Sequential Monte Carlo Approach Research Articles

Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach

AbstractBayesian inversions followed by estimations of rare event probabilities are often needed to analyze groundwater hazards. Instead of focusing on the posterior distribution of model parameters, the main interest lies then in the distribution of a specific quantity of interest contingent upon these parameters. To address the associated methodological challenges, we introduce a two‐stage Sequential Monte Carlo approach. In the first stage, it generates particles that approximate the posterior distribution; in the second stage, it employs subset sampling techniques to assess the probability of the rare event of interest. By considering two hydrogeological problems of increasing complexity, we showcase the efficiency and accuracy of the resulting PostRisk‐SMC method for rare event probability estimation related to groundwater hazards. We compare the performance of the PostRisk‐SMC method with a traditional Monte Carlo approach that relies on Markov chain Monte Carlo samples. We showcase that our estimates align with those of the traditional method, but the coefficients of variation are notably lower for the same computational budget when targeting more rare events. Furthermore, we highlight that the PostRisk‐SMC method allows estimating rare event probabilities approaching one in a billion using less than one hundred thousand forward simulations. Even if the presented examples are related to groundwater hazards, the methodology is well‐suited for addressing a wide range of topics in the geosciences and beyond.

Sequential Monte Carlo with cross-validated neural networks for complexity of hyperbolic black hole solutions in 4D

This paper investigates the self-similar solutions of the Einstein-axion-dilaton configuration from type IIB string theory and the global SL(2,R) symmetry. We consider the Continuous Self Similarity (CSS), where the scale transformation is controlled by an SL(2, R) boost or hyperbolic translation. The solutions stay invariant under the combination of space-time dilation with internal SL(2,R) transformations. We develop a new formalism based on Sequential Monte Carlo (SMC) and artificial neural networks (NNs) to estimate the self-similar solutions to the equations of motion in the hyperbolic class in four dimensions. Due to the complex and highly nonlinear patterns, researchers typically have to use various constraints and numerical approximation methods to estimate the equations of motion; thus, they have to overlook the measurement errors in parameter estimation. Through a Bayesian framework, we incorporate measurement errors into our models to find the solutions to the hyperbolic equations of motion. It is well known that the hyperbolic class suffers from multiple solutions where the critical collapse functions have overlap domains for these solutions. To deal with this complexity, for the first time in literature on the axion-dilaton system, we propose the SMC approach to obtain the multi-modal posterior distributions. Through a probabilistic perspective, we confirm the deterministic α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} solutions available in the literature and determine all possible solutions that may occur due to measurement errors. We finally proposed the penalized Leave-One-Out Cross-validation (LOOCV) to combine the Bayesian NN-based estimates optimally. The approach enables us to determine the optimum weights while dealing with the co-linearity issue in the NN-based estimates and better predict the critical functions corresponding to multiple solutions of the equations of motion.

Optimal fusion‐based localization method for tracking of smartphone user in tall complex buildings

AbstractIn the event of a fire breaking out or in other complicated situations, a mobile computing solution combining the Internet of Things and wearable devices can actually assist tracking solutions for rescuing and evacuating people in multistory structures. Thus, it is crucial to increase the positioning technology's accuracy. The sequential Monte Carlo (SMC) approach is used in various applications such as target tracking and intelligent surveillance, which rely on smartphone‐based inertial data sequences. However, the SMC method has intrinsic flaws, such as sample impoverishment and particle degeneracy. A novel SMC approach is presented, which is built on the weighted differential evolution (WDE) algorithm. Sequential Monte Carlo approaches start with random particle placements and arrives at the desired distribution with a slower variance reduction, like in a high‐dimensional space, such as a multistory structure. Weighted differential evolution is included before the resampling procedure to guarantee the appropriate variety of the particle set, prevent the usage of an inadequate number of valid samples, and preserve smartphone user position accuracy. The values of the smartphone‐based sensors and BLE‐beacons are set as input to the SMC, which aids in fast approximating the posterior distributions, to speed up the particle congregation process in the proposed SMC‐based WDE approach. Lastly, the robustness and efficacy of the suggested technique more accurately reflect the actual situation of smartphone users. According to simulation findings, the suggested approach provides improved location estimation with reduced localization error and quick convergence. The results confirm that the proposed optimal fusion‐based SMC‐WDE scheme performs 9.92% better in terms of MAPE, 15.24% for the case of MAE, and 0.031% when evaluating based on the R2 Score.

