TY - JOUR
T1 - The multiset sampler
AU - Leman, Scotland C.
AU - Chen, Yuguo
AU - Lavine, Michael
N1 - Funding Information:
Scotland C. Leman is Assistant Professor of Statistics, Department of Statistics, Virginia Polytechnic Institute, Blacksburg, VA 24061 (E-mail: [email protected]). Yuguo Chen is Associate Professor of Statistics, Department of Statistics, University of Illinois at Urbana–Champaign, Champaign, IL 61820 (E-mail: [email protected]). Michael Lavine is Professor of Mathematics and Statistics, Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01002 (E-mail: [email protected]). This work was supported by National Science Foundation grants DMS-0503981 and DMS-0806175. The authors thank the editor, associate editor, and three anonymous referees for their careful reading and helpful suggestions.
PY - 2009
Y1 - 2009
N2 - We introduce the multiset sampler (MSS), a new Metropolis-Hastings algorithm for drawing samples from a posterior distribution. The MSS is designed to be effective when the posterior has the feature that the parameters can be divided into two sets, X, the parameters of interest and Y, the nuisance parameters.We contemplate a sampler that iterates between X moves and Y moves.We consider the case where either (a) Y is discrete and lives on a finite set or (b) Y is continuous and lives on a bounded set. After presenting some background, we define a multiset and show how to construct a distribution on one. The construction may seem artificial and pointless at first, but several small examples illustrate its value. Finally, we demonstrate the MSS in several realistic examples and compare it with alternatives.
AB - We introduce the multiset sampler (MSS), a new Metropolis-Hastings algorithm for drawing samples from a posterior distribution. The MSS is designed to be effective when the posterior has the feature that the parameters can be divided into two sets, X, the parameters of interest and Y, the nuisance parameters.We contemplate a sampler that iterates between X moves and Y moves.We consider the case where either (a) Y is discrete and lives on a finite set or (b) Y is continuous and lives on a bounded set. After presenting some background, we define a multiset and show how to construct a distribution on one. The construction may seem artificial and pointless at first, but several small examples illustrate its value. Finally, we demonstrate the MSS in several realistic examples and compare it with alternatives.
KW - Data augmentation
KW - Gibbs sampler
KW - Markov chain Monte Carlo
KW - Metropolis-hastings algorithm
KW - Multimodal
KW - Proposal distribution
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U2 - 10.1198/jasa.2009.tm08047
DO - 10.1198/jasa.2009.tm08047
M3 - Article
AN - SCOPUS:70349766098
SN - 0162-1459
VL - 104
SP - 1029
EP - 1041
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 487
ER -