears}{{12.9}{353}} \@writefile{toc}{\contentsline {section}{\numberline {12.4}Space-Time Model}{353}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.4.1}Lattice data}{354}} \newlabel{subsec:spacetimelatticedata}{{12.4.1}{354}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.4.2}Local independent regressions}{359}} \@writefile{lof}{\contentsline {figure}{\numberline {12.10}{\ignorespaces Poisson regression coefficients of counts on local SST and SOI.}}{361}} \newlabel{fig:poissonregressions}{{12.10}{361}} \citation{Bivand2011} \@writefile{lof}{\contentsline {figure}{\numberline {12.11}{\ignorespaces Factor by which hurricane rates have changed per year.}}{362}} \newlabel{fig:annualratechange}{{12.11}{362}} \@writefile{lof}{\contentsline {figure}{\numberline {12.12}{\ignorespaces Model residuals for the 2005 hurricane season.}}{363}} \newlabel{fig:residuals2005}{{12.12}{363}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.4.3}Spatial autocorrelation}{363}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.4.4}BUGS data}{364}} \citation{BesagEtAl1991} \@writefile{toc}{\contentsline {subsection}{\numberline {12.4.5}MCMC output}{365}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.4.6}Convergence and mixing}{367}} \@writefile{lof}{\contentsline {figure}{\numberline {12.13}{\ignorespaces MCMC from a space-time model of cyclone counts in hexagon one.}}{368}} \newlabel{fig:traceplots1}{{12.13}{368}} \citation{GelmanRubin1992} \@writefile{lof}{\contentsline {figure}{\numberline {12.14}{\ignorespaces Autocorrelation of the SST coefficient in hexagon (a) one and (b) 60.}}{370}} \newlabel{fig:acfMCMCsamples}{{12.14}{370}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.4.7}Updates}{371}} \@writefile{lof}{\contentsline {figure}{\numberline {12.15}{\ignorespaces MCMC trace of the SST coefficients for hexagon (a) one and (b) 60.}}{372}} \newlabel{fig:traceplots2}{{12.15}{372}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.4.8}Relative risk maps}{372}} \@writefile{lof}{\contentsline {figure}{\numberline {12.16}{\ignorespaces Hurricane risk per change in (a) local SST and (b) SOI.}}{373}} \newlabel{fig:riskchange}{{12.16}{373}} \@setckpt{Chap12/Chapter12}{ \setcounter{page}{375} \setcounter{equation}{13} \setcounter{enumi}{2} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} \setcounter{footnote}{4} \setcounter{mpfootnote}{0} \setcounter{part}{2} \setcounter{chapter}{12} \setcounter{section}{4} \setcounter{subsection}{8} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} \setcounter{figure}{16} \setcounter{table}{1} \setcounter{LT@tables}{0} \setcounter{LT@chunks}{0} \setcounter{FancyVerbLine}{7} \setcounter{NAT@ctr}{0} \setcounter{density}{420} }