Monte Carlo Estimation Research Articles

Laplace-based strategies for Bayesian optimal experimental design with nuisance uncertainty

Finding the optimal design of experiments in the Bayesian setting typically requires estimation and optimization of the expected information gain functional. This functional consists of one outer and one inner integral, separated by the logarithm function applied to the inner integral. When the mathematical model of the experiment contains uncertainty about the parameters of interest and nuisance uncertainty, (i.e., uncertainty about parameters that affect the model but are not themselves of interest to the experimenter), two inner integrals must be estimated. Thus, the already considerable computational effort required to determine good approximations of the expected information gain is increased further. The Laplace approximation has been applied successfully in the context of experimental design in various ways, and we propose two novel estimators featuring the Laplace approximation to alleviate the computational burden of both inner integrals considerably. The first estimator applies Laplace’s method followed by a Laplace approximation, introducing a bias. The second estimator uses two Laplace approximations as importance sampling measures for Monte Carlo approximations of the inner integrals. Both estimators use Monte Carlo approximation for the remaining outer integral estimation. We provide four numerical examples demonstrating the applicability and effectiveness of our proposed estimators.

Object-Oriented Zero-Information-Optimised Product of Monte Carlo Integrations

Abstract We propose an object-oriented Monte Carlo framework for computation of definite integrals with a primary focus on generality and simplicity, improving in find points existing software libraries. We introduce an optimised sampling method for a product of Monte Carlo integrations. The method does not require any a-priori knowledge of the integrands or the integration domains, and can be combined with other optimisation methods. Using our framework, we implement a naive uniform sampling method and the optimised one, and empirically compare them on the Monte Carlo computation of volumes of N-dimensional balls. The experiments confirm our theoretical expectations.

Bayesian Inference for Long Memory Stochastic Volatility Models

We explore the application of integrated nested Laplace approximations for the Bayesian estimation of stochastic volatility models characterized by long memory. The logarithmic variance persistence in these models is represented by a Fractional Gaussian Noise process, which we approximate as a linear combination of independent first-order autoregressive processes, lending itself to a Gaussian Markov Random Field representation. Our results from Monte Carlo experiments indicate that this approach exhibits small sample properties akin to those of Markov Chain Monte Carlo estimators. Additionally, it offers the advantages of reduced computational complexity and the mitigation of posterior convergence issues. We employ this methodology to estimate volatility dependency patterns for both the SP&500 index and major cryptocurrencies. We thoroughly assess the in-sample fit and extend our analysis to the construction of out-of-sample forecasts. Furthermore, we propose multi-factor extensions and apply this method to estimate volatility measurements from high-frequency data, underscoring its exceptional computational efficiency. Our simulation results demonstrate that the INLA methodology achieves comparable accuracy to traditional MCMC methods for estimating latent parameters and volatilities in LMSV models. The proposed model extensions show strong in-sample fit and out-of-sample forecast performance, highlighting the versatility of the INLA approach. This method is particularly advantageous in high-frequency contexts, where the computational demands of traditional posterior simulations are often prohibitive.

A novel conditional generative model for efficient ensemble forecasts of state variables in large-scale geological carbon storage

