Efficient Monte Carlo Method Research Articles

A multivariate student-t process model for dependent tail-weighted degradation data

Traditionally, the Gaussian assumption, implied by the Wiener process, is widely admitted for modeling degradation processes. However, when degradation data exhibit heavy tails, this assumption is not suitable. To overcome this limitation, this article proposes a novel class of tail-weighted multivariate degradation model, which is built upon Student-t process. The model is able to account for both between-unit variability and process dependency, while allowing the adjustment of tail heaviness through tuning the parameter of the degree of freedom. For reliability assessment, we derive the system reliability function and present an efficient Monte Carlo method for its evaluation. Further, we introduce an expectation–maximization algorithm for parameter estimation and design a bootstrap method for interval estimation. Comprehensive simulation studies are conducted to validate the effectiveness of the inference method. Finally, the proposed methodology is applied to analyze two real-world degradation datasets.

Optimal oversampling ratio in two-step simulation

Abstract This paper analyses a novel two-step Monte Carlo simulation algorithm to estimate the weighted volume of a polytope of the form A ⁢ z ≤ T {Az\leq T} . The essential idea is to partition the columns of A into two categories – a lightweight category and a heavyweight category. Simulation is done in a two-step manner where, for every sample of the lightweight category variables we use multiple samples of the heavyweight category variables. Thus, the heavyweight category variables are oversampled with respect to the lightweight category variables and increasing samples of the heavyweight variables at the expense of the lightweight variables will lead to a more efficient Monte Carlo method. In this paper we present a fast heuristic approximate for estimating the optimal oversampling ratio and substantiate with experimental results which confirm the effectiveness of the method.

Effective T-matrix of a cylinder filled with a random two-dimensional particulate

When a wave, such as sound or light, scatters within a densely packed particulate, it can be rescattered many times between the particles, which is called multiple scattering. Multiple scattering can be unavoidable when trying to use sound waves to measure a dense particulate, such as a composite with reinforcing fibres. Here, we solve from first principles multiple scattering of scalar waves, including acoustic, for any frequency from a set of two-dimensional particles confined in a circular area. This case has not been solved yet, and its solution is important to perform numerical validation, as particles within a cylinder require only a finite number of particles to perform direct numerical simulations. The method we use involves ensemble averaging over particle configurations, which leads us to deduce an effective T-matrix for the whole cylinder, which can be used to easily describe the scattering from any incident wave. In the specific case when the particles are monopole scatterers, the expression of this effective T-matrix simplifies and reduces to the T-matrix of a homogeneous cylinder with an effective wavenumber k ⋆ . To validate our theoretical predictions, we develop an efficient Monte Carlo method and conclude that our theoretical predictions are highly accurate for a broad range of frequencies.

A Metropolized Adaptive Subspace Algorithm for High-Dimensional Bayesian Variable Selection

A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable selection. The MAdaSub algorithm is based on an independent Metropolis-Hastings sampler, where the individual proposal probabilities of the explanatory variables are updated after each iteration using a form of Bayesian adaptive learning, in a way that they finally converge to the respective covariates’ posterior inclusion probabilities. We prove the ergodicity of the algorithm and present a parallel version of MAdaSub with an adaptation scheme for the proposal probabilities based on the combination of information from multiple chains. The effectiveness of the algorithm is demonstrated via various simulated and real data examples, including a high-dimensional problem with more than 20,000 covariates.

Bayesian transformation model for spatial partly interval-censored data

The transformation model with partly interval-censored data offers a highly flexible modeling framework that can simultaneously support multiple common survival models and a wide variety of censored data types. However, the real data may contain unexplained heterogeneity that cannot be entirely explained by covariates and may be brought on by a variety of unmeasured regional characteristics. Due to this, we introduce the conditionally autoregressive prior into the transformation model with partly interval-censored data and take the spatial frailty into account. An efficient Markov chain Monte Carlo method is proposed to handle the posterior sampling and model inference. The approach is simple to use and does not include any challenging Metropolis steps owing to four-stage data augmentation. Through several simulations, the suggested method's empirical performance is assessed and then the method is used in a leukemia study.

FROM OFFSHORE TO ONSHORE PROBABILISTIC TSUNAMI HAZARD ASSESSMENT WITH QUANTIFIED UNCERTAINTY: EFFICIENT MONTE CARLO TECHNIQUES

Offshore probabilistic tsunami hazard assessments (PTHAs) are increasingly available for earthquake generated tsunamis. They provide standardized representations of tsunami scenarios, their uncertain occurrence-rates, and models of the deep ocean waveforms. To quantify onshore hazards it is natural to combine this information with a site-specific inundation model, but this is computationally challenging to do accurately, especially if accounting for uncertainties in the offshore PTHA. This study reviews an efficient Monte Carlo method recently proposed to solve this problem. The efficiency comes from preferential sampling of scenarios that are likely important near the site of interest, using a user-defined importance measure derived from the offshore PTHA. The theory of importance sampling enables this to be done without biasing the final results. Techniques are presented to help design and test Monte Carlo schemes for a site of interest (before inundation modelling) and to quantify errors in the final results (after inundation modelling). The methods are illustrated with examples from studies in Tongatapu and Western Australia.

