Importance Sampling Research Articles

The efficient method of lattice dynamics calculation: Monte Carlo integration with importance sampling.

In this study, we aimed to accelerate the thermal conductivity calculations of crystalline nanostructures using anharmonic lattice dynamics. For this we implemented Monte Carlo integration for relaxation time calculations and achieved a dramatic acceleration of
approximately two orders of magnitude. The relaxation times can be calculated by computing the scattering rates for all phonon combinations; however, in this Monte Carlo integration, we instead calculated the scattering rates of a randomly sampled subset of combinations. Then, we estimated the overall scattering rate. Simple Monte Carlo integration samples the
scattering channels that do not contribute to the total scattering rate, leading to inefficiencies. To address this issue, we implemented an importance sampling method (ISM) for improving sampling efficiency. In this study, we compared the computational speeds of both methods and investigated the differences in accuracy by comparing the results with the exact values obtained
from traditional relaxation time calculations. The comparison showed similarity between both the methods in terms of speed; however, ISM was faster when the error margin was ∼5%. Furthermore, while simple Monte Carlo integration risks significantly worse accuracy as the system size increases, the ISM remains relatively robust and reliable.

Estimation and Bayesian Prediction for the Generalized Exponential Distribution Under Type-II Censoring

This research focuses on the prediction and estimation problems for the generalized exponential distribution under Type-II censoring. Firstly, maximum likelihood estimations for the parameters of the generalized exponential distribution are computed using the EM algorithm. Additionally, confidence intervals derived from the Fisher information matrix are developed and analyzed alongside two bootstrap confidence intervals for comparison. Compared to classical maximum likelihood estimation, Bayesian inference proves to be highly effective in handling censored data. This study explores Bayesian inference for estimating the unknown parameters, considering both symmetrical and asymmetrical loss functions. Utilizing Gibbs sampling to produce Markov Chain Monte Carlo samples, we employ an importance sampling approach to obtain Bayesian estimates and compute the corresponding highest posterior density (HPD) intervals. Furthermore, for one-sample prediction and, separately, for the two-sample case, we provide the corresponding posterior distributions, along with methods for computing point predictions and predictive intervals. Through Monte Carlo simulations, we evaluate the performance of Bayesian estimation in contrast to maximum likelihood estimation. Finally, we conduct an analysis of a real dataset derived from deep groove ball bearings, calculating Bayesian point predictions and predictive intervals for future samples.

An information-theoretic learning model based on importance sampling with application in face verification

An information-theoretic learning model based on importance sampling with application in face verification

A novel active learning Kriging based on improved Metropolis-Hastings and importance sampling for small failure probabilities

A novel active learning Kriging based on improved Metropolis-Hastings and importance sampling for small failure probabilities

Decarceration and COVID-19 infections in U.S. Immigration and Customs Enforcement detention facilities: a simulation modeling study.

U.S. Immigration and Customs Enforcement (ICE) facilities had high rates of COVID-19 infections and mortality during the global pandemic. We sought to quantify how many COVID-19 infections could have been averted through different decarceration strategies. We developed a set of stochastic simulation models of SARS-CoV-2 transmission in ICE facilities. Employing incremental mixture importance sampling (IMIS), we calibrated them to empirical targets derived from publicly available case time series for ICE facilities, and publicly available facility population censuses prior to vaccine availability (May 6, 2020 to December 31, 2020). The models included infection importation from extra-facility sources. We evaluated reduction of the incarcerated population by 10-90%. People who were decarcerated faced background cumulative risks of infection and detection based on a weighted average of county-level estimates from the covidestim model, which is a Bayesian evidence synthesis model. Without decarceration, the infection rate was 5.05 per 1000 person-days (95% CrI 3.40-6.81) and case rate was 1.53 per 1000 person-days (95% CrI 1.04-2.02). Rates declined linearly when decarceration did not reduce contacts of people remaining in facilities and faster than linearly when it did reduce contacts. At all decarceration levels, rates were substantially higher when contacts were not reduced. Even with 90% decarceration, infection rates for people remaining in facilities were higher than or comparable to otherwise similar free-living people. The decline in COVID-19 infection rates with decarceration was linear or faster than linear depending on how decarceration was implemented. Our findings highlight infection risks associated with incarceration, which compound other health harms of incarceration. Stanford's COVID-19 Emergency Response Fund; the National Institute on Drug Abuse; and the National Institute of Mental Health.

