Importance Sampling Research Articles

Religious coping and delinquent behaviors: Moderated mediation roles of religion affiliation and prosocial moral reasoning.

Religion has been shown to have a positive impact for developing adolescents; however, the processes underlying this relation are not well known. In his almighty prosocial theory, Anazonwu (Conceptualizing and testing almighty prosociality theory for a more peaceful world, SCOA Heritage Nigeria, 2017) proposed that the activation of learnt prosocial moral reasoning through religion enabled performance of prosocial peace behavior that will benefit society. Thus, religion coping enhances the development of prosocial reasoning which in turn propagate prosocial acts while reducing delinquent behaviors. Similarly, developmental system theory (Lerner, Developmental science, developmental systems, and contemporary theories of human development, John Wiley & Sons, 2006) assumed that in every individual three mechanisms: plasticity (potential to change), context (environment), and developmental regulation (learnable principles) interact to describe the direction of the transactions between individuals and their various embedded sociocultural context of development which will also determine other developmental outcomes. Based on these two theoretical assumptions, the present study examined whether prosocial moral reasoning (developmental regulation) was the mechanism in the negative correlation between religious coping (plasticity) and delinquent behaviors (outcome), and if religious affiliation(context) (Christianity and Islam) moderated these paths. We hypothesized that the link from prosocial moral reasoning to lower delinquent behaviors would be stronger for Muslim compared with Christian youth. These questions were tested among Nigerian adolescence, an important sample because of high interreligious and interethnic tension among youth in the country. 298 adolescents (Mean age = 15.03 years, SD = 1.76; male = 176, female = 122; 46.3% Muslim, 53.7% Christian) were sampled using questionnaires in senior secondary schools in Nigeria. Moderated mediation result shows that greater religious coping was linked with higher prosocial moral reasoning, which in turn predicted fewer delinquent behaviors. Religious coping interacted with religion affiliation to influence delinquent behavior; there was a stronger link between these two constructs for Muslim compared to Christian youth. Thus, interventions aiming to reduce youth delinquent behaviors should consider promoting prosocial moral reasoning, particularly among the various religions (i.e., Christian/Muslim) communities.

Bayesian Inference for Multiple Datasets

Estimating parameters for multiple datasets can be time consuming, especially when the number of datasets is large. One solution is to sample from multiple datasets simultaneously using Bayesian methods such as adaptive multiple importance sampling (AMIS). Here, we use the AMIS approach to fit a von Mises distribution to multiple datasets for wind trajectories derived from a Lagrangian Particle Dispersion Model driven from 3D meteorological data. A posterior distribution of parameters can help to characterise the uncertainties in wind trajectories in a form that can be used as inputs for predictive models of wind-dispersed insect pests and the pathogens of agricultural crops for use in evaluating risk and in planning mitigation actions. The novelty of our study is in testing the performance of the method on a very large number of datasets (>11,000). Our results show that AMIS can significantly improve the efficiency of parameter inference for multiple datasets.

Time varying reliability analysis of corroded gas pipelines using copula and importance sampling

Ensuring the safety of gas pipelines is crucial for the reliable and efficient transportation of natural gas. This study introduces a methodology for evaluating the time-varying reliability of corroded gas pipelines. The proposed approach employs both importance sampling and copula theory to effectively address the uncertainties associated with random variables involved and provide efficient estimates of failure probability. Small leak and burst failure modes are specifically investigated within this study. The methodology first establishes a step-by-step procedure for analysis. Subsequently, the study investigates the failure probability of corroded gas pipelines, taking into account both small leak and burst failures, under scenarios involving single and multiple defects. Furthermore, the study examines the influence of correlation strength and dependence structure among the involved random variables using the copula theory. Additionally, the generation of newly formed defects is thoroughly investigated, along with its impact on failure probability. Numerical examples are provided to evaluate the performance of the proposed methodology, comparing it with the benchmark failure probability estimated through Monte Carlo simulation. The results validate the precision and efficiency of the proposed methodology, while offering practical and insightful suggestions for reliability analysis of real-world gas pipelines.