Integrating monitoring data to efficiently update reservoir pressure and CO2 plume distribution forecasts presents a significant challenge in geological carbon storage (GCS) applications. Inverse modeling techniques are commonly used to fuse observational data and refine reservoir model parameters, thereby improving state variable forecasts. However, these techniques often rely on linear or Gaussian assumptions, which can limit their effectiveness in accurately predicting state variables. Moreover, simulating large-scale three-dimensional (3D) GCS problems is computationally expensive, making iterative runs in inverse problems prohibitive. To address these challenges, we propose a conditional generative model utilizing the score-based diffusion method for real-time 3D pressure and saturation field distribution predictions. Our approach involves solving the score function with a mini-batch-based Monte Carlo estimator to generate labeled data. This data is subsequently employed to train a fully connected neural network, enabling it to learn the conditional sample generator within a supervised learning framework. This method enables the rapid generation of a large ensemble of predictions, facilitating comprehensive uncertainty quantification of state variables. We applied our method to forecast the dynamic 3D distributions of pressure and saturation fields over a 30-year injection period. The statistical assessment with low root mean square error (RMSE) values demonstrates that our method can accurately predict the spatiotemporal distributions of both pressure and saturation fields. Moreover, the developed conditional generative model shows high computational efficiency by generating 100 ensemble forecasts of 3D state variables in less than 10 min. The consistency between ensemble averages and ground truth values further illustrates the model’s capability to capture state variable dynamics during the CO2 plume injection process. Notably, the ground truth values fall within the ensemble forecasts, indicating that our uncertainty quantification effectively captures variability and potential noise in the observations. Thus, the developed conditional generative model proves to be a more efficient, accurate, and practical tool for GCS applications, facilitating timely risk analysis and informed decision-making.

A computationally efficient algorithm to leverage average information REML for (co)variance component estimation in the genomic era

BackgroundMethods for estimating variance components (VC) using restricted maximum likelihood (REML) typically require elements from the inverse of the coefficient matrix of the mixed model equations (MME). As genomic information becomes more prevalent, the coefficient matrix of the MME becomes denser, presenting a challenge for analyzing large datasets. Thus, computational algorithms based on iterative solving and Monte Carlo approximation of the inverse of the coefficient matrix become appealing. While the standard average information REML (AI-REML) is known for its rapid convergence, its computational intensity imposes limitations. In particular, the standard AI-REML requires solving the MME for each VC, which can be computationally demanding, especially when dealing with complex models with many VC. To bridge this gap, here we (1) present a computationally efficient and tractable algorithm, named the augmented AI-REML, which facilitates the AI-REML by solving an augmented MME only once within each REML iteration; and (2) implement this approach for VC estimation in a general framework of a multi-trait GBLUP model. VC estimation was investigated based on the number of VC in the model, including a two-trait, three-trait, four-trait, and five-trait GBLUP model. We compared the augmented AI-REML with the standard AI-REML in terms of computing time per REML iteration. Direct and iterative solving methods were used to assess the advances of the augmented AI-REML.ResultsWhen using the direct solving method, the augmented AI-REML and the standard AI-REML required similar computing times for models with a small number of VC (the two- and three-trait GBLUP model), while the augmented AI-REML demonstrated more notable reductions in computing time as the number of VC in the model increased. When using the iterative solving method, the augmented AI-REML demonstrated substantial improvements in computational efficiency compared to the standard AI-REML. The elapsed time of each REML iteration was reduced by 75%, 84%, and 86% for the two-, three-, and four-trait GBLUP models, respectively.ConclusionsThe augmented AI-REML can considerably reduce the computing time within each REML iteration, particularly when using an iterative solver. Our results demonstrate the potential of the augmented AI-REML as an appealing approach for large-scale VC estimation in the genomic era.

Practical Implementation of Advanced Causal Inference Method: Development of an R Package for Bayesian Marginal Structural Models with Time-Varying Treatment

Background: Observational studies offer a viable, efficient, and low-cost design to readily gather evidence on exposure effects. Although more practical, the exposure mechanism is non-randomized and causal inference methods are required to draw causal conclusions. Objectives: Bayesian approaches to causal inference have unique estimation features that are useful in many settings; however, there is a lack of open-access software packages to carry out these analyses. Our project seeks to address this gap by developing a user-friendly R package named “bayesmsm” for the implementation of the Bayesian Marginal Structural Models for longitudinal observational data with extensions to handle right-censoring which is common for longitudinal health data. This R package provides an elegant approach to conduct Bayesian causal inference with time-varying exposure and confounding. Methods: We use simulated datasets to assess the performance of the package and to illustrate its use. This package first implements Bayesian parametric treatment assignment weight estimation through Markov Chain Monte Carlo (MCMC) computation. It then uses Bayesian non-parametric bootstrap to maximize the utility function with respect to the causal effect. The bootstrap calculation process was optimized for performance through parallel computing. The package has additional features, including handling right-censored data and generating analysis summaries and visualizations. Results: Using simulated datasets with and without right-censoring, the subject-specific treatment assignment weights were estimated using the package's weight estimation functions. The Bayesian posterior bootstrap results were further visualized by functions built within this package. Conclusions: The “bayesmsm” package provides a reliable tool to implement complex Bayesian Marginal Structural Model analysis. Future work will focus on extending this package to handle time-to-event data.

