[R] Hybrid Monte Carlo algorithm (MCMC)

[Christophe Pouzat]

Hi,

A clear introduction to Hybrid MC can be found in Neal (1993) and an 
example of its use in Chen et al (2001). A good alternative to it when 
you have slowly relaxing chains is the Replica Exchange / Parallel 
Tempering Method, which was introduced by Geyer (1991) and Hukushima and 
Nemoto (1996). Its well discribed in Iba (2001).

HTH,

Christophe.

PS: The references:

@TechReport{Neal_1993,
  Author = {Neal, Radford M},
  Title= {Probabilistic {I}nference {U}sing {M}arkov {C}hain
                   {M}onte {C}arlo {M}ethods},
  Institution= {Department of Computer Science. University of Toronto},
  Number = {CRG-TR-91-1},
  url        = {http://www.cs.toronto.edu/~radford/papers-online.html},
  year       = 1993
}

@InProceedings{ChenEtAl_2001,
  Author = {Chen, Lingyu and Qin, Zhaohui and Liu, Jun S.},
  Title = {Exploring hybrid {M}onte {C}arlo in {B}ayesian
                   computation},
  BookTitle = {I{SBA} 2000, {P}roceedings},
  url = {http://www.people.fas.harvard.edu/~junliu/TechRept/01.html},
  year = 2001
}

@InProceedings{Geyer_1991b,
  Author = {Geyer, C. J.},
  Title = {Markov chain {M}onte {C}arlo maximum likelihood},
  BookTitle = {Computing {S}cience and {S}tatistics: {P}roc. 23rd
                   {S}ymp. {I}nterface},
  Pages = {156-163},
  year = 1991
}

@Article{HukushimaNemoto_1996,
  Author = {Hukushima, K. and Nemoto, K.},
  Title = {Exchange {M}onte {C}arlo and {A}pplication to {S}pin
                   {G}lass {S}imulations},
  Journal = {J Phys Soc Japan},
  Volume = {65},
  Pages = {1604-1608},
  eprint = {cond-mat/9512035},
  year = 1996
}

@Article{Iba_2001,
  Author = "Iba, Yukito",
  Title = "Extended Ensemble Monte Carlo",
  Journal = "Int. J. Mod. Phys.",
  Volume = "C12",
  Pages = "623-656",
  eprint = "cond-mat/0012323",
  url = {http://fr.arxiv.org/abs/cond-mat/0012323},
  year = 2001
}


Naji wrote:

>Hi all,
>
>I'm trying to estimate a nested model (purchase decision, cloglog formula, &
>quantity bought given a purchase, truncated Poisson). Some of the parameters
>are mixed (6) and 4 are fixed for all the respondent.
>The simulated ML (500 simulations) method forwards highly correlated
>estimates.
>After some research, Hybrid Monte Carlo seems to be a good alternative to
>estimate the model. I found neither article nor reference in order to
>establish some code.
>
>I would appreciate a good reference describing the algorithm in detail or
>some code. Other ideas performing the model estimation are welcome.
>
>
>I have established the log-likelihood function and its gradient.
>Best regards
>Naji
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
>
>  
>


-- 
A Master Carpenter has many tools and is expert with most of them.If you
only know how to use a hammer, every problem starts to look like a nail.
Stay away from that trap.
Richard B Johnson.
--

Christophe Pouzat
Laboratoire de Physiologie Cerebrale
CNRS UMR 8118
UFR biomedicale de l'Universite Paris V
45, rue des Saints Peres
75006 PARIS
France

tel: +33 (0)1 42 86 38 28
fax: +33 (0)1 42 86 38 30
web: www.biomedicale.univ-paris5.fr/physcerv/C_Pouzat.html