FastHGNN: A New Sampling Technique for Learning with Hypergraph Neural Networks

Hypergraphs can represent higher-order relations among objects. Traditional hypergraph neural networks involve node-edge-node transform, leading to high computational cost and timing. The main aim of this paper is to propose a new sampling technique for learning with hypergraph neural networks. The core idea is to design a layer-wise sampling scheme for nodes and hyperedges to approximate the original hypergraph convolution. We rewrite hypergraph convolution in the form of double integral and leverage Monte Carlo to achieve a discrete and consistent estimator. In addition, we use importance sampling and finally derive feasible probability mass functions for both nodes and hyperedges in consideration of variance reduction, based on some assumptions. Notably, the proposed sampling technique allows us to handle large-scale hypergraph learning, which is not feasible with traditional hypergraph neural networks. Experiment results demonstrate that our proposed model keeps a good balance between running time and prediction accuracy.

Importance sampling method for Feldman-Cousins confidence intervals

In various high-energy physics contexts, such as neutrino-oscillation experiments, several assumptions underlying the typical asymptotic confidence interval construction are violated, such that one has to resort to computationally expensive methods like the Feldman-Cousins method for obtaining confidence intervals with proper statistical coverage. By construction, the computation of intervals at high confidence levels requires fitting millions or billions of pseudoexperiments, while wasting most of the computational cost on overly precise intervals at low confidence levels. In this work, a simple importance sampling method is introduced that reuses pseudoexperiments produced for all tested parameter values in a single mixture distribution. This results in a significant error reduction on the estimated critical values, especially at high confidence levels, and simultaneously yields a correct interpolation of these critical values between the parameter values at which the pseudoexperiments were produced. The theoretically calculated performance is demonstrated numerically using a simple example from the analysis of neutrino oscillations. The relationship to similar techniques applied in statistical mechanics and p-value computations is discussed. Published by the American Physical Society 2024

A physics and data co-driven surrogate modeling method for high-dimensional rare event simulation

This paper presents a physics and data co-driven surrogate modeling method for efficient rare event simulation of civil and mechanical systems with high-dimensional input uncertainties. The method fuses interpretable low-fidelity physical models with data-driven error corrections. The hypothesis is that a well-designed and well-trained simplified physical model can preserve salient features of the original model, while data-fitting techniques can fill the remaining gaps between the surrogate and original model predictions. The coupled physics-data-driven surrogate model is adaptively trained using active learning, aiming to achieve a high correlation and small bias between the surrogate and original model responses in the critical parametric region of a rare event. A final importance sampling step is introduced to correct the surrogate model-based probability estimations. Static and dynamic problems with input uncertainties modeled by random field and stochastic process are studied to demonstrate the proposed method.

A double-loop adaptive relevant vector machine combined with Harris Hawks optimization-based importance sampling

PurposeEnsuring the safety of structures is important. However, when a structure possesses both an implicit performance function and an extremely small failure probability, traditional methods struggle to conduct a reliability analysis. Therefore, this paper proposes a reliability analysis method aimed at enhancing the efficiency of rare event analysis, using the widely recognized Relevant Vector Machine (RVM).Design/methodology/approachDrawing from the principles of importance sampling (IS), this paper employs Harris Hawks Optimization (HHO) to ascertain the optimal design point. This approach not only guarantees precision but also facilitates the RVM in approximating the limit state surface. When the U learning function, designed for Kriging, is applied to RVM, it results in sample clustering in the design of experiment (DoE). Therefore, this paper proposes a FU learning function, which is more suitable for RVM.FindingsThree numerical examples and two engineering problem demonstrate the effectiveness of the proposed method.Originality/valueBy employing the HHO algorithm, this paper innovatively applies RVM in IS reliability analysis, proposing a novel method termed RVM-HIS. The RVM-HIS demonstrates exceptional computational efficiency, making it eminently suitable for rare events reliability analysis with implicit performance function. Moreover, the computational efficiency of RVM-HIS has been significantly enhanced through the improvement of the U learning function.

Ethraid: A Simple Method for Characterizing Long-period Companions Using Doppler, Astrometric, and Imaging Constraints

We present ethraid, an open-source Python package designed to measure the mass (m c ) and separation (a) of a bound companion from measurements covering a fraction of the orbital period. ethraid constrains m c and a by jointly modeling radial velocity, astrometric, and/or direct imaging data in a Bayesian framework. Partial orbit data sets, especially those with highly limited phase coverage, are represented well by a few method-specific summary statistics. By modeling these statistics rather than the original data, ethraid optimizes computational efficiency with minimal reduction in accuracy. ethraid uses importance sampling to efficiently explore the often broad posteriors that arise from partial orbits. The core computations of ethraid are implemented in Cython for speed. We validate ethraid's performance by using it to constrain the masses and separations of the planetary companions to HD 117207 and TOI-1694. We designed ethraid to be both fast and simple, as well as to give broad, “quick look” constraints on companion parameters using minimal data. ethraid is pip installable and available on Zenodo and GitHub.

