Sequential Monte Carlo Sampling Research Articles

Simulating multi-hazard event sets for life cycle consequence analysis

Abstract. In the context of natural hazard risk quantification and modeling of hazard interactions, some literature separates “Level I” (or occurrence) interactions from “Level II” (or consequence) interactions. The Level I interactions occur inherently due to the nature of the hazards, independently of the presence of physical assets. In such cases, one hazard event triggers or modifies the occurrence of another (e.g., flooding due to heavy rain, liquefaction and landslides triggered by an earthquake), thus creating a dependency between the features characterizing such hazard events. They differ from Level II interactions, which instead occur through impacts/consequences on physical assets/components and systems (e.g., accumulation of physical damage or social impacts due to earthquake sequences, landslides due to the earthquake-induced collapse of a retaining structure). Multi-hazard life cycle consequence (LCCon) analysis aims to quantify the consequences (e.g., repair costs, downtime, casualty rates) throughout a system’s service life and should account for both Level I and II interactions. The available literature generally considers Level I interactions – the focus of this study – mainly defining relevant taxonomies, often qualitatively, without providing a computational framework to simulate a sequence of hazard events incorporating the identified interrelations among them. This paper addresses this gap, proposing modeling approaches associated with different types of Level I interactions. It describes a simulation-based method for generating multi-hazard event sets (i.e., a sequence of hazard events and associated features throughout the system’s life cycle) based on the theory of competing Poisson processes. The proposed approach incorporates the different types of interactions in a sequential Monte Carlo sampling method. The method outputs multi-hazard event sets that can be integrated into LCCon frameworks to quantify interacting hazard consequences. An application incorporating several hazard interactions is presented to illustrate the potential of the proposed method.

Mathematical Modelling of Parasite Dynamics: A Stochastic Simulation-Based Approach and Parameter Estimation via Modified Sequential-Type Approximate Bayesian Computation

The development of mathematical models for studying newly emerging and re-emerging infectious diseases has gained momentum due to global events. The gyrodactylid-fish system, like many host-parasite systems, serves as a valuable resource for ecological, evolutionary, and epidemiological investigations owing to its ease of experimental manipulation and long-term monitoring. Although this system has an existing individual-based model, it falls short in capturing information about species-specific microhabitat preferences and other biological details for different Gyrodactylus strains across diverse fish populations. This current study introduces a new individual-based stochastic simulation model that uses a hybrid τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}-leaping algorithm to incorporate this essential data, enhancing our understanding of the complexity of the gyrodactylid-fish system. We compare the infection dynamics of three gyrodactylid strains across three host populations. A modified sequential-type approximate Bayesian computation (ABC) method, based on sequential Monte Carlo and sequential importance sampling, is developed. Additionally, we establish two penalised local-linear regression methods (based on L1 and L2 regularisations) for ABC post-processing analysis to fit our model using existing empirical data. With the support of experimental data and the fitted mathematical model, we address open biological questions for the first time and propose directions for future studies on the gyrodactylid-fish system. The adaptability of the mathematical model extends beyond the gyrodactylid-fish system to other host-parasite systems. Furthermore, the modified ABC methodologies provide efficient calibration for other multi-parameter models characterised by a large set of correlated or independent summary statistics.

Auxiliary two-filter particle smoothing for one generalized hidden Markov model

This paper develops two-filter particle smoothing (TFPS) algorithms for the nonlinear fixed-interval smoothing problem of one generalized hidden Markov model (GHMM), where the current observation depends not only on the current state, but also on one-step previous state. Firstly, by Bayesian approach, the two-filter smoothing (TFS) formula for GHMM is established to calculate smoothing densities. In this TFS formula, the backward information prediction density is generally not a density of the state. This results in a difficulty that the normal sequential Monte Carlo (SMC) sampling technique cannot be directly applied to design corresponding TFPS algorithms based on the TFS formula. To solve this difficulty, a generalized TFS formula for GHMM is then proposed by introducing a sequence of artificial densities. By combining this generalized TFS formula, SMC, and the auxiliary variable sampling technique, a basic auxiliary TFPS (ATFPS) algorithm with quadratic computational complexity is proposed, and a simplified ATFPS algorithm with linear computational complexity is further developed. Finally, the effectiveness and superiority of the two proposed ATFPS algorithms for GHMM are verified via simulation examples and real experimental data.