A sequential Monte Carlo approach to estimate a time-varying reproduction number in infectious disease models: the Covid-19 case

Abstract The Covid-19 pandemic has required most countries to implement complex sequences of non-pharmaceutical interventions, with the aim of controlling the transmission of the virus in the population. To be able to take rapid decisions, a detailed understanding of the current situation is necessary. Estimates of time-varying, instantaneous reproduction numbers represent a way to quantify the viral transmission in real time. They are often defined through a mathematical compartmental model of the epidemic, like a stochastic SEIR model, whose parameters must be estimated from multiple time series of epidemiological data. Because of very high dimensional parameter spaces (partly due to the stochasticity in the spread models) and incomplete and delayed data, inference is very challenging. We propose a state-space formalization of the model and a sequential Monte Carlo approach which allow to estimate a daily-varying reproduction number for the Covid-19 epidemic in Norway with sufficient precision, on the basis of daily hospitalization and positive test incidences. The method was in regular use in Norway during the pandemics and appears to be a powerful instrument for epidemic monitoring and management.

Ideal parameter distribution in renewable integrated rapid charging electric vehicle station

ABSTRACT In this paper, we provide extensive modeling of fast-charging electric vehicle stations (FCEVS) allied to a grid integrated renewable energy sources (RES like hydro and solar) system considering an electric vehicle (EV) demand characteristics, state of charge (SOC), battery ratings, arrival, and departure time. This aids in maximizing the revenue and lowering the grid energy utilization. Investigations are carried with a novel meta-heuristic technique known as the emperor penguin optimization (EPO) algorithm, which is utilized to optimize the FCEVS parameters and maximize net present value (NPV). The investigations wih EPO has shown significant improvent of 1% with particle swarm optimization (PSO) and 1.25% with crow search algorithm (CSA). Also, studies are carried using a probabilistic demand distribution based on EV behaviors considering a sequential Monte-Carlo approach with hourly intervals. The acquired economic deliberations with EPO algorithm are compared with PSO, CSA, and EPO extracts maximum revenue. Simulations with FCEVS fed by grid, RES, and hybrid grid-RES reveal that FCEVS fed by hybrid grid-RES extracts the highest NPV. Further, 78.09% increase in NPV is observed with RES feeds the Grid over Grid feeds FCEVS alone, 25.23% hike of NPV is observed with both RES and battery storage system (BSS) over RES system, 10.56% increase with considering EVs arrival time and 2.3% increase with considering flow of EVs. Further, simulations with detailed modeling of FCEVS enhance NPV values over the hybrid grid-RES system.

A Divide and Conquer Sequential Monte Carlo Approach to High Dimensional Filtering

A Divide and Conquer Sequential Monte Carlo Approach to High Dimensional Filtering

Hamiltonian sequential Monte Carlo with application to consumer choice behavior

The practical use of nonparametric Bayesian methods requires the availability of efficient algorithms for posterior inference. The inherently serial nature of traditional Markov chain Monte Carlo (MCMC) methods imposes limitations on their efficiency and scalability. In recent years, there has been a surge of research activity devoted to developing alternative implementation methods that target parallel computing environments. Sequential Monte Carlo (SMC), also known as a particle filter, has been gaining popularity due to its desirable properties. SMC uses a genetic mutation-selection sampling approach with a set of particles representing the posterior distribution of a stochastic process. We propose to enhance the performance of SMC by utilizing Hamiltonian transition dynamics in the particle transition phase, in place of random walk used in the previous literature. We call the resulting procedure Hamiltonian Sequential Monte Carlo (HSMC). Hamiltonian transition dynamics have been shown to yield superior mixing and convergence properties relative to random walk transition dynamics in the context of MCMC procedures. The rationale behind HSMC is to translate such gains to the SMC environment. HSMC will facilitate practical estimation of models with complicated latent structures, such as nonparametric individual unobserved heterogeneity, that are otherwise difficult to implement. We demonstrate the behavior of HSMC in a challenging simulation study and contrast its favorable performance with SMC and other alternative approaches. We then apply HSMC to a panel discrete choice model with nonparametric consumer heterogeneity, allowing for multiple modes, asymmetries, and data-driven clustering, providing insights for consumer segmentation, individual level marketing, and price micromanagement.