Multilevel importance sampling for rare events associated with the McKean–Vlasov equation

This work combines multilevel Monte Carlo with importance sampling to estimate rare-event quantities that can be expressed as the expectation of a Lipschitz observable of the solution to a broad class of McKean–Vlasov stochastic differential equations. We extend the double loop Monte Carlo (DLMC) estimator introduced in this context in Ben Rached et al. (Stat Comput, 2024. https://doi.org/10.1007/s11222-024-10497-3) to the multilevel setting. We formulate a novel multilevel DLMC estimator and perform a comprehensive cost-error analysis yielding new and improved complexity results. Crucially, we devise an antithetic sampler to estimate level differences guaranteeing reduced computational complexity for the multilevel DLMC estimator compared with the single-level DLMC estimator. To address rare events, we apply the importance sampling scheme, obtained via stochastic optimal control in Ben Rached et al. (2024), over all levels of the multilevel DLMC estimator. Combining importance sampling and multilevel DLMC reduces computational complexity by one order and drastically reduces the associated constant compared to the single-level DLMC estimator without importance sampling. We illustrate the effectiveness of the proposed multilevel DLMC estimator on the Kuramoto model from statistical physics with Lipschitz observables, confirming the reduced complexity from O(TOLr-4)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}(\ extrm{TOL}_{\ extrm{r}}^{-4})}$$\\end{document} for the single-level DLMC estimator to O(TOLr-3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}(\ extrm{TOL}_{\ extrm{r}}^{-3})}$$\\end{document} while providing a feasible estimate of rare-event quantities up to prescribed relative error tolerance TOLr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{TOL}_{\ extrm{r}}$$\\end{document}.

Cyber attacks detection and mitigation in hybrid power system using type-2 fuzzy controller

Abstract This paper presents a novel control technique using Fuzzy Type-2 controller for regulating the frequency deviations in an independent Hybrid Power System (HPS). The HPS comprises of a wind system and a solar photovoltaic (PV) system as primary energy sources, along with Fuel Cells (FCs) as additional generation systems and Double Layer Capacitor (DLC) Banks as storage devices to meet the load demand. The frequency variations occur in the HPS due to the intermittency in power outputs from the primary sources, the load changes as well as any attacks in the system. The frequency regulation is achieved by effective coordination control of FC and DLC with the aid of a Fuzzy Type-2 controller and a high pass filter (HPF). The DLC technology adequately satisfies the residual power of hybrid systems resulting from the slow dynamics of FCs. The Fuzzy Type-2 controller is trained using an input-output data set of a PID controller whose gains are tuned to their optimal values using Monte-Carlo state estimators. The proposed system is simulated using real weather data to validate the capability of the Hybrid Power System (HPS) in supplying isolated loads while maintaining power frequency balance conditions. Also the HPS is subjected to attacks in daily load variation and the results are compared with the system without attacks. The simulation results show that the peak over shoots are reduced considerably but the settling time is 0.2 s in the system with no attacks where as the settling time is prolonged to 1.2 s with the attacks. This paper demonstrates the effectiveness of the Fuzzy Type-2 controller for the coordination control of DLC and FC to achieve generation-load balance condition in comparison with that of the PID controller for HPS system with and without attacks.

Regularized Bayesian algorithms for Q-matrix inference based on saturated cognitive diagnosis modelling.