Data-Driven Bayesian Inference for Stochastic Model Identification of Nonlinear Aeroelastic Systems

The objective of this work is to propose a data-driven Bayesian inference framework to efficiently identify parameters and select models of nonlinear aeroelastic systems. The framework consists of the use of Bayesian theory together with advanced kriging surrogate models to effectively represent the limit cycle oscillation response of nonlinear aeroelastic systems. Three types of sampling methods, namely, Markov chain Monte Carlo, transitional Markov chain Monte Carlo, and the sequential Monte Carlo sampler, are implemented into Bayesian model updating. The framework has been demonstrated using a nonlinear wing flutter test rig. It is modeled by a two-degree-of-freedom aeroelastic system and solved by the harmonic balance methods. The experimental data of the flutter wing is obtained using control-based continuation techniques. The proposed methodology provided up to a 20% improvement in accuracy compared to conventional deterministic methods and significantly increased computational efficiency in the updating and uncertainty quantification processes. Transitional Markov chain Monte Carlo was identified as the optimal choice of sampling method for stochastic model identification. In selecting alternative nonlinear models, multimodal solutions were identified that provided a closer representation of the physical behavior of the complex aeroelastic system than a single solution.

Unlocking ensemble ecosystem modelling for large and complex networks.

The potential effects of conservation actions on threatened species can be predicted using ensemble ecosystem models by forecasting populations with and without intervention. These model ensembles commonly assume stable coexistence of species in the absence of available data. However, existing ensemble-generation methods become computationally inefficient as the size of the ecosystem network increases, preventing larger networks from being studied. We present a novel sequential Monte Carlo sampling approach for ensemble generation that is orders of magnitude faster than existing approaches. We demonstrate that the methods produce equivalent parameter inferences, model predictions, and tightly constrained parameter combinations using a novel sensitivity analysis method. For one case study, we demonstrate a speed-up from 108 days to 6 hours, while maintaining equivalent ensembles. Additionally, we demonstrate how to identify the parameter combinations that strongly drive feasibility and stability, drawing ecological insight from the ensembles. Now, for the first time, larger and more realistic networks can be practically simulated and analysed.

Inferring transmission routes for foot-and-mouth disease virus within a cattle herd using approximate Bayesian computation

To control an outbreak of an infectious disease it is essential to understand the different routes of transmission and how they contribute to the overall spread of the pathogen. With this information, policy makers can choose the most efficient methods of detection and control during an outbreak. Here we assess the contributions of direct contact and environmental contamination to the transmission of foot-and-mouth disease virus (FMDV) in a cattle herd using an individual-based model that includes both routes. Model parameters are inferred using approximate Bayesian computation with sequential Monte Carlo sampling (ABC-SMC) applied to data from transmission experiments and the 2007 epidemic in Great Britain. This demonstrates that the parameters derived from transmission experiments are applicable to outbreaks in the field, at least for closely related strains. Under the assumptions made in the model we show that environmental transmission likely contributes a majority of infections within a herd during an outbreak, although there is a lot of variation between simulated outbreaks. The accumulation of environmental contamination not only causes infections within a farm, but also has the potential to spread between farms via fomites. We also demonstrate the importance and effectiveness of rapid detection of infected farms in reducing transmission between farms, whether via direct contact or the environment.

The No-U-Turn Sampler as a Proposal Distribution in a Sequential Monte Carlo Sampler without Accept/Reject

The No-U-Turn Sampler as a Proposal Distribution in a Sequential Monte Carlo Sampler without Accept/Reject

Cost free hyper-parameter selection/averaging for Bayesian inverse problems with vanilla and Rao-Blackwellized SMC samplers