Flexible and Robust Particle Tempering for State Space Models

Density tempering (also called density annealing) is a sequential Monte Carlo approach to Bayesian inference for general state models which is an alternative to Markov chain Monte Carlo. When applied to state space models, it moves a collection of parameters and latent states (which are called particles) through a number of stages, with each stage having its own target distribution. The particles are initially generated from a distribution that is easy to sample from, e.g. the prior; the target at the final stage is the posterior distribution. Tempering is usually carried out either in batch mode, involving all the data at each stage, or sequentially with observations added at each stage, which is called data tempering. Efficient Markov moves for generating the parameters and states for each stage of particle based density tempering are proposed. This allows the proposed SMC methods to increase (scale up) the number of parameters and states that can be handled. Most current methods use a pseudo-marginal Markov move step with the states “integrated out”, and the parameters generated by a random walk proposal; although this strategy is general, it can be very inefficient when the states or parameters are high dimensional. By adding batch tempering at each stage, previous methods are extended to make data tempering more robust to outliers and structural changes for models with intractable likelihoods. The performance of the proposed methods is evaluated using univariate stochastic volatility models with outliers and structural breaks, and high dimensional factor stochastic volatility models having many parameters and many latent states.11This article has an online supplement that contains additional technical details and empirical results.

Characterising the security of power system topologies through a combined assessment of reliability, robustness, and resilience

Electricity has a prominent role in modern economies; therefore, ensuring the availability of electricity supply should be a top priority for policymakers. The joint assessment of reliability, robustness, and resilience can be a useful criterion to characterise different topologies and improve the security of supply. This paper proposes a novel integrated analysis of these three attributes to quantify the security of power grid topologies. Hence, eight case studies with different topologies created using the IEEE 24-bus reliability test system were analysed. Reliability was evaluated by applying the sequential Monte Carlo approach, robustness was evaluated by simulating cascading failures, and resilience was evaluated by analysing recovery curves. The different indicators associated with each of the three evaluations were then calculated. The results obtained were discussed both graphically and quantitatively in a novel three-dimensional representation, where the importance of joint analysis was also highlighted. The proposed method can serve as an additional tool for planners to identify possible investments or improvements in power system topologies.

Fast and Numerically Stable Particle-Based Online Additive Smoothing: The AdaSmooth Algorithm

We present a novel sequential Monte Carlo approach to online smoothing of additive functionals in a very general class of path-space models. Hitherto, the solutions proposed in the literature suffer from either long-term numerical instability due to particle-path degeneracy or, in the case that degeneracy is remedied by particle approximation of the so-called backward kernel, high computational demands. In order to balance optimally computational speed against numerical stability, we propose to furnish a (fast) naive particle smoother, propagating recursively a sample of particles and associated smoothing statistics, with an adaptive backward-sampling-based updating rule which allows the number of (costly) backward samples to be kept at a minimum. This yields a new, function-specific additive smoothing algorithm, AdaSmooth, which is computationally fast, numerically stable and easy to implement. The algorithm is provided with rigorous theoretical results guaranteeing its consistency, asymptotic normality and long-term stability as well as numerical results demonstrating empirically the clear superiority of AdaSmooth to existing algorithms. Supplementary materials for this article are available online.

A Logistic Regression Approach to Field Estimation Using Binary Measurements

In this letter, we consider the problem of field estimation using binary measurements. Previous work has formulated the problem as a parameter estimation problem, which can be solved in an online manner using sequential Monte Carlo (SMC) techniques. In the current work, we consider an alternative approach to the parameter estimation problem based on online logistic regression. The developed algorithm is less computationally intensive than the SMC approach, while having more reliable estimation performance.