Q-matrices are crucial components of cognitive diagnosis models (CDMs), which are used to provide diagnostic information and classify examinees according to their attribute profiles. The absence of an appropriate Q-matrix that correctly reflects item-attribute relationships often limits the widespread use of CDMs. Rather than relying on expert judgment for specification and post-hoc methods for validation, there has been a notable shift towards Q-matrix estimation by adopting Bayesian methods. Nevertheless, their dependency on Markov chain Monte Carlo (MCMC) estimation requires substantial computational burdens and their exploratory tendency is unscalable to large-scale settings. As a scalable and efficient alternative, this study introduces the partially confirmatory framework within a saturated CDM, where the Q-matrix can be partially defined by experts and partially inferred from data. To address the dual needs of accuracy and efficiency, the proposed framework accommodates two estimation algorithms-an MCMC algorithm and a Variational Bayesian Expectation Maximization (VBEM) algorithm. This dual-channel approach extends the model's applicability across a variety of settings. Based on simulated and real data, the proposed framework demonstrated its robustness in Q-matrix inference.

Gaussian Particle Filtering for Nonlinear Systems With Heavy-Tailed Noises: A Progressive Transform-Based Approach.

The Gaussian particle filter (GPF) is a type of particle filter that employs the Gaussian filter approximation as the proposal distribution. However, the linearization errors are introduced during the calculation of the proposal distribution. In this article, a progressive transform-based GPF (PT-GPF) is proposed to solve this problem. First, a progressive transformation is applied to the measurement model to circumvent the necessity of linearization in the calculation of the proposal distribution, thereby ensuring the generation of optimal Gaussian proposal distributions in sense of linear minimum mean-square error (LMMSE). Second, to mitigate the potential impact of outliers, a supplementary screening process is employed to enhance the Monte Carlo approximation of the posterior probability density function. Finally, simulations of a target tracking example demonstrate the effectiveness and superiority of the proposed method.

An R Package for Nonparametric Inference on Dynamic Populations with Infinitely Many Types.

Fleming-Viot diffusions are widely used stochastic models for population dynamics that extend the celebrated Wright-Fisher diffusions. They describe the temporal evolution of the relative frequencies of the allelic types in an ideally infinite panmictic population, whose individuals undergo random genetic drift and at birth can mutate to a new allelic type drawn from a possibly infinite potential pool, independently of their parent. Recently, Bayesian nonparametric inference has been considered for this model when a finite sample of individuals is drawn from the population at several discrete time points. Previous works have fully described the relevant estimators for this problem, but current software is available only for the Wright-Fisher finite-dimensional case. Here, we provide software for the general case, overcoming some nontrivial computational challenges posed by this setting. The R package FVDDPpkg efficiently approximates the filtering and smoothing distribution for Fleming-Viot diffusions, given finite samples of individuals collected at different times. A suitable Monte Carlo approximation is also introduced in order to reduce the computational cost.

Expected constraints on Phobos interior from the MMX gravity and rotation observations

The origin of the Martian moons is still uncertain, and knowledge about their interior could provide support to some of its leading theories. In preparation for the JAXA Martian Moons eXploration (MMX) mission, we review our current knowledge on the interior of Phobos, and provide synthetic tests showing how the gravity and rotation determination could allow the detection of specific interior-structure properties. The inversion of the geodetic observables for the retrieval of the internal mass distribution of a set of synthetic interior models is performed via non-linear least-squares, where the interior parameterization is based on the level-set method. We additionally provide simple expressions allowing to relate some of these interior models to the geodetic observables of Phobos. The results, based on realistic measurement resolution and noise scenarios, show good retrievals for most of the models at the data resolutions expected from MMX. Specifically, we find the gravity information is realistically sufficient for the detection of mass anomalies below the Stickney crater, as well as large scale heterogeneous regions within plausible rubble-pile structures. Libration helps retrieve the more degenerate models for gravity, such as those with concentric layers or with density varying linearly with depth. The incremental improvement from further adding a hypothetical mean obliquity measurement is marginal. Finally, we apply the level-set inversion and the analytical formulas to estimate possible interior characteristics of the ‘real’ Phobos from the currently-available scarce geodetic observables. The level-set solutions for the real-data inversion generally converge to a higher mass concentration towards the surface in the equatorial region. Markov chain Monte Carlo estimations of parameters relative to a simple 2-layer model or a radial density distribution similarly hint at a lighter region inside of Phobos.

