AIS_MarLik.tex

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\begin{document}

\begin{frontmatter}
\title{Adaptive Annealed Importance Sampling for Multi-Modal Posterior Exploration
  and Model Selection  with Application to Extrasolar Planet
  Detection\protect\thanksref{T1}}
\runtitle{AAIS for Exoplanet Detection}
\thankstext{T1}{This work has been supported by Statistical and
  Applied Mathematical Sciences Institute through National Science
  Foundation grant DMS--042240.  Any opinions, findings, conclusions
  or recommendations expressed in this material are those of the
  authors and do not necessarily reflect the views of the NSF.}

% Bin + Alphabetical authorship for now
\begin{aug}
\author{\fnms{Bin} \snm{Liu}\thanksref{t2,m4} \ead[label=e1]{bliu.81@gmail.com}},
\author{\fnms{Jim} \snm{Berger}\thanksref{t2,m1}\ead[label=e4]{berger@stat.duke.edu}},
\author{\fnms{Merlise A.}
  \snm{Clyde}\thanksref{t2,m1}\ead[label=e2]{clyde@stat.duke.edu}},
\author{\fnms{James L.}  \snm{Crooks}\thanksref{t2,m3}\ead[label=e5]{tba}},
\and
\author{\fnms{Tom} \snm{Loredo}\thanksref{t3,m2}\ead[label=e3]{loredo@cornell.edu}}


\thankstext{t2}{Partially supported by National Science Foundation Grant AST--0507481}
\thankstext{t3}{Partially supported by National Science Foundation
  Grant AST--XXXXX}
\runauthor{Liu et al.}

\affiliation{Kuang-Chi Institute of Advanced
  Technology\thanksmark{m4}, 
  Duke University\thanksmark{m1},
  U.S.~Environmental Protection
  Agency\thanksmark{m3} and Cornell University\thanksmark{m2}}

\address{Department of Electrical and Computer Engineering \\
  Duke University \\
Durham, NC 27705 USA \\
  \printead{e1}}

\address{Department of Statistical Science \\
  Duke University \\
Durham, NC 27705 USA \\
 \printead{e2}\\
\phantom{E-mail:\ }\printead*{e4}}

\address{Department of Astronomy \\Cornell University \\
Ithaca, NY  USA \\
 \printead{e3}}
\end{aug}


\begin{abstract}
  The search for extrasolar planets presents several statistical
  challenges including model selection and inference within models
  that involve multi-modal posterior distributions.  To address these
  problems, we propose an adaptive annealed importance sampling
  algorithm (AAIS) which facilitates simulation from multi-modal joint
  posterior distribution and provides an effective and
  easy-to-implement method for estimating marginal likelihoods that
  are required for Bayesian model comparison.  Using a sequential
  importance sampling framework, we construct mixtures of Student $t$
  distributions to approximate a sequence of ``annealed''
  distributions that gradually approximates the target posterior
  density.  Borrowing ideas of birth/death and split/merge steps from
  reversible jump Markov-chain Monte Carlo, we propose an adaptive
  online method to increase/decrease the number of  mixture
  components guided by the effective sample size of the importance sample.
  We use simulation studies and several
  examples from exo-planet searches to demonstrate the greater
  efficiency of the method.
  The combination of annealing and heavier
  tails of the Student $t$ components in the mixture greatly
  facilitate capturing the ``spikey'' posterior densities present in
  the highly nonlinear models in the exo-planet problem, while importance sampling permits
  straightforward estimation of marginal likelihoods and posterior
  model probabilities to address the uncertainty of whether planets
  are indeed present.   We illustrate the methodology with several
  star systems and a simulation study.
\end{abstract}

\begin{keyword}
\kwd{Bayes Factor}
\kwd{Model Selection}
\kwd{Nonlinear Regression}
\end{keyword}

\end{frontmatter}


\include{intro}

\include{model}

\include{IS}

\include{sim}

\include{exo-examp}

\include{disc}


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