Generating Accurate Activity Patterns for Cattle Farm Management Using MCMC Simulation of Multiple-Sensor Data System

Posterior distributions are commonly approximated by samples produced from a Markov chain Monte Carlo (MCMC) simulation. Every MCMC simulation has to be checked for convergence, that is, that sufficiently many samples have been obtained and that these samples indeed represent the true posterior distribution. Here we develop and test different approaches for convergence assessment in phylogenetics. We analytically derive a threshold for a minimum effective sample size (ESS) of 625. We observe that only the initial sequence estimator provides robust ESS estimates for common types of MCMC simulations (autocorrelated samples, adaptive MCMC, Metropolis‐coupled MCMC). We show that standard ESS computation can be applied to phylogenetic trees if the tree samples are converted into traces of absence/presence of splits. Convergence in distribution between replicated MCMC runs can be assessed with the Kolmogorov–Smirnov test. The commonly used potential scale reduction factor (PSRF) is biased when applied to skewed posterior distribution. Additionally, we provide how the distribution of differences in split frequencies can be computed exactly akin to standard exact tests and show that it depends on the true frequency of a split. Hence, the average standard deviation of split frequencies is too simplistic and the expected difference based on the 95% quantile should be used instead to check for convergence in split frequencies. We implemented the methods described here in the open‐source R package Convenience (https://github.com/lfabreti/convenience), which allows users to easily test for convergence using output from standard phylogenetic inference software.

The estimation of time-invariant parameters of noisy nonlinear oscillatory systems

The determination of the correct prediction of claims frequency and claims severity is very important in the insurance business to determine the outstanding claims reserve which should be prepared by an insurance company. One approach which may be used to predict a future value is the Bayesian approach. This approach combines the sample and the prior information The information is used to construct the posterior distribution and to determine the estimate of the parameters. However, in this approach, integrations of functions with high dimensions are often encountered. In this Thesis, a Markov Chain Monte Carlo (MCMC) simulation is used using the Gibbs Sampling algorithm to solve the problem. The MCMC simulation uses ergodic chain property in Markov Chain. In Ergodic Markov Chain, a stationary distribution, which is the target distribution, is obtained. The MCMC simulation is applied in Hierarchical Poisson Model. The OpenBUGS software is used to carry out the tasks. The MCMC simulation in Hierarchical Poisson Model can predict the claims frequency.

The determination of the correct prediction of claims frequency and claims severity is very important in the insurance business to determine the outstanding claims reserve which should be prepared by an insurance company. One approach which may be used to predict a future value is the Bayesian approach. This approach combines the sample and the prior information The information is used to construct the posterior distribution and to determine the estimate of the parameters. However, in this approach, integrations of functions with high dimensions are often encountered. In this Thesis, a Markov Chain Monte Carlo (MCMC) simulation is used using the Gibbs Sampling algorithm to solve the problem. The MCMC simulation uses ergodic chain property in Markov Chain. In Ergodic Markov Chain, a stationary distribution, which is the target distribution, is obtained. The MCMC simulation is applied in Hierarchical Poisson Model. The OpenBUGS software is used to carry out the tasks. The MCMC simulation in Hierarchical Poisson Model can predict the claims frequency.

The autoregressive neural networks are emerging as a powerful computational tool to solve relevant problems in classical and quantum mechanics. One of their appealing functionalities is that, after they have learned a probability distribution from a dataset, they allow exact and efficient sampling of typical system configurations. Here we employ a neural autoregressive distribution estimator (NADE) to boost Markov chain Monte Carlo (MCMC) simulations of a paradigmatic classical model of spin-glass theory, namely, the two-dimensional Edwards-Anderson Hamiltonian. We show that a NADE can be trained to accurately mimic the Boltzmann distribution using unsupervised learning from system configurations generated using standard MCMC algorithms. The trained NADE is then employed as smart proposal distribution for the Metropolis-Hastings algorithm. This allows us to perform efficient MCMC simulations, which provide unbiased results even if the expectation value corresponding to the probability distribution learned by the NADE is not exact. Notably, we implement a sequential tempering procedure, whereby a NADE trained at a higher temperature is iteratively employed as proposal distribution in a MCMC simulation run at a slightly lower temperature. This allows one to efficiently simulate the spin-glass model even in the low-temperature regime, avoiding the divergent correlation times that plague MCMC simulations driven by local-update algorithms. Furthermore, we show that the NADE-driven simulations quickly sample ground-state configurations, paving the way to their future utilization to tackle binary optimization problems.

<h3>Summary</h3> Posterior distributions are commonly approximated by samples produced from a Markov chain Monte Carlo (MCMC) simulation. Every MCMC simulation has to be checked for convergence, i.e., that sufficiently many...