Fokker–Planck equation and Feynman–Kac formula for multidimensional stochastic dynamical systems with Lévy noises and time-dependent coefficients

The aim of this paper is to establish a version of the Feynman–Kac formula for the time-dependent multidimensional nonlocal Fokker–Planck equation corresponding to a class of time-dependent stochastic differential equations driven by multiplicative symmetric (or asymmetric) α-stable Lévy noise. First the forward nonlocal Fokker–Planck equation is derived by the adjoint operator method, overcoming the challenges posed by time-dependent multidimensional nonlinear symmetric α-stable Lévy noise. Subsequently, the Feynman–Kac formula for the forward multidimensional time-dependent nonlocal Fokker–Planck equation is established by applying techniques for the backward nonlocal Fokker–Planck equations, which is associated with the backward stochastic differential equation driven by the multiplicative symmetric α-stable Lévy noise. Notably, in the case of asymmetric α-stable Lévy noise case, the presence of the characteristic function in the nonlocal operator adds complexity to the analysis. Using the Feynman–Kac formula, it is demonstrated that the solution of the forward nonlocal Fokker–Planck equation can be readily simulated through Monte Carlo approximation, especially in scenarios involving long-time simulation settings with large steps. These concepts are illustrated with intriguing examples, and the dynamic evolution of the probability density function corresponding to the stochastic SIS model and the stochastic model for the MeKS network (reflecting the interactions among the MecA complex, ComK and ComS) are investigated over an extended period.

Double-loop importance sampling for McKean–Vlasov stochastic differential equation

This paper investigates Monte Carlo (MC) methods to estimate probabilities of rare events associated with the solution to the d-dimensional McKean–Vlasov stochastic differential equation (MV-SDE). MV-SDEs are usually approximated using a stochastic interacting P-particle system, which is a set of P coupled d-dimensional stochastic differential equations (SDEs). Importance sampling (IS) is a common technique for reducing high relative variance of MC estimators of rare-event probabilities. We first derive a zero-variance IS change of measure for the quantity of interest by using stochastic optimal control theory. However, when this change of measure is applied to stochastic particle systems, it yields a P×d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P \ imes d$$\\end{document}-dimensional partial differential control equation (PDE), which is computationally expensive to solve. To address this issue, we use the decoupling approach introduced in (dos Reis et al. 2023), generating a d-dimensional control PDE for a zero-variance estimator of the decoupled SDE. Based on this approach, we develop a computationally efficient double loop MC (DLMC) estimator. We conduct a comprehensive numerical error and work analysis of the DLMC estimator. As a result, we show optimal complexity of OTOLr-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( \ extrm{TOL}_{\ extrm{r}}^{-4}\\right) $$\\end{document} with a significantly reduced constant to achieve a prescribed relative error tolerance TOLr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{TOL}_{\ extrm{r}}$$\\end{document}. Subsequently, we propose an adaptive DLMC method combined with IS to numerically estimate rare-event probabilities, substantially reducing relative variance and computational runtimes required to achieve a given TOLr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{TOL}_{\ extrm{r}}$$\\end{document} compared with standard MC estimators in the absence of IS. Numerical experiments are performed on the Kuramoto model from statistical physics.