Importance sampling of seismic tsunami sources with near-field emphasis for inundation PTHA: benchmarking with complete ensembles

Summary Site-specific Probabilistic Tsunami Hazard Assessment (PTHA) is a powerful tool for coastal planning against tsunami risk. However, its typically high computational demands led to the introduction of a Monte Carlo Stratified Importance Sampling (SIS) approach, which selects a representative subset of scenarios for numerical inundation simulations. We here empirically validate this sampling approach, for the first time to our knowledge, using an existing extensive dataset of numerical inundation simulations for two coastal sites in the Mediterranean Sea (Catania and Siracusa, both located in Sicily, Italy). Moreover, we propose a modified importance sampling function to prioritise seismic tsunami scenarios based on their arrival time at an offshore point near the target site, in addition to their wave amplitude and occurrence rate as leveraged in the previous work. This sampling function is applied separately in each earthquake magnitude bin, and allows denser sampling of near-field earthquakes to whose variations tsunamis are very sensitive. We compare the confidence intervals of the offshore PTHA estimates obtained with the new and the original importance sampling functions. Then, we benchmark our onshore PTHA estimates obtained with both functions against the inundation PTHA calculated using the full set of scenarios. We also test the assumption that onshore random errors follow a normal distribution, as found previously for the offshore case. As a result of the benchmarks, we find that the SIS approach works satisfactorily. Introducing the arrival time as an additional sampling factor enhances the precision of the estimates of both the mean and the percentiles for the two coastal sites considered. With this modification it is possible to deal efficiently with heterogeneous near-field earthquake sources involving coastal deformation at Catania and Siracusa, in addition to regional crustal and subduction sources. By comparing the sampling errors with the model (epistemic) uncertainty, an optimal trade-off between the number of simulations employed and the uncertainty of the PTHA model can be found, even for such a complex situation. A relatively small number of scenarios, on the order of a few thousand, is sufficient to perform site-specific PTHA for practical applications. These numbers correspond to 4–8% of the already reduced ensembles used in previous assessments at the same sites.

Unsupervised data imputation with multiple importance sampling variational autoencoders

Recently, deep latent variable models have made significant progress in dealing with missing data problems, benefiting from their ability to capture intricate and non-linear relationships within the data. In this work, we further investigate the potential of Variational Autoencoders (VAEs) in addressing the uncertainty associated with missing data via a multiple importance sampling strategy. We propose a Missing data Multiple Importance Sampling Variational Auto-Encoder (MMISVAE) method to effectively model incomplete data. Our approach consists of a learning step and an imputation step. During the learning step, the mixture components are represented by multiple separate encoder networks, which are later combined through simple averaging to enhance the latent representation capabilities of the VAEs when dealing with incomplete data. The statistical model and variational distributions are iteratively updated by maximizing the Multiple Importance Sampling Evidence Lower Bound (MISELBO) on the joint log-likelihood. In the imputation step, missing data is estimated using conditional expectation through multiple importance resampling. We propose an efficient imputation algorithm that broadens the scope of Missing data Importance Weighted Auto-Encoder (MIWAE) by incorporating multiple proposal probability distributions and the resampling schema. One notable characteristic of our method is the complete unsupervised nature of both the learning and imputation processes. Through comprehensive experimental analysis, we present evidence of the effectiveness of our method in improving the imputation accuracy of incomplete data when compared to current state-of-the-art VAEs-based methods.

Statistical Inference for Generalized Half‐Normal Model Under Step‐Stress Accelerated Life Test in the Presence of Hybrid Censoring

ABSTRACTIn this paper, we consider the problem of estimating the unknown parameters of a generalized half‐normal (GHN) distribution when lifetime data are observed from accelerated life test (ALT) experiments in the presence of hybrid censoring. To relate the lifetime of products under different stress levels, we make use of a cumulative exposure model (CEM), and obtain maximum likelihood estimates using a numerical approach and stochastic expectation–maximization (SEM) algorithm. We further obtain the expected Fisher information matrix, and use it to compute associated confidence interval estimates for the unknown parameters of the distribution. The expected Fisher information matrix is also used to select the optimal time to conduct an experiment based on three considered optimality criteria. Next, we consider independent and conditional gamma priors and obtain the associated posterior distributions for the unknown parameters. We then make use of samples generated from the posterior distributions using importance sampling and the MH algorithm to compute the Bayesian estimates under the squared error loss function. Furthermore, the highest associated posterior density interval estimates are also computed. Finally, we conduct a simulation study to evaluate the efficiency of the suggested approaches in various situations and analyze a real data set for illustration purposes.

Inference for a dependent competing risks model on Marshall-Olkin bivariate Lomax-geometric distribution

. The study of competing risk models is of great significance to survival and reliability analysis in statistics and it is more reasonable that they are assumed to have dependent failure causes in the actual situation. Therefore, statistical inference of five-parameter Marshall–Olkin bivariate Lomax-geometric distribution is considered in combination with dependent failure causes in this article. From the perspective of classical frequency, the estimates of unknown parameters are derived by the EM algorithm and the existence and uniqueness of solutions are also proved. In the Bayesian framework, a rather flexible class of prior distributions and the importance sampling technique are considered to obtain the estimates of all parameters for two types of data under the squared error loss function, and the credible intervals are also constructed. Finally, some simulation results and real data analysis are provided to show the effectiveness of the constructed model and the performance of various methods.