In Bayesian inverse problems, one aims at characterizing the posterior distribution of a set of unknowns, given indirect measurements. For non-linear/non-Gaussian problems, analytic solutions are seldom available: Sequential Monte Carlo samplers offer a powerful tool for approximating complex posteriors, by constructing an auxiliary sequence of densities that smoothly reaches the posterior. Often the posterior depends on a scalar hyper-parameter, for which limited prior information is available. In this work, we show that properly designed Sequential Monte Carlo (SMC) samplers naturally provide an approximation of the marginal likelihood associated with this hyper-parameter for free, i.e. at a negligible additional computational cost. The proposed method proceeds by constructing the auxiliary sequence of distributions in such a way that each of them can be interpreted as a posterior distribution corresponding to a different value of the hyper-parameter. This can be exploited to perform selection of the hyper-parameter in Empirical Bayes (EB) approaches, as well as averaging across values of the hyper-parameter according to some hyper-prior distribution in Fully Bayesian (FB) approaches. For FB approaches, the proposed method has the further benefit of allowing prior sensitivity analysis at a negligible computational cost. In addition, the proposed method exploits particles at all the (relevant) iterations, thus alleviating one of the known limitations of SMC samplers, i.e. the fact that all samples at intermediate iterations are typically discarded. We show numerical results for two distinct cases where the hyper-parameter affects only the likelihood: a toy example, where an SMC sampler is used to approximate the full posterior distribution; and a brain imaging example, where a Rao-Blackwellized SMC sampler is used to approximate the posterior distribution of a subset of parameters in a conditionally linear Gaussian model.

Multicanonical sequential Monte Carlo sampler for uncertainty quantification

Multicanonical sequential Monte Carlo sampler for uncertainty quantification

Parameter estimation from aggregate observations: a Wasserstein distance-based sequential Monte Carlo sampler.

In this work, we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a Bayesian inference framework. However, in many practical problems, only data at the aggregate level is available and as a result the likelihood function is not available, which poses a challenge for Bayesian methods. In particular, we consider the situation where the distributions of the particles are observed. We propose a Wasserstein distance (WD)-based sequential Monte Carlo sampler to solve the problem: the WD is used to measure the similarity between the observed and the simulated particle distributions and the sequential Monte Carlo samplers is used to deal with the sequentially available observations. Two real-world examples are provided to demonstrate the performance of the proposed method.

An improved sequential importance sampling method for reliability assessment of renewable power systems with energy storage

Due to the temporal coupling constraints of energy storage, the reliability of modern renewable power systems can no longer be assessed by non-sequential methods. However, the existing sequential methods cannot be combined with variance reduction methods as easily as the non-sequential ones. Hence, the power system reliability assessment is faced with incredible computational burden. In this paper, we propose an improved sequential importance sampling method to accelerate the computation of power system reliability indices. The proposed method is composed of two stages, namely the pre-simulation and main simulation stages. In the pre-simulation stage, we design a customized probability distribution parameter optimization process for load curves in the cross entropy based importance sampling method. In the main simulation stage, the derived probability distribution parameters in the pre-simulation stage are converted and further used to carry out a sequential Monte Carlo sampling process to efficiently estimate the reliability indices of renewable power systems with energy storage. The proposed method is validated by numerical tests performed on the modified IEEE-RTS 79 and IEEE-RTS 96 test systems, both of which are integrated with three wind farms, one photovoltaic station and one battery energy storage power station. Results show that the proposed method is much faster than existing sequential importance sampling methods in both test systems because of exploiting the acceleration potential of the load. Therefore, the proposed method can be used to assess the reliability of the renewable power systems with more energy storage devices in the future.

Sequential Ensemble Monte Carlo Sampler for On-Line Bayesian Inference of Time-Varying Parameter in Engineering Applications

Abstract Several on-line identification approaches have been proposed to identify parameters and evolution models of engineering systems and structures when sequential datasets are available via Bayesian inference. In this work, a robust and “tune-free” sampler is proposed to extend one of the sequential Monte Carlo implementations for the identification of time-varying parameters which can be assumed constant within each set of data collected but might vary across different sequences of datasets. The proposed approach involves the implementation of the affine-invariant Ensemble sampler in place of the Metropolis–Hastings sampler to update the samples. An adaptive-tuning algorithm is also proposed to automatically tune the step-size of the affine-invariant ensemble sampler which, in turn, controls the acceptance rate of the samples across iterations. Furthermore, a numerical investigation behind the existence of inherent lower and upper bounds on the acceptance rate, making the algorithm robust by design, is also conducted. The proposed method allows for the off-line and on-line identification of the most probable models under uncertainty. The proposed sampling strategy is first verified against the existing sequential Monte Carlo sampler in a numerical example. Then, it is validated by identifying the time-varying parameters and the most probable model of a nonlinear dynamical system using experimental data.