Model Optimization and Application of Straw Mulch Quantity Using Remote Sensing

Straw mulch quantity is an important indicator in the detection of straw returned to the field in conservation tillage, but there is a lack of large-scale automated measurement methods. In this study, we estimated global straw mulch quantity and completed the detection of straw returned to the field. We used an unmanned aerial vehicle (UAV) carrying a multispectral camera to acquire remote sensing images of straw in the field. First, the spectral index was selected using the Elastic-net (ENET) algorithm. Then, we used the Genetic Algorithm Hybrid Particle Swarm Optimization (GA-HPSO) algorithm, which embeds crossover and mutation operators from the Genetic Algorithm (GA) into the improved Particle Swarm Optimization (PSO) algorithm to solve the problem of machine learning model prediction performance being greatly affected by parameters. Finally, we used the Monte Carlo method to achieve a global estimation of straw mulch quantity and complete the rapid detection of field plots. The results indicate that the inversion model optimized using the GA-HPSO algorithm performed the best, with the coefficient of determination (R2) reaching 0.75 and the root mean square error (RMSE) only being 0.044. At the same time, the Monte Carlo estimation method achieved an average accuracy of 88.69% for the estimation of global straw mulch quantity, which was effective and applicable in the detection of global mulch quantity. This study provides a scientific reference for the detection of straw mulch quantity in conservation tillage and also provides a reliable model inversion estimation method for the estimation of straw mulch quantity in other crops.

Development of an EGSnrc multi-leaf collimator component module and treatment head model for a low-field MRI linear accelerator.

Monte Carlo (MC) modeling of MR-guided radiotherapy (MRgRT) treatment machines enables the characterization of photon/electron interactions in the presence of a magnetic field. The EGSnrc MC code system is a well-established system for radiation dose calculations. The multi-leaf collimator (MLC) component modules presently available within the EGSnrc MC code system do not include a model of the double-focused MLC available on a low-field (0.35T) MRI linear accelerator (MR linac). Here we developed and validated a new component module (CM) for the low-field MRgRT MLC using the EGSnrc/BEAMnrc/DOSXYZnrc code system. We performed detailed modeling of the treatment head and validated the model using measurements and calculations from the vendor-specific treatment planning system (TPS). The detailed geometry of the low-field MR linac MLC and other treatment head structures were modeled using BEAMnrc. Comparisons of DOSXYZnrc simulated dose against measurements and the low-field MR linac TPS for a variety of AAPM TG-53 task group report suggested square and shaped fields, as well as a step-and-shoot intensity-modulated radiotherapy (IMRT) plan, are presented. Our model agrees with both measured and TPS calculated data on average within 2%/2mm (dose/DTA) criterion for square field profiles. Output factors agreed within 1% for field sizes down to 2.49×2.49cm2 and within 2% of TPS data for the smallest field size of 0.83×0.83cm2. Shaped field and IMRT MC calculations agreed with measured and TPS data such that the gamma pass rates (3%/2mm) were 99.5% and (3%/3mm) 96.2%, respectively. We developed and validated an MLC CM (SYNCVRMLC) for the low-field MR linac using the EGSnrc MC code systems. This new CM will facilitate MC computation of fluence and dose distributions using BEAMnrc/DOSXYZnrc for patients treated on the low-field MR linac.

Laplace approximation of J factors for rigid base and rigid basepair models of DNA cyclization

We apply the Laplace approximation to a mathematical formulation of DNA cyclization J factors, leading to a formula that involves energies of local minima of the DNA energy, factors coming from the Hessian of the energy near each minimum, and geometric factors arising from the orientational portion of J. The approximation is derived in a quite general setting that encompasses both rigid base and rigid basepair models common in the literature. The approximation is applied to several families of 200–400 bp DNA, some relatively straight (fragments of λ-phage) and others quite bent (constructs that include up to 10 A tracts). The accuracy of the approximation is assessed by comparing with (more time-consuming) Monte Carlo computations: Laplace is within 20% of Monte Carlo for most 200 bp molecules and undershoots Monte Carlo by about 30% for 300 bp and 50% for 400 bp. We explore length and sequence dependence, both for our overall approximation of J and for its energy and entropic components, and make comparisons to a different approximation of J proposed in the literature.