Modified Particle Filters for Detection of False Data Injection Attacks and State Estimation in Networked Nonlinear Systems

Networked control systems which transfer data over communication networks may suffer from malicious cyber attacks by injecting false data to the transferred information. Such attacks can cause performance degradation of the closed-loop system and the filtering problem. The sequential importance sampling (SIS) particle filtering (PF) methods employ the sequential Monte Carlo approach to estimate the generally non-Gaussian posterior probability density function (pdf) for Bayesian estimation of generally non-linear non-Gaussain systems. In this paper, it is firstly shown that with the normal SIS PF, the injected false data to the networked systems remains stealthy and therefore it is not possible to reduce the degrading effect of the attack on the estimation. However, with a modification in the proposal pdf, a modified SIS PF is then proposed which guarantees the attack detectability where the attacked measurements are incorporated in the particle generation process and thus the particles are updated and make the attack detectable. Using the derived thresholds and under small enough measurement noises, it is also proved that no false alarm occurs. After estimation of the attack value, the posterior pdf conditioned on truly detected attack leads to an estimation equivalent to the attack free SIS PF in terms of estimation bias and estimation covariance error. Finally, the accuracy of the presented concepts is demonstrated for a networked interconnected four-tank system.

Sequential Monte Carlo estimation for Present-Value model

ABSTRACT Multi-modal likelihood function of Present-Value model makes traditional estimation approach sensitive to initial values. In this article, we apply Sequential Monte Carlo (SMC) approach in the estimation of Present-Value model, since it is robust to multi-modality. Simulation studies show that SMC approach is preferable than Simulated Annealing (SA) since the latter is sensitive to initial values. Finally, we find that stock market return in the U.S. is more persistent than dividend growth rate according to our empirical study.

Sequential Dynamic Leadership Inference Using Bayesian Monte Carlo Methods

Hierarchy and leadership interactions commonly occur in animal groups, crowds of people, and in vehicle motions. Such interactions are often affected by one or more individuals who possess key domain information (e.g., final destination, environmental constraints, and best routes) or pertinent traits (e.g., better navigation, sensing, and decision making capabilities) compared with the rest of the group. This article presents a framework for the automatic identification of group structure and leadership from noisy sensory observations of tracked groups. Accordingly, a new leader-follower model is developed, which assumes the dynamics of the group to be a multivariate Ornstein-Uhlenbeck process with the designated leader(s) drifting to the destination and followers reverting to the leaders' state. Sequential Monte Carlo approaches, and specifically the sequential Markov chain Monte Carlo approach, are adopted to infer, probabilistically, the evolving leadership structure. A Rao-Blackwellisation scheme is employed such that the kinematic state of the objects in the group is inferred in closed form by Kalman filtering. Experiments show that the proposed techniques can successfully determine the leadership structures in challenging scenarios with a corresponding enhancement in tracking accuracy through direct consideration of the leadership interactions of the group.

Adaptive sequential Monte Carlo for posterior inference and model selection among complex geological priors

SUMMARY Bayesian model selection enables comparison and ranking of conceptual subsurface models described by spatial prior models, according to the support provided by available geophysical data. Deep generative neural networks can efficiently encode such complex spatial priors, thereby, allowing for a strong model dimensionality reduction that comes at the price of enhanced non-linearity. In this setting, we explore a recent adaptive sequential Monte Carlo (ASMC) approach that builds on annealed importance sampling (AIS); a method that provides both the posterior probability density function (PDF) and the evidence (a central quantity for Bayesian model selection) through a particle approximation. Both techniques are well suited to parallel computation and rely on importance sampling over a sequence of intermediate distributions, linking the prior and the posterior PDF. Each subsequent distribution is approximated by updating the particle weights and states, compared with the previous approximation, using a small pre-defined number of Markov chain Monte Carlo (MCMC) proposal steps. Compared with AIS, the ASMC method adaptively tunes the tempering between neighboring distributions and performs resampling of particles when the variance of the particle weights becomes too large. We evaluate ASMC using two different conceptual models and associated synthetic cross-hole ground penetrating radar tomography data. For the most challenging test case, we find that the ASMC method is faster and more reliable in locating the posterior PDF than state-of-the-art adaptive MCMC. The evidence estimates are found to be robust with respect to the choice of ASMC algorithmic variables and much less sensitive to the model proposal type than MCMC. The variance of the evidence estimates are best estimated by replication of ASMC runs, while approximations based on single runs provide comparable estimates when using a sufficient number of proposal steps in approximating each intermediate distribution.

