20,403 research outputs found
N-fold way simulated tempering for pairwise interaction point processes
Pairwise interaction point processes with strong interaction are usually difficult to
sample. We discuss how Besag lattice processes can be used in a simulated tempering
MCMC scheme to help with the simulation of such processes. We show how
the N-fold way algorithm can be used to sample the lattice processes efficiently
and introduce the N-fold way algorithm into our simulated tempering scheme. To
calibrate the simulated tempering scheme we use the Wang-Landau algorithm
Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models
We study the preconditioning of Markov chain Monte Carlo (MCMC) methods using coarse-scale models with applications to subsurface characterization. The purpose of preconditioning is to reduce the fine-scale computational cost and increase the acceptance rate in the MCMC sampling. This goal is achieved by generating Markov chains based on two-stage computations. In the first stage, a new proposal is first tested by the coarse-scale model based on multiscale finite volume methods. The full fine-scale computation will be conducted only if the proposal passes the coarse-scale screening. For more efficient simulations, an approximation of the full fine-scale computation using precomputed multiscale basis functions can also be used. Comparing with the regular MCMC method, the preconditioned MCMC method generates a modified Markov chain by incorporating the coarse-scale information of the problem. The conditions under which the modified Markov chain will converge to the correct posterior distribution are stated in the paper. The validity of these assumptions for our application and the conditions which would guarantee a high acceptance rate are also discussed. We would like to note that coarse-scale models used in the simulations need to be inexpensive but not necessarily very accurate, as our analysis and numerical simulations demonstrate. We present numerical examples for sampling permeability fields using two-point geostatistics. The Karhunen--Loève expansion is used to represent the realizations of the permeability field conditioned to the dynamic data, such as production data, as well as some static data. Our numerical examples show that the acceptance rate can be increased by more than 10 times if MCMC simulations are preconditioned using coarse-scale models
Inference of Temporally Varying Bayesian Networks
When analysing gene expression time series data an often overlooked but
crucial aspect of the model is that the regulatory network structure may change
over time. Whilst some approaches have addressed this problem previously in the
literature, many are not well suited to the sequential nature of the data. Here
we present a method that allows us to infer regulatory network structures that
may vary between time points, utilising a set of hidden states that describe
the network structure at a given time point. To model the distribution of the
hidden states we have applied the Hierarchical Dirichlet Process Hideen Markov
Model, a nonparametric extension of the traditional Hidden Markov Model, that
does not require us to fix the number of hidden states in advance. We apply our
method to exisiting microarray expression data as well as demonstrating is
efficacy on simulated test data
Bayesian inference from photometric redshift surveys
We show how to enhance the redshift accuracy of surveys consisting of tracers
with highly uncertain positions along the line of sight. Photometric surveys
with redshift uncertainty delta_z ~ 0.03 can yield final redshift uncertainties
of delta_z_f ~ 0.003 in high density regions. This increased redshift precision
is achieved by imposing an isotropy and 2-point correlation prior in a Bayesian
analysis and is completely independent of the process that estimates the
photometric redshift. As a byproduct, the method also infers the three
dimensional density field, essentially super-resolving high density regions in
redshift space. Our method fully takes into account the survey mask and
selection function. It uses a simplified Poissonian picture of galaxy
formation, relating preferred locations of galaxies to regions of higher
density in the matter field. The method quantifies the remaining uncertainties
in the three dimensional density field and the true radial locations of
galaxies by generating samples that are constrained by the survey data. The
exploration of this high dimensional, non-Gaussian joint posterior is made
feasible using multiple-block Metropolis-Hastings sampling. We demonstrate the
performance of our implementation on a simulation containing 2.0 x 10^7
galaxies. These results bear out the promise of Bayesian analysis for upcoming
photometric large scale structure surveys with tens of millions of galaxies.Comment: 17 pages, 12 figure
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