An introduction of Markov chain Monte Carlo method to geochemical inverse problems: Reading melting parameters from REE abundances in abyssal peridotites

The increasing availability of multi-core and multiprocessor architectures provides new opportunities for improving the performance of many computer simulations. Markov Chain Monte Carlo (MCMC) simulations are widely used for approximate counting problems, Bayesian inference and as a means for estimating very high-dimensional integrals. As such MCMC has had a wide variety of applications in fields including computational biology and physics, financial econometrics, machine learning and image processing. One method for improving the performance of Markov Chain Monte Carlo simulations is to use SMP machines to perform ‘speculative moves’, reducing the runtime whilst producing statistically identical results to conventional sequential implementations. In this paper we examine the circumstances under which the original speculative moves method performs poorly, and consider how some of the situations can be addressed by refining the implementation. We extend the technique to perform Markov Chains speculatively, expanding the range of algorithms that maybe be accelerated by speculative execution to those with non-uniform move processing times. By simulating program runs we can predict the theoretical reduction in runtime that may be achieved by this technique. We compare how efficiently different architectures perform in using this method, and present experiments that demonstrate a runtime reduction of up to 35–42% where using conventional speculative moves would result in execution as slow, if not slower, than sequential processing.

Confronting uncertainty in model-based geostatistics using Markov Chain Monte Carlo simulation

A key issue in assessment on tunnel face stability is a reliable evaluation of required support pressure on the tunnel face and its variations during tunnel excavation. In this paper, a Bayesian framework involving Markov Chain Monte Carlo (MCMC) simulation is implemented to estimate the uncertainties of limit support pressure. The probabilistic analysis for the three-dimensional face stability of tunnel below river is presented. The friction angle and cohesion are considered as random variables. The uncertainties of friction angle and cohesion and their effects on tunnel face stability prediction are evaluated using the Bayesian method. The three-dimensional model of tunnel face stability below river is based on the limit equilibrium theory and is adopted for the probabilistic analysis. The results show that the posterior uncertainty bounds of friction angle and cohesion are much narrower than the prior ones, implying that the reduction of uncertainty in cohesion and friction significantly reduces the uncertainty of limit support pressure. The uncertainty encompassed in strength parameters are greatly reduced by the MCMC simulation. By conducting uncertainty analysis, MCMC simulation exhibits powerful capability for improving the reliability and accuracy of computational time and calculations.

Summary With the prevalence of renewable energy source in power system, it is necessary to appraise the voltage stability of the integration system by probabilistic methods. The traditional Markov Chain Monte Carlo (MCMC) simulation could show great calculation precision for the probabilistic assessment, but it is always involved with complicated sampling iterations because of the Gibbs sampling method currently used in MCMC simulation. Instead of Gibbs sampling method, this paper presents the application of slice sampling in MCMC simulation for the voltage stability probabilistic assessment of the power system with renewable source. Firstly, the probabilistic models of renewable source generation are constructed. Then, the sample space of renewable source outputs is obtained by slice sampling, and the samples from the sample space are calculated by power flow. Finally, the voltage stability margin is obtained by the result of the power flow calculation, and the probabilistic assessment of the voltage stability is implemented. Furthermore, the MCMC simulations using Gibbs sampling and slice sampling are compared by Gelman-Rubin diagnostic and Kullback-Leibler divergence tests on IEEE 14-bus system and IEEE 39-bus system, respectively. The results show that the slice sampling method is simpler and more efficient than Gibbs sampling method in the voltage stability probabilistic assessment.

A new ANN driven MCMC method for multi-parameter estimation in two-dimensional conduction with heat generation

Bayesian model updating of a coupled-slab system using field test data utilizing an enhanced Markov chain Monte Carlo simulation algorithm

Combined state and parameter identification of nonlinear structural dynamical systems based on Rao-Blackwellization and Markov chain Monte Carlo simulations

The increasing availability of multi-core and multiprocessor architectures provides new opportunities for improving the performance of many computer simulations. Markov chain Monte Carlo (MCMC) simulations are widely used for approximate counting problems, Bayesian inference and as a means for estimating very high-dimensional integrals. As such MCMC has found a wide variety of applications infields including computational biology and physics, financial econometrics, machine learning and image processing. This paper presents a new method for reducing the run-time of Markov chain Monte Carlo simulations by using SMP machines to speculatively perform iterations in parallel, reducing the runtime of MCMC programs whilst producing statistically identical results to conventional sequential implementations. We calculate the theoretical reduction in runtime that may be achieved using our technique under perfect conditions, and test and compare the method on a selection of multi-core and multi-processor architectures. Experiments are presented that show reductions in runtime of 35% using two cores and 55% using four cores.