Optimal Allocation and Sizing of Decentralized Solar Photovoltaic Generators Using Unit Financial Impact Indicator

A novel financial metric denominated unit financial impact indicator (UFII) is proposed to minimize the payback period for solar photovoltaic (PV) systems investments and quantify the financial efficiency of allocation and sizing strategies. However, uncontrollable environmental conditions and operational uncertainties, such as variable power demands, component failures, and weather conditions, can threaten the robustness of the investment, and their effect needs to be accounted for. Therefore, a new probabilistic framework is proposed for the robust and optimal positioning and sizing of utility-scale PV systems in a transmission network. The probabilistic framework includes a new cloud intensity simulator to model solar photovoltaic power production based on historical data and quantified using an efficient Monte Carlo method. The optimized solution obtained using weighted sums of expected UFII and its variance is compared against those obtained by using well-established economic metrics from literature. The efficiency and usefulness of the proposed approach are tested on the 14-bus IEEE power grid case study. The results prove the applicability and efficacy of the new probabilistic metric to quantify the financial effectiveness of solar photovoltaic investments on different nodes and geographical regions in a power grid, considering the unavoidable conditional and operational uncertainty.

Optimal reinsurance-investment game for two insurers with SAHARA utilities under correlated markets

In this paper, we study the optimal reinsurance-investment game between two insurers with the same insurance business but different wealth and risk preferences. Assume that the insurers who have the symmetric asymptotic hyperbolic absolute risk aversion (SAHARA) utilities and the price of risky asset obeys the constant elasticity of variance (CEV) model. It is impossible to obtain closed-form solution of the optimal reinsurance-investment strategy due to the non-homothetic property and the complicity of SAHARA utilities. According to establish a strong duality relationship of the value function, we successfully propose an efficient dual control Monte Carlo method for computing the Nash equilibrium strategies. Finally, numerical analysis is given to illustrate the impact of model parameters to Nash equilibrium strategies.

Reliability Estimation for Stochastic Flow Networks With Dependent Arcs

The creation and the destruction processes (CPs and DPs) are the basis of many efficient Monte Carlo methods for estimating the unreliability of highly reliable networks on both, the static and the stochastic flow network models, for the case of independent components. Some of these methods are based on the splitting variance reduction techniques. Due to the splitting basic mechanism, they operate over CP. Here, we propose a splitting-based Monte Carlo method, using the Marshall–Olkin copula for the case of nonindependent components. This proposal operates on the DP, because the Marshall–Olkin copula model over networks is quite related—and somehow similar—to DP, which is unusual but here necessary. Before addressing the proposal, the article presents a review of the methods based on CP and DP. At the end, a comparative experimental analysis shows the efficiency of the proposed approach.

Uncertainty in systemic risks rankings: Bayesian and frequentist analysis

We propose efficient Bayesian Hamiltonian Monte Carlo method for estimation of systemic risk measures, LRMES, SRISK and ΔCoVaR, and apply it for thirty global systemically important banks and for eighteen largest US financial institutions over the period of 2000–2020. The advantage of the Hamiltonian method is an efficient estimation of all parameters jointly in high dimensional models and providing posterior distributions incorporating parameter uncertainty. The systemic risk measures are computed based on the Dynamic Conditional Correlations model with generalized asymmetric volatility. We estimate the systemic risks posterior distributions and two-step maximum likelihood distributions with bootstrap simulations for LRMES. The systemic risk rankings at different quantiles of the distributions vary considerably using bootstrap approach for computation of LRMES and SRISK, and are more stable with Bayesian posterior distributions using a parametric model. A policymaker may choose to rank the firms using some quantile of their systemic risk distributions such as 90, 95, or 99% depending on risk preferences with higher quantiles being more conservative.

Dimension‐independent Markov chain Monte Carlo on the sphere

AbstractWe consider Bayesian analysis on high‐dimensional spheres with angular central Gaussian priors. These priors model antipodally symmetric directional data, are easily defined in Hilbert spaces and occur, for instance, in Bayesian density estimation and binary level set inversion. In this paper we derive efficient Markov chain Monte Carlo methods for approximate sampling of posteriors with respect to these priors. Our approaches rely on lifting the sampling problem to the ambient Hilbert space and exploit existing dimension‐independent samplers in linear spaces. By a push‐forward Markov kernel construction we then obtain Markov chains on the sphere which inherit reversibility and spectral gap properties from samplers in linear spaces. Moreover, our proposed algorithms show dimension‐independent efficiency in numerical experiments.

