Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants

2014 ◽  
Vol 71 ◽  
pp. 402-416 ◽  
Author(s):  
Ick Hoon Jin ◽  
Faming Liang
Keyword(s):  
Bayesian Analysis ◽  
Statistical Models ◽  
Normalizing Constants ◽  
Intractable Normalizing Constants

A Monte Carlo Metropolis-Hastings Algorithm for Sampling from Distributions with Intractable Normalizing Constants

2013 ◽  
Vol 25 (8) ◽  
pp. 2199-2234 ◽  
Author(s):  
Faming Liang ◽  
Ick-Hoon Jin
Keyword(s):  
Monte Carlo ◽  
Random Effect ◽  
Auxiliary Variable ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Perfect Sampling ◽  
Exponential Random Graph ◽  
Normalizing Constants ◽  
Exchange Algorithms ◽  
Intractable Normalizing Constants

Simulating from distributions with intractable normalizing constants has been a long-standing problem in machine learning. In this letter, we propose a new algorithm, the Monte Carlo Metropolis-Hastings (MCMH) algorithm, for tackling this problem. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. It replaces the unknown normalizing constant ratio by a Monte Carlo estimate in simulations, while still converges, as shown in the letter, to the desired target distribution under mild conditions. The MCMH algorithm is illustrated with spatial autologistic models and exponential random graph models. Unlike other auxiliary variable Markov chain Monte Carlo (MCMC) algorithms, such as the Møller and exchange algorithms, the MCMH algorithm avoids the requirement for perfect sampling, and thus can be applied to many statistical models for which perfect sampling is not available or very expensive. The MCMH algorithm can also be applied to Bayesian inference for random effect models and missing data problems that involve simulations from a distribution with intractable integrals.

scholarly journals Absolute chronology of the Zedmar culture: Re-thinking radiocarbon dates

2017 ◽  
Vol 44 (1) ◽  
pp. 256-268
Author(s):  
Magdalena Kozicka
Keyword(s):  
Bayesian Analysis ◽  
Statistical Models ◽  
Archaeological Sites ◽  
Baltic Region ◽  
The South ◽  
Radiocarbon Dates ◽  
South Eastern ◽  
Calibration Methods ◽  
Eastern Baltic

Abstract The Zedmar culture is linked with the subneolithic circle of the South-Eastern Baltic region. So far, excavations have been carried out only on seven archaeological sites. Nonetheless, there are quite a lot of radiocarbon measurements. Most of them refer to the stratigraphic contexts. This allows to integrate all of the data into statistical models. With these, it is possible to query some statements about the Zedmar culture origin and its duration. At least as long as placing the Zedmar culture into an absolute timescale may offer any solution to those issues. The idea that radiocarbon dates could provide solutions or even final answers to some arguable questions in prehistorical studies was dropped, as soon as it became clear that in the whole approach the key role is played by calibration methods and the general variability of sampled material. However – thanks to including Bayesian analysis, a better understanding of dated materials and more complex examination of received results – it has been asserted again.

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