Single-Loop Sampling for Estimating Failure-Probability Upper-Bound Function

Under random-interval mixed uncertainties of structures, failure-probability upper-bound function (FPUBF), which varies with the distribution parameters of random inputs, can not only provide the influence of distribution parameters on the failure-probability upper bound (FPUB), but also contribute to decoupling a reliability-based design optimization model. Although FPUBF can be estimated by repeatedly evaluating FPUBs at different distribution parameter realizations, it suffers from unaffordable computational cost resulting from this double-loop framework. To address this issue, this paper proposes a single-loop sampling strategy (SL) to estimate FPUBF at arbitrary realizations in the interested distribution parameter region. Instead of the huge computational cost of a double-loop framework, the SL estimates the entire FPUBF only by one simulation analysis. Moreover, importance sampling (IS) variance reduction technique is introduced, and a single-loop IS probability density function (PDF), or SL-IS-PDF, is constructed to more efficiently estimate FPUBF by reducing the required size of the candidate sample pool. For approximating the optimal SL-IS-PDF and identifying the states of candidate samples efficiently, the double-loop adaptive Kriging model of performance function is introduced to further reduce the number of performance function evaluations. A numerical example and two composite structure examples are employed to verify the accuracy, efficiency, and feasibility of the proposed methods.

VizNav: A Modular Off-Policy Deep Reinforcement Learning Framework for Vision-Based Autonomous UAV Navigation in 3D Dynamic Environments

Unmanned aerial vehicles (UAVs) provide benefits through eco-friendliness, cost-effectiveness, and reduction of human risk. Deep reinforcement learning (DRL) is widely used for autonomous UAV navigation; however, current techniques often oversimplify the environment or impose movement restrictions. Additionally, most vision-based systems lack precise depth perception, while range finders provide a limited environmental overview, and LiDAR is energy-intensive. To address these challenges, this paper proposes VizNav, a modular DRL-based framework for autonomous UAV navigation in dynamic 3D environments without imposing conventional mobility constraints. VizNav incorporates the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm with Prioritized Experience Replay and Importance Sampling (PER) to improve performance in continuous action spaces and mitigate overestimations. Additionally, VizNav employs depth map images (DMIs) to enhance visual navigation by accurately estimating objects’ depth information, thereby improving obstacle avoidance. Empirical results show that VizNav, by leveraging TD3, improves navigation, and the inclusion of PER and DMI further boosts performance. Furthermore, the deployment of VizNav across various experimental settings confirms its flexibility and adaptability. The framework’s architecture separates the agent’s learning from the training process, facilitating integration with various DRL algorithms, simulation environments, and reward functions. This modularity creates a potential to influence RL simulation in various autonomous navigation systems, including robotics control and autonomous vehicles.

Enhancing Spatiotemporal Resampling with a Novel MIS Weight

AbstractIn real‐time rendering, optimizing the sampling of large‐scale candidates is crucial. The spatiotemporal reservoir resampling (ReSTIR) method provides an effective approach for handling large candidate samples, while the Generalized Resampled Importance Sampling (GRIS) theory provides a general framework for resampling algorithms. However, we have observed that when using the generalized multiple importance sampling (MIS) weight in previous work during spatiotemporal reuse, variances gradually amplify in the candidate domain when there are significant differences. To address this issue, we propose a new MIS weight suitable for resampling that blends samples from different sampling domains, ensuring convergence of results as the proportion of non‐canonical samples increases. Additionally, we apply this weight to temporal resampling to reduce noise caused by scene changes or jitter. Our method effectively reduces energy loss in the biased version of ReSTIR DI while incurring no additional overhead, and it also suppresses artifacts caused by a high proportion of temporal samples. As a result, our approach leads to lower variance in the sampling results.