Dynamic information transfer in stochastic biochemical networks

We develop numerical and analytical approaches to calculate mutual information between complete paths of two molecular components embedded into a larger reaction network. In particular, we focus on a continuous-time Markov chain formalism, frequently used to describe intracellular processes involving lowly abundant molecular species. Previously, we have shown how the path mutual information can be calculated for such systems when two molecular components interact directly with one another with no intermediate molecular components being present. In this paper, we generalize this approach to biochemical networks involving an arbitrary number of molecular components. We present an efficient Monte Carlo method as well as an analytical approximation to calculate the path mutual information and show how it can be decomposed into a pair of transfer entropies that capture the directed flow of information between two network components. We apply our methodology to study information transfer in a simple three-node feedforward network, as well as a more complex positive-feedback system that switches stochastically between two metastable modes.

Sticky PDMP samplers for sparse and local inference problems

We construct a new class of efficient Monte Carlo methods based on continuous-time piecewise deterministic Markov processes (PDMPs) suitable for inference in high dimensional sparse models, i.e. models for which there is prior knowledge that many coordinates are likely to be exactly 0. This is achieved with the fairly simple idea of endowing existing PDMP samplers with “sticky” coordinate axes, coordinate planes etc. Upon hitting those subspaces, an event is triggered during which the process sticks to the subspace, this way spending some time in a sub-model. This results in non-reversible jumps between different (sub-)models. While we show that PDMP samplers in general can be made sticky, we mainly focus on the Zig-Zag sampler. Compared to the Gibbs sampler for variable selection, we heuristically derive favourable dependence of the Sticky Zig-Zag sampler on dimension and data size. The computational efficiency of the Sticky Zig-Zag sampler is further established through numerical experiments where both the sample size and the dimension of the parameter space are large.

Hierarchical Bayesian hedonic regression analysis of Japanese rice wine: is the price right?

Purpose This paper aims to formulate a hedonic pricing model for Japanese rice wine, sake, via hierarchical Bayesian modeling estimated using an efficient Markov chain Monte Carlo (MCMC) method. Using the estimated model, the authors examine how producing regions, rice breeds and taste characteristics affect sake prices. Design/methodology/approach The datasets in the estimation consist of cross-sectional observations of 403 sake brands, which include sake prices, taste indicators, premium categories, rice breeds and regional dummy variables. Data were retrieved from Rakuten, Japan’s largest online shopping site. The authors used the Bayesian estimation of the hedonic pricing model and used an ancillarity–sufficiency interweaving strategy to improve the sampling efficiency of MCMC. Findings The estimation results indicate that Japanese consumers value sweeter sake more, and the price of sake reflects the cost of rice preprocessing only for the most-expensive category of sake. No distinctive differences were identified among rice breeds or producing regions in the hedonic pricing model. Originality/value To the best of the authors’ knowledge, this study is the first to estimate a hedonic pricing model of sake, despite the rich literature on alcoholic beverages. The findings may contribute new insights into consumer preference and proper pricing for sake breweries and distributors venturing into the e-commerce market.

An Efficient MultiModes Monte Carlo Homogenization Method for Random Materials

In this paper, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homogenized solutions are sought through a two-stage procedure. In the first stage, the original oscillatory diffusion equation is approximated, for each fixed random sample $\omega$, by a spatially homogenized diffusion equation with piecewise constant coefficients, resulting in a random diffusion equation. In the second stage, the resulting random diffusion equation is approximated and computed by using an efficient multimodes Monte Carlo method which only requires solving a diffusion equation with a constant diffusion coefficient and a random right-hand side. The main advantage of the proposed method is that it separates the computational difficulty caused by the spatial fast oscillation of the solution and caused by the randomness of the solution, so they can be overcome separately using different strategies. The convergence of the solution of the spatially homogenized equation (from the first stage) to the solution of the original random diffusion equation is established, and the optimal rate of convergence is also obtained for the proposed multimodes Monte Carlo method. Numerical experiments on some benchmark test problems for random composite materials are also presented to gauge the efficiency and accuracy of the proposed two-stage stochastic homogenization method.

Monte Carlo method with SNBCK nongray gas model for thermal radiation in containment flows

During a postulated severe accident in light water reactors, containment flows are characterized by relatively low velocities and modest temperature differences after depressurization of the reactor cooling system. Owing to the low gas temperature level and small temperature differences, gas radiation heat transfer was neglected in CFD simulations of hydrogen transport and mixing in containment flows. During the natural mixing and dilution processes, thermal radiation can affect the fluid temperatures and thereby influence the buoyancy forces in the presence of large amounts of steam. In order to quantify the effect of thermal radiation, an efficient Monte Carlo method with statistical narrow band correlated-k (SNBCK) nongray gas model has been implemented to solve the radiative transfer equation within the framework of containmentFOAM. The tailored Monte Carlo solver is validated against the OECD/NEA SETH-2 PANDA ST1 experiments, and it is proven that gas radiation has a significant effect on the gas temperature field and the helium-steam mixing process. The results clearly indicate that gas radiation cannot be neglected in containment flows even at modest temperature differences (ΔT<50K).