Probabilistic Modeling and Inference for Sequential Space-Varying Blur Identification

The identification of parameters of spatially variant blurs given a clean image and its blurry noisy version is a challenging inverse problem of interest in many application fields, such as biological microscopy and astronomical imaging. In this paper, we consider a parametric model of the blur and introduce an 1D state-space model to describe the statistical dependence among the neighboring kernels. We apply a Bayesian approach to estimate the posterior distribution of the kernel parameters given the available data. Since this posterior is intractable for most realistic models, we propose to approximate it through a sequential Monte Carlo approach by processing all data in a sequential and efficient manner. Additionally, we propose a new sampling method to alleviate the particle degeneracy problem, which is present in approximate Bayesian filtering, particularly in challenging concentrated posterior distributions. The considered method allows us to process sequentially image patches at a reasonable computational and memory costs. Moreover, the probabilistic approach we adopt in this paper provides uncertainty quantification which is useful for image restoration. The practical experimental results illustrate the improved estimation performance of our novel approach, demonstrating also the benefits of exploiting the spatial structure the parametric blurs in the considered models.

A Semiautomatic Method for History Matching Using Sequential Monte Carlo

The aim of the history matching method is to locate nonimplausible regions of the parameter space of complex deterministic or stochastic models by matching model outputs with data. It does this via a series of waves where at each wave an emulator is fitted to a small number of training samples. An implausibility measure is defined which takes into account the closeness of simulated and observed outputs as well as emulator uncertainty. As the waves progress, the emulator becomes more accurate so that training samples are more concentrated on promising regions of the space and poorer parts of the space are rejected with more confidence. While history matching has proved to be useful, existing implementations are not fully automated, and some ad hoc choices are made during the process, which involves user intervention and is time consuming. This occurs especially when the nonimplausible region becomes small and it is difficult to sample this space uniformly to generate new training points. In this article we develop a sequential Monte Carlo (SMC) algorithm for implementing history matching that is semiautomated. Our novel SMC approach reveals that the history matching method yields a nonimplausible region that can be multimodal, highly irregular, and very difficult to sample uniformly. Our SMC approach offers a much more reliable sampling of the nonimplausible space, which requires additional computation compared to other approaches used in the literature.

Nonparametric Bayesian multiarmed bandits for single-cell experiment design

The problem of maximizing cell type discovery under budget constraints is a fundamental challenge for the collection and analysis of single-cell RNA-sequencing (scRNA-seq) data. In this paper we introduce a simple, computationally efficient and scalable Bayesian nonparametric sequential approach to optimize the budget allocation when designing a large-scale experiment for the collection of scRNA-seq data for the purpose of, but not limited to, creating cell atlases. Our approach relies on the following tools: (i) a hierarchical Pitman–Yor prior that recapitulates biological assumptions regarding cellular differentiation, and (ii) a Thompson sampling multiarmed bandit strategy that balances exploitation and exploration to prioritize experiments across a sequence of trials. Posterior inference is performed by using a sequential Monte Carlo approach which allows us to fully exploit the sequential nature of our species sampling problem. We empirically show that our approach outperforms state-of-the-art methods and achieves near-Oracle performance on simulated and scRNA-seq data alike. HPY-TS code is available at https://github.com/fedfer/HPYsinglecell.

An algorithm for non-parametric estimation in state–space models

State–space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state–space model is specified through a parametric model. However, the specification of such a parametric model may require an important modeling effort or may lead to models which are not flexible enough to reproduce all the complexity of the phenomenon of interest. In such situations, an appealing alternative consists in inferring the state–space model directly from the data using a non-parametric framework. The recent developments of powerful simulation techniques have permitted to improve the statistical inference for parametric state–space models. It is proposed to combine two of these techniques, namely the Stochastic Expectation–Maximization (SEM) algorithm and Sequential Monte Carlo (SMC) approaches, for non-parametric estimation in state–space models. The performance of the proposed algorithm is assessed though simulations on toy models and an application to environmental data is discussed.

Adaptive Tuning of Hamiltonian Monte Carlo Within Sequential Monte Carlo

Sequential Monte Carlo (SMC) samplers are an alternative to MCMC for Bayesian computation. However, their performance depends strongly on the Markov kernels used to rejuvenate particles. We discuss how to calibrate automatically (using the current particles) Hamiltonian Monte Carlo kernels within SMC. To do so, we build upon the adaptive SMC approach of Fearnhead and Taylor (2013), and we also suggest alternative methods. We illustrate the advantages of using HMC kernels within an SMC sampler via an extensive numerical study.