On Filtering and Smoothing Algorithms for Linear State-Space Models Having Quantized Output Data

The problem of state estimation of a linear, dynamical state-space system where the output is subject to quantization is challenging and important in different areas of research, such as control systems, communications, and power systems. There are a number of methods and algorithms to deal with this state estimation problem. However, there is no consensus in the control and estimation community on (1) which methods are more suitable for a particular application and why, and (2) how these methods compare in terms of accuracy, computational cost, and user friendliness. In this paper, we provide a comprehensive overview of the state-of-the-art algorithms to deal with state estimation subject to quantized measurements, and an exhaustive comparison among them. The comparison analysis is performed in terms of the accuracy of the state estimation, dimensionality issues, hyperparameter selection, user friendliness, and computational cost. We consider classical approaches and a new development in the literature to obtain the filtering and smoothing distributions of the state conditioned to quantized data. The classical approaches include the extended Kalman filter/smoother, the quantized Kalman filter/smoother, the unscented Kalman filter/smoother, and the sequential Monte Carlo sampling method, also called particle filter/smoother, with its most relevant variants. We also consider a new approach based on the Gaussian sum filter/smoother. Extensive numerical simulations—including a practical application—are presented in order to analyze the accuracy of the state estimation and the computational cost.

Adaptation of the tuning parameter in general Bayesian inference with robust divergence

We introduce a novel methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or gamma -divergence), indexed by tuning parameters. It is well known that the posterior density induced by robust divergence gives highly robust estimators against outliers if the tuning parameter is appropriately and carefully chosen. In a Bayesian framework, one way to find the optimal tuning parameter would be using evidence (marginal likelihood). However, we theoretically and numerically illustrate that evidence induced by the density power divergence does not work to select the optimal tuning parameter since robust divergence is not regarded as a statistical model. To overcome the problems, we treat the exponential of robust divergence as an unnormalisable statistical model, and we estimate the tuning parameter by minimising the Hyvarinen score. We also provide adaptive computational methods based on sequential Monte Carlo samplers, enabling us to obtain the optimal tuning parameter and samples from posterior distributions simultaneously. The empirical performance of the proposed method through simulations and an application to real data are also provided.

Land Surfaces at the Tipping‐Point for Water and Energy Balance Coupling

AbstractThe surface water and energy balances can be coupled or uncoupled depending on whether the evaporation regime is water‐limited or energy‐limited. As the landscape loses soil moisture during drydowns, a transition between the regimes may occur, which signifies a nonlinear change in water‐energy‐carbon coupling. Regions that switch often between these two regimes, that is, are dominated by neither regime, are particularly vulnerable to climate variability and change. To robustly identify these tipping points, we identify drydown events based on global soil moisture data sets from remote sensing. The event identification does not rely on precipitation information and is robust with respect to measurement noise. Then, the soil moisture thresholds delineating the evaporation regime transitions are determined by Sequential Monte Carlo Sampling and a two‐stage parametrization strategy. Based on the estimated soil moisture thresholds across the globe, we estimate observation‐based water availability indices which quantify the nonlinear controls of soil moisture on evaporation. This framework is tested and applied globally using Soil Moisture Active Passive soil moisture retrievals. Combined with a new tippling‐point metric that describes the frequency of evaporation regime transitions, we identify regions that switch often between different evaporation regimes at the global scale. Given unit shifts in soil moisture, these regions will experience the most change in how their surface water and energy are coupled.

How precisely can transporter mechanisms be determined from electrophysiology data? A Bayesian investigation.

Membrane transporter proteins perform the critical task of moving nutrients, ions, and potentially toxic molecules across a membrane and have biomedical significance as drug targets and biomarkers. The mechanisms of these proteins are not fully understood, in part due to the difficulty in directly measuring the individual biochemical reaction steps and also because of the possibility of multiple pathways. Solid-supported membrane (SSM)-based electrophysiology methods have recently emerged as an efficient means of collecting aggregate ion flux data from transporter proteins under various conditions. However, it is unknown how much information is contained within these datasets and how well the relevant biophysical parameters can be estimated. Here we explore a Bayesian pipeline using sequential Monte Carlo sampling to estimate kinetic parameter distributions using synthetic data motivated by SSM-based electrophysiology experiments for a 1:1 transporter: the distribution widths directly characterize the degree to which parameters are ‘identifiable.’ Based on assumed models of varying complexity, we examine the effects of different experimental conditions and combinations of experiments on parameter estimation and uncertainty. We hope a Bayesian pipeline can be used to aid the design of experiments for transporter mechanism discovery.

