TY - GEN
AU - Walsh, B.
A2 -
T1 - Markov Chain Monte Carlo and Gibbs Sampling
JO -
PB -
AD -
PY - 2004/04
VL -
IS -
SP -
EP -
UR - http://nitro.biosci.arizona.edu/courses/EEB581-2004/handouts/Gibbs.pdf
M3 -
KW - carlo
KW - estimation
KW - gibbs
KW - lda
KW - markov
KW - monte
KW - parameter
KW - sampling
L1 -
N1 -
N1 -
AB - A major limitation towards more widespread implementation of Bayesian approaches is that obtaining the posterior distribution often requires the integration of high-dimensional functions. This can be computationally very difficult, but several approaches short of direct integration have been proposed (reviewed by Smith 1991, Evans and Swartz 1995, Tanner 1996). We focus here on Markov Chain Monte Carlo (MCMC) methods, which attempt to simulate direct draws from some complex distribution of interest. MCMC approaches are so-named because one uses the previous sample values to randomly generate the next sample value, generating a Markov chain (as the transition probabilities between sample values are only a function of the most recent sample value). The realization in the early 1990’s (Gelfand and Smith 1990) that one particular MCMC method, the Gibbs sampler, is very widely applicable to a broad class of Bayesian problems has sparked a major increase in the application of Bayesian analysis, and this interest is likely to continue expanding for sometime to come. MCMC methods have their roots in the Metropolis algorithm (Metropolis and Ulam 1949, Metropolis et al. 1953), an attempt by physicists to compute complex integrals by expressing them as expectations for some distribution and then estimate this expectation by drawing samples from that distribution. The Gibbs sampler (Geman and Geman 1984) has its origins in image processing. It is thus somewhat ironic that the powerful machinery ofMCMCmethods had essentially no impact on the field of statistics until rather recently. Excellent (and detailed) treatments of MCMC methods are found in Tanner (1996) and Chapter two of Draper (2000). Additional references are given in the particular sections below.
ER -
TY - JOUR
AU - Snijders, T.A.B.
T1 - Markov chain Monte Carlo estimation of exponential random graph models
JO - Journal of Social Structure
PY - 2002/
VL - 3
IS - 2
SP - 1
EP - 40
UR -
M3 -
KW - carlo
KW - estimation
KW - exponential
KW - generation
KW - graph
KW - model
KW - monte
KW - p*
KW - parameter
KW - sna
L1 -
SN -
N1 -
N1 -
AB -
ER -
TY - JOUR
AU - Anderson, C.J.
AU - Wasserman, S.
AU - Crouch, B.
T1 - A p* primer: Logit models for social networks
JO - Social Networks
PY - 1999/
VL - 21
IS - 1
SP - 37
EP - 66
UR -
M3 -
KW - carlo
KW - exponential
KW - generation
KW - graph
KW - model
KW - monte
KW - random
KW - simulation
KW - sna
L1 -
SN -
N1 -
N1 -
AB -
ER -
TY - BOOK
AU - Gilks, W.R.
AU - Spiegelhalter, DJ
A2 -
T1 - Markov chain Monte Carlo in practice
PB - Chapman & Hall/CRC
AD -
PY - 1996/
VL -
IS -
SP -
EP -
UR - http://scholar.google.de/scholar.bib?q=info:AN5YKWErdFAJ:scholar.google.com/&output=citation&hl=de&ct=citation&cd=0
M3 -
KW - carlo
KW - chain
KW - gibbs
KW - learning
KW - markov
KW - mchine
KW - ml
KW - monte
L1 -
SN -
N1 -
N1 -
AB -
ER -
TY - JOUR
AU - Tierney, L.
T1 - Markov chains for exploring posterior distributions
JO - The Annals of Statistics
PY - 1994/
VL - 22(4)
IS -
SP - 1701
EP - 1727
UR -
M3 -
KW - carlo
KW - chains
KW - gibbs
KW - markov
KW - ml
KW - monte
KW - sampling
L1 -
SN -
N1 -
N1 -
AB -
ER -