### Abstract

Original language | English |
---|---|

Journal | Biometrika |

Volume | 93 |

Issue number | 2 |

Pages (from-to) | 451-458 |

Number of pages | 8 |

ISSN | 0006-3444 |

Publication status | Published - 2006 |

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### Cite this

*Biometrika*,

*93*(2), 451-458.

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*Biometrika*, vol. 93, no. 2, pp. 451-458.

**An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants.** / Møller, Jesper; Pettitt, A. N.; Reeves, R.; Berthelsen, Kasper Klitgaard.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants

AU - Møller, Jesper

AU - Pettitt, A. N.

AU - Reeves, R.

AU - Berthelsen, Kasper Klitgaard

PY - 2006

Y1 - 2006

N2 - Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so that the normalising constant cancels from the Metropolis–Hastings ratio. The method is illustrated by producing posterior samples for parameters of the Ising model given a particular lattice realisation.

AB - Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so that the normalising constant cancels from the Metropolis–Hastings ratio. The method is illustrated by producing posterior samples for parameters of the Ising model given a particular lattice realisation.

M3 - Journal article

VL - 93

SP - 451

EP - 458

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 2

ER -