Optimal bipartite graph matching-based goal selection for policy-based hindsight learning

The sparse reward problem stands as a significant challenge in the field of reinforcement learning. Hindsight Experience Replay (HER) addresses this by goal relabeling, allowing the agent to learn from unsuccessful experiences. Some studies combine policy gradient methods with HER, resulting in policy-based hindsight learning algorithms. However, Policy-based hindsight learning involves the use of importance sampling, where the distribution of hindsight goals and the distribution of desired goals contribute to the computation of importance weights. When there is a significant difference between the two distributions, importance weights may become skewed, thereby impacting the evaluation of the policy and leading to suboptimal policies. To address this, we propose modeling the goal selection as an optimization problem for distribution matching. After we augment the original desired goals using Kernel Density Estimation (KDE), we further convert the optimization problem for distribution matching into a bipartite graph matching problem that minimizes the sum of weights. Our optimal bipartite graph matching-based hindsight goal selection method can select hindsight goals that are the most closely aligned with the original goals. Experimental results show that algorithms combined with the optimal bipartite graph matching-based hindsight goal selection outperform the original algorithms. Visualizations also demonstrate the superiority of our method in selecting hindsight goals.

Occupation time of a system of Brownian particles on the line with steplike initial condition.

We consider a system of noninteracting Brownian particles on the line with steplike initial condition and study the statistics of the occupation time on the positive half-line. We demonstrate that even at large times, the behavior of the occupation time exhibits long-lasting memory effects of the initialization. Specifically, we calculate the mean and the variance of the occupation time, demonstrating that the memory effects in the variance are determined by a generalized compressibility (or Fano factor), associated with the initial condition. In the particular case of the uncorrelated uniform initial condition we conduct a detailed study of two probability distributions of the occupation time: annealed (averaged over all possible initial configurations) and quenched (for a typical configuration). We show that at large times both the annealed and the quenched distributions admit large deviation form and we compute analytically the associated rate functions. We verify our analytical predictions via numerical simulations using importance sampling Monte Carlo strategy.

Distance and T-square sampling for spatial measures of tree diversity

Distance sampling and its statistically improved variant, T-square sampling, are important sampling methods in plant ecology. They have often been applied in the context of plant density estimations and are comparatively easy to implement, since they intuitively follow the nearest-neighbour principle and thus do not require the layout of sample plots. Previous research studying distance sampling suggested that T-square sampling may also lead to an improved estimation of spatial tree diversity indices. We simulated distance and T-square sampling in six large fully mapped forest areas for seven tree diversity indices of which some competed for the same diversity aspect, i.e. tree location (dispersion), tree species and tree size diversity. Our results demonstrated that both distance and T-square sampling are indeed robust methods for sampling spatial measures of tree diversity. The sample size required for a sampling error of 10% does not exceed 20% of the total number of trees in a sampling area. T-square sampling has the ability to adapt to different spatial patterns of tree locations and this ability is key to the way the method controls estimation bias. The sample size required for species mingling and size differentiation clearly depends on the underlying spatial tree pattern in the sampling area. With most diversity indices, sample size reductions between 0.06% and 40% could be achieved by the application of T-square sampling compared to traditional distance sampling. All other conditions being equal, we could identify the uniform angle index, the species mingling index and the size differentiation index as those diversity indices achieving lower sampling error values than their competitors. For tree density estimations the Diggle and Byth estimators performed best. Based on our results, T-square sampling can be considered a robust sampling method for spatial tree diversity indices that is easy to apply in the field.

Alchemical Enhanced Sampling with Optimized Phase Space Overlap.

An alchemical enhanced sampling (ACES) method has recently been introduced to facilitate importance sampling in free energy simulations. The method achieves enhanced sampling from Hamiltonian replica exchange within a dual topology framework while utilizing new smoothstep softcore potentials. A common sampling problem encountered in lead optimization is the functionalization of aromatic rings that exhibit distinct conformational preferences when interacting with the protein. It is difficult to converge the distribution of ring conformations due to the long time scale of ring flipping events; however, the ACES method addresses this issue by modeling the syn and anti ring conformations within a dual topology. ACES thereby samples the conformer distributions by alchemically tunneling between states, as opposed to traversing a physical pathway with a high rotational barrier. We demonstrate the use of ACES to overcome conformational sampling issues involving ring flipping in ML300-derived noncovalent inhibitors of SARS-CoV-2 Main Protease (Mpro). The demonstrations explore how the use of replica exchange and the choice of softcore selection affects the convergence of the ring conformation distributions. Furthermore, we examine how the accuracy of the calculated free energies is affected by the degree of phase space overlap (PSO) between adjacent states (i.e., between neighboring λ-windows) and the Hamiltonian replica exchange acceptance ratios. Both of these factors are sensitive to the spacing between the intermediate states. We introduce a new method for choosing a schedule of λ values. The method analyzes short "burn-in" simulations to construct a 2D map of the nonlocal PSO. The schedule is obtained by optimizing an alchemical pathway on the 2D map that equalizes the PSO between the λ intervals. The optimized phase space overlap λ-spacing method (Opt-PSO) leads to more numerous end-to-end single passes and round trips due to the correlation between PSO and Hamiltonian replica exchange acceptance ratios. The improved exchange statistics enhance the efficiency of ACES method. The method has been implemented into the FE-ToolKit software package, which is freely available.