A Novel Particle Filter Based on One-Step Smoothing for Nonlinear Systems with Random One-Step Delay and Missing Measurements.

In this paper, a novel particle filter based on one-step smoothing is proposed for nonlinear systems with random one-step delay and missing measurements. Such problems are commonly encountered in networked control systems, where random one-step delay and missing measurements significantly increase the difficulty of dynamic state estimation. The particle filter is a nonlinear filtering method based on sequential Monte Carlo sampling. It shows excellent state estimation performance when dealing with nonlinear and non-Gaussian dynamic systems. However, the particle filter has certain limitations in complex dynamic scenarios, with particle degradation being the most typical issue, which can significantly reduce estimation accuracy. To address particle degradation, the proposed particle filter iteratively incorporates current measurement information derived from sensors into the prior distribution to construct a new importance function. This approach can limit particle degeneracy and improve the efficiency of importance sampling in the bootstrap particle filter. Simulation experiments demonstrate that the proposed particle filter effectively limits particle degradation and improves estimation accuracy compared to the existing bootstrap particle filter for nonlinear systems with random one-step delay and missing measurements.

Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: Dipolar planar rotor chain.

In this work, we propose a path integral Monte Carlo approach based on discretized continuous degrees of freedom and rejection-free Gibbs sampling. The ground state properties of a chain of planar rotors with dipole-dipole interactions are used to illustrate the approach. Energetic and structural properties are computed and compared to exact diagonalization and numerical matrix multiplication for N ≤ 3 to assess the systematic Trotter factorization error convergence. For larger chains with up to N = 100 rotors, Density Matrix Renormalization Group calculations are used as a benchmark. We show that using Gibbs sampling is advantageous compared to traditional Metropolis-Hastings rejection importance sampling. Indeed, Gibbs sampling leads to lower variance and correlation in the computed observables.

On the estimation of the stress-strength parameter for the inverse Lindley distribution based on lower record values

In this article, we consider the estimation of the stress-strength reliability parameter for the inverse Lindley distribution based on lower record values. The maximum likelihood estimator and its asymptotic distribution are obtained. An approximate classical confidence interval, as well as two bootstrap-type confidence intervals for the reliability parameter are derived. The Bayesian inference for the parameter has been considered using Tierney and Kadane’s approximation method, as well as two Monte Carlo methods, namely the Metropolis-Hastings and importance sampling techniques under both symmetric and asymmetric loss functions. Besides, the Chen and Shao shortest width credible intervals are constructed for the stress-strength parameter. A simulation study and a real data example are conducted to explore and compare the performances of the presented results.

State Space Emulation and Annealed Sequential Monte Carlo for High Dimensional Optimization

Many high dimensional optimization problems can be reformulated into a problem of finding theoptimal state path under an equivalent state space model setting. In this article, we present a general emulation strategy for developing a state space model whose likelihood function (or posterior distribution) shares the same general landscape as the objective function of the original optimization problem. Then the solution of the optimization problem is the same as the optimal state path that maximizes the likelihood function or the posterior distribution under the emulated system. To find such an optimal path, we adapt a simulated annealing approach by inserting a temperature control into the emulated dynamic system and propose a novel annealed Sequential Monte Carlo (SMC) method that effectively generating Monte Carlo sample paths utilizing samples obtained on the high temperature scale. Compared to the vanilla simulated annealing implementation, annealed SMC is an iterative algorithm for state space model optimization that directly generates state paths from the equilibrium distributions with a decreasing sequence of temperatures through sequential importance sampling which does not require burn-in or mixing iterations to ensure quasi-equilibrium condition. Several applications of state space model emulation and the corresponding annealed SMC results are demonstrated.