Accelerated simulation method for charge regulation effects.

The net charge of solvated entities, ranging from polyelectrolytes and biomolecules to charged nanoparticles and membranes, depends on the local dissociation equilibrium of individual ionizable groups. Incorporation of this phenomenon, charge regulation (CR), in theoretical and computational models requires dynamic, configuration-dependent recalculation of surface charges and is therefore typically approximated by assuming constant net charge on particles. Various computational methods exist that address this. We present an alternative, particularly efficient CR Monte Carlo method (CR-MC), which explicitly models the redistribution of individual charges and accurately samples the correct grand-canonical charge distribution. In addition, we provide an open-source implementation in the large-scale Atomic/Molecular Massively Parallel Simulator molecular dynamics (MD) simulation package, resulting in a hybrid MD/CR-MC simulation method. This implementation is designed to handle a wide range of implicit-solvent systems that model discreet ionizable groups or surface sites. The computational cost of the method scales linearly with the number of ionizable groups, thereby allowing accurate simulations of systems containing thousands of individual ionizable sites. By matter of illustration, we use the CR-MC method to quantify the effects of CR on the nature of the polyelectrolyte coil-globule transition and on the effective interaction between oppositely charged nanoparticles.

Bond bipolarons: Sign-free Monte Carlo approach

Polarons originating from phonon displacement modulated hopping have relatively light masses and, thus, are of significant current interest as candidates for bipolaron mechanism of high-temperature superconductivity [Phys. Rev. Lett. {\bf 121}, 247001 (2018)]. We observe that the bond model, when the dominant coupling comes from atomic vibrations on lattice bonds, can be solved by efficient sign-free Monte Carlo methods based on the path-integral formulation of the particle sector in combination with either the (real-space) diagrammatic or Fock-path-integral representation of the phonon sector. We introduce the corresponding algorithms and provide illustrative results for bipolarons in two dimensions. The results suggest that the route towards high-temperature superconductivity (if any) in the multiparametric space of the model lies between the Scylla of large size of moderately light bipolarons and Charybdis of large mass of compact bipolarons. As a result, on-site repulsion is helping $s$-wave superconductivity in sharp contrast with existing expectations.

Bayesian Poisson Factorization With Side Information for User Interest Prediction in Hierarchical Edge-Caching Systems

Edge-caching is an effective solution to cope with the unprecedented data traffic growth by storing contents in the vicinity of end-users. In this paper, we formulate a hierarchical caching policy where the end-users and cellular base station (BS) are equipped with limited cache capacity with the objective of minimizing the total data traffic load in the network. The caching policy is a nonlinear combinatorial programming problem and difficult to solve. To tackle the issue, we design a heuristic algorithm as an approximate solution which can be solved efficiently. Moreover, to proactively serve the users, it is of high importance to extract useful information from data requests and predict user interest about contents. In practice, the data often contain <i>implicit feedback</i> from users which is quite noisy and complicates the reliable prediction of user interest. In this regard, we introduce a Bayesian Poisson matrix factorization model which utilizes the available side information about contents to effectively filter out the noise in the data and provide accurate prediction. Subsequently, we design an efficient Markov chain Monte Carlo (MCMC) method to perform the posterior approximation. Finally, a real-world dataset is applied to the proposed proactive caching-prediction scheme and our results show significant improvement over several commonly-used methods. For example, when the BS and the users have caches with storage of 25&#x0025; and 10&#x0025; of the total contents size respectively, our approach yields around 8&#x0025; improvement with respect to the state-of-the-art approach in terms of caching performance.

Bayesian transformation models with partly interval‐censored data

In many scientific fields, partly interval-censored data, which consist of exactly observed and interval-censored observations on the failure time of interest, appear frequently. However, methodological developments in the analysis of partly interval-censored data are relatively limited and have mainly focused on additive or proportional hazards models. The general linear transformation model provides a highly flexible modeling framework that includes several familiar survival models as special cases. Despite such nice features, the inference procedure for this class of models has not been developed for partly interval-censored data. We propose a fully Bayesian approach coped with efficient Markov chain Monte Carlo methods to fill this gap. A four-stage data augmentation procedure is introduced to tackle the challenges presented by the complex model and data structure. The proposed method is easy to implement and computationally attractive. The empirical performance of the proposed method is evaluated through two simulation studies, and the model is then applied to a dental health study.