On the Statistical Mechanics of Mass Accommodation at Liquid-Vapor Interfaces.

We propose a framework for describing the dynamics associated with the adsorption of small molecules to liquid-vapor interfaces using an intermediate resolution between traditional continuum theories that are bereft of molecular detail and molecular dynamics simulations that are replete with them. In particular, we develop an effective single particle equation of motion capable of describing the physical processes that determine thermal and mass accommodation probabilities. The effective equation is parametrized with quantities that vary through space away from the liquid-vapor interface. Of particular importance in describing the early time dynamics is the spatially dependent friction, for which we propose a numerical scheme to evaluate from molecular simulation. Taken together with potentials of mean force computable with importance sampling methods, we illustrate how to compute the mass accommodation coefficient and residence time distribution. Throughout, we highlight the case of ozone adsorption in aqueous solutions and its dependence on electrolyte composition.

Sequential Monte Carlo with adaptive lookahead support for improved importance sampling

Sequential Monte Carlo with adaptive lookahead support for improved importance sampling

RPEM: Randomized Monte Carlo parametric expectation maximization algorithm.

Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis-Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi-Random Parametric Expectation Maximization (QRPEM) for a realistic two-compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log-normal cases.

Improved hierarchical Bayesian modeling framework with arbitrary polynomial chaos for probabilistic model updating

Bayesian finite element model updating techniques have found widespread application in the structural health monitoring. The conventional Bayesian modeling framework (CBMF) identifies the posterior distribution of structural parameters using data from a single experiment. However, structural parameters exhibit variability due to changes in environmental or experimental conditions, an aspect overlooked by CBMF. In recent years, the hierarchical Bayesian modeling framework (HBMF) has gradually attracted attention. This framework incorporates an additional layer of hyperparameters and utilizes multiple sets of experimental data to describe the variability in structural parameters caused by changes in experimental conditions. Unfortunately, the increase in hyperparameters and data size leads the HBMF to face the dilemma of exceedingly high computational costs. To address this issue, this study proposes an improved hierarchical Bayesian modeling framework (IHBMF). To enhance the computational efficiency of IHBMF, the importance sampling method is employed to simplify the computation of the likelihood function for hyperparameters. Subsequently, a surrogate model based on arbitrary polynomial chaos expansion is introduced to further reduce the computational cost of IHBMF. The framework's accuracy and efficiency were validated through analysis of a simply supported beam and a steel pedestrian bridge. The results demonstrate that IHBMF not only delivers a more accurate quantification of structural parameter uncertainty than CBMF but also exhibits higher computational efficiency compared to HBMF, showcasing its superior capability in structural health monitoring applications.

A distributed particle filter with sampling-based consensus density fusion for speaker tracking in distributed microphone networks

This paper proposes a novel distributed particle filter with sampling-based consensus density fusion for speaker tracking in distributed microphone networks (DMNs). Firstly, to combat the reverberation and ambient noise, multi-hypothesis likelihood model is applied to describe the likelihood distribution in the state-space model of speaker tracking problem. Then, the sequential importance resampling (SIR) is performed on each node to obtain the local posteriors of the state vector of the speaker. Since the non-Gaussian noise and the reverberation may make local posteriors presenting non-Gaussian and multi-modal characters, in this paper, the local posterior densities are approximated by Gaussian mixtures whose parameters are further transmitted to neighboring nodes to complete the distributed fusion based on the consensus method. We investigate a novel adaptive multiple importance sampling (AMIS) algorithm combining parallel tempering Monte Carlo (PTMC) samplers to achieve the sampling-based consensus density fusion of the non-Gaussian local posteriors and estimate the global posterior locally on each node. At last, the optimal global estimation of the speaker state vector could be calculated by using the estimated global posterior on each node in DMNs. Simulation and real-world recording experiment results show that the proposed speaker tracking method exhibits satisfactory tracking performance under reverberant and noisy environments. Moreover, it is easy and feasible to extend the proposed tracking algorithm to solve the multi-speaker tracking problem.