An Adaptive and Scalable Multi-Object Tracker Based on the Non-Homogeneous Poisson Process

This paper proposes a new adaptive framework for tracking multiple objects in the presence of data association uncertainty and heavy clutter, either with or without knowledge of the measurement rates and/or target shapes. Built upon an online Gibbs sequential Markov chain Monte Carlo sampling scheme, the adaptive tracker is Bayesian optimal and robust, requiring no additional approximations or measurement partition steps. With a non-homogeneous Poisson process measurement model, our tracker can tackle the data association task with linear computational complexity. Meanwhile, we study generalised inverse Gaussian and inverse Wishart distributions for modelling Poisson rates and object shapes, respectively; these prior models ensure closed-form full conditionals in our online Gibbs sampling steps, under which object states and shapes can be jointly estimated with associations and Poisson rates in a parallel fashion. Furthermore, a fast Rao-Blackwellisation scheme for linear Gaussian dynamics is designed and demonstrated to significantly improve both tracking efficiency and accuracy. We validate the efficacy of our method on real and simulated data.

Efficient Quasi-Bayesian Estimation of Affine Option Pricing Models Using Risk-Neutral Cumulants

We propose a general, accurate and fast econometric approach for the estimation of affine option pricing models. The algorithm belongs to the class of Laplace-Type Estimation (LTE) techniques and exploits Sequential Monte Carlo (SMC) methods. We employ functions of the risk-neutral cumulants given in closed form to marginalize latent states, and we address parameter estimation by designing a density tempered SMC sampler. We test our algorithm on simulated data by tackling the challenging inference problem of estimating an option pricing model which displays two stochastic volatility factors, allows for co-jumps between price and volatility, and stochastic jump intensity. Furthermore, we consider real data and estimate the model on a large panel of option prices. Numerical studies confirm the accuracy of our estimates and the superiority of the proposed approach compared to its natural benchmark.

Sequential Monte Carlo samplers to fit and compare insurance loss models

Insurance loss distributions are characterized by a high frequency of small claim amounts and a lower, but not insignificant, occurrence of large claim amounts. Composite models, which link two probability distributions, one for the ‘body’ and the other for the ‘tail’ of the loss distribution, have emerged in the actuarial literature to take this specificity into account. The parameters of these models summarize the distribution of the losses. One of them corresponds to the breaking point between small and large claim amounts. The composite models are usually fitted using maximum likelihood estimation. A Bayesian approach is considered in this work. Sequential Monte Carlo samplers are used to sample from the posterior distribution and compute the posterior model evidence to both fit and compare the competing models. The method is validated via a simulation study and illustrated on an insurance loss dataset.

FMCW-MIMO Radar-Based Pedestrian Trajectory Tracking Under Low- Observable Environments

Pedestrian trajectory perception is always a challenging task for autonomous urban driving since the weak echoes from pedestrians may be masked by strong background clutters, for example, road infrastructures and other vehicles. As a consequence, this article presents a frequency-modulated continuous wave-multiple input multiple output (FMCW-MIMO) radar-based trajectory tracking method to realize continuous pedestrian detection and tracking under low-observable environments. More specifically, the keystone transform-constant false alarm ratio (KT-CFAR) is first proposed to maximize the output signal-to-interference plus noise ratio (SINR) depending on the time–space correlations of a sequence of consecutive echoes, for the sake of improving the pedestrian detection probability under low-observable conditions. Then, the multiple signal classification (MUSIC) algorithm is employed to provide a high azimuth resolution to improve the multitarget resolving ability. After that, a pedestrian trajectory tracking framework is constructed by means of Bayesian theory and sequential Monte Carlo (SMC) sampling. Finally, simulation and experimental results show that the proposed method can obtain high-precision pedestrian trajectory tracking under low SINR conditions compared with conventional Kalman filter (KF)-based tracking methods.