Applying Importance Sampling to MCTS for Mahjong

Applying Importance Sampling to MCTS for Mahjong

Coupling importance sampling neural network for imbalanced data classification with multi-level learning bias

Coupling importance sampling neural network for imbalanced data classification with multi-level learning bias

Flow matching for atmospheric retrieval of exoplanets: Where reliability meets adaptive noise levels

Context. Inferring atmospheric properties of exoplanets from observed spectra is key to understanding their formation, evolution, and habitability. Since traditional Bayesian approaches to atmospheric retrieval (e.g., nested sampling) are computationally expensive, a growing number of machine learning (ML) methods such as neural posterior estimation (NPE) have been proposed. Aims. We seek to make ML-based atmospheric retrieval (1) more reliable and accurate with verified results, and (2) more flexible with respect to the underlying neural networks and the choice of the assumed noise models. Methods. First, we adopted flow matching posterior estimation (FMPE) as a new ML approach to atmospheric retrieval. FMPE maintains many advantages of NPE, but provides greater architectural flexibility and scalability. Second, we used importance sampling (IS) to verify and correct ML results, and to compute an estimate of the Bayesian evidence. Third, we conditioned our ML models on the assumed noise level of a spectrum (i.e., error bars), and thus made them adaptable to different noise models. Results. Both our noise-level-conditional FMPE and NPE models perform on a par with nested sampling across a range of noise levels when tested on simulated data. FMPE trains about three times faster than NPE and yields higher IS efficiencies. IS successfully corrects inaccurate ML results, identifies model failures via low efficiencies, and provides accurate estimates of the Bayesian evidence. Conclusions. FMPE is a powerful alternative to NPE for fast, amortized, and parallelizable atmospheric retrieval. IS can verify results, helping to build confidence in ML-based approaches, while also facilitating model comparison via the evidence ratio. Noise level conditioning allows design studies for future instruments to be scaled up; for example, in terms of the range of signal-to-noise ratios.

An adaptive optimal importance sampling method for efficiently calibrating augmented failure probability

An adaptive optimal importance sampling method for efficiently calibrating augmented failure probability

An Extension of the Unified Skew-Normal Family of Distributions and its Application to Bayesian Binary Regression

We consider the Bayesian binary regression model and we introduce a new class of distributions, the Perturbed Unified Skew-Normal ( pSUN , henceforth), which generalizes the Unified Skew-Normal ( SUN ) class. We show that the new class is conjugate to any binary regression model, provided that the link function may be expressed as a scale mixture of Gaussian CDFs. We discuss in detail the popular logit case, and we show that, when a logistic regression model is combined with a Gaussian prior, posterior summaries such as cumulants and normalizing constants can easily be obtained through the use of an importance sampling approach, opening the way to straightforward variable selection procedures. For more general prior distributions, the proposed methodology is based on a simple Gibbs sampler algorithm. We also claim that, in the p > n case, our proposal presents better performances - both in terms of mixing and accuracy - compared to the existing methods. We illustrate the performance through several simulation studies and two data analyses. Supplementary Materials for this article, including the R package pSUN , are available online.

Efficient Importance Variational Approximations for State Space Models

Variational methods are a potentially scalable estimation approach for state space models. However, existing methods are inaccurate or computationally infeasible for many state space models. This article proposes a variational approximation that is accurate and fast for any model with a closed-form measurement density function and a state transition distribution within the exponential family of distributions. Our approach constructs a variational approximation to the states that is close to the exact conditional posterior distribution of the states using insights from the efficient importance sampling literature. We show that our method can accurately and quickly estimate a multivariate Skellam stochastic volatility model with high-frequency tick-by-tick discrete price changes of four stocks.

Retrievals on NIRCam Transmission and Emission Spectra of HD 189733b with PLATON 6, a GPU Code for the JWST Era

We present the 2.4–5.0 μm JWST/NIRCam emission spectrum of HD 189733b, along with an independent re-reduction of the previously published transmission spectrum at the same wavelengths. We use an upgraded version of PLanetary Atmospheric Tool for Observer Noobs (PLATON) to retrieve atmospheric parameters from both geometries. In transit, we obtain [M/H] = 0.53−0.12+0.13 and C/O = 0.41−0.12+0.13 , assuming a power-law haze and equilibrium chemistry with methane depletion. In eclipse, we obtain [M/H] = 0.68−0.11+0.15 and C/O = 0.43−0.05+0.06 , assuming a clear atmosphere and equilibrium chemistry without methane depletion. These results are consistent with each other, and with a rerun of our previously published joint retrieval of Hubble Space Telescope and Spitzer transmission and emission spectra. Accounting for methane depletion decreases the C/O ratio by 0.14/0.04 (transmission/emission), but changing the limb cloud parameterization does not affect the C/O ratio by more than 0.06. We detect H2O, CO2, CO, and H2S in both the NIRCam transmission and emission spectra, find that methane is depleted on the terminator, and confirm with VULCAN that photochemistry is a potential cause of this depletion. We also find tentative (1.8σ) evidence of a dayside thermal inversion at millibar pressures. Finally, we take this opportunity to introduce a new version of PLATON. PLATON 6 supports GPU computation, speeding up the code up to 10×. It also supports free retrievals using both volume mixing ratio and centered-log ratio priors; emission from planetary surfaces of different compositions; updated opacities at improved resolution; and Pareto smoothed importance sampling leave-one-out cross-validation.