Adaptive formulation for probabilistic storm surge predictions through sharing of numerical simulation results across storm advisories

As a tropical storm/cyclone approaches landfall, real-time probabilistic predictions for the anticipated surge provide valuable information for emergency preparedness/response decisions. These probabilistic predictions are made through an uncertainty quantification process that involves: (i) generating a sufficiently large ensemble of storm scenarios based on the nominal storm advisory and the anticipated forecast errors; (ii) performing high-fidelity numerical simulations to obtain surge predictions for each storm scenario; and (iii) estimating surge statistics of interest by assembling the simulation results. This process is repeated whenever the nominal storm advisory is updated. The number of storm scenarios utilized in the analysis directly impacts the statistical accuracy of the probabilistic predictions; a larger ensemble improves accuracy but requires greater computational resources to provide predictions with the desired expediency to guide real-time decisions. This paper revisits two recently proposed Monte-Carlo (MC) frameworks that aim to improve accuracy without increasing the computational burden: adaptive importance sampling (AIS) and adaptive multi-fidelity Monte Carlo (AMFMC). The foundational concept behind them is similar: share numerical simulation results across the probabilistic predictions performed for different storm advisories to accelerate the MC estimation. This is achieved differently for each approach, through adaptive development of an importance sampling proposal density (for AIS) or a surrogate model (for AMFMC). Here, a direct comparison between these frameworks is established, focusing on the mechanisms for the information sharing and the challenges encountered in tuning the algorithm adaptive characteristics to provide probabilistic estimates across a large number of quantities of interest (QoIs), corresponding to the surge predictions for different locations within the coastal region of interest. As this large number results in conflicting choices for the adaptive characteristics, a compromise solution needs to be promoted. The efficacy of the two frameworks is examined in detail in this setting, comparing the accuracy of idealized implementations (adaptive decisions independently made for each QoI) to the accuracy of practical implementations (single, compromise decision within the MC implementation). The study also showcases the importance of information sharing across storm advisories in real-time probabilistic storm surge predictions and provides guidelines for an efficient adaptive MC formulation in such settings.

A Weak MLMC Scheme for Lévy-Copula-Driven SDEs with Applications to the Pricing of Credit, Equity and Interest Rate Derivatives

This paper develops a novel weak multilevel Monte-Carlo (MLMC) approximation scheme for Lévy-driven Stochastic Differential Equations (SDEs). The scheme is based on the state space discretization (via a continuous-time Markov chain approximation [Mijatović, Aleksandar, Matija Vidmar, and Saul Jacka. 2012. “Markov Chain Approximations for Transition Densities of Lévy Processes.” Electronic Journal of Probability 19]) of the pure-jump component of the driving Lévy process and is particularly suited if the multidimensional driver is given by a Lévy copula. The multilevel version of the algorithm requires a new coupling of the approximate Lévy drivers in the consecutive levels of the scheme, which is defined via a coupling of the corresponding Poisson point processes. The multilevel scheme is weak in the sense that the bound on the level variances is based on the coupling alone without requiring strong convergence. Moreover, the coupling is natural for the proposed discretization of jumps and is easy to simulate. The approximation scheme and its multilevel analogous are applied to examples taken from mathematical finance, including the pricing of credit, equity and interest rate derivatives.

Peer effects affect the adaptation behaviour of rural residents to geohazards in China: a new policy pathway

ABSTRACT Disaster prevention and mitigation (DPM) is one of the responses to extreme climate change impacts and depends on the adoption of risk adaptation behaviour by rural residents. While residents exhibit a high willingness to adapt, they also show low behaviour with reference to DPM. While adaptation behaviour of individuals has been studied extensively, the mutual impact of adaptation behaviour among residents has so far been neglected in the literature. Evaluating this interaction could serve as an important foundation for refining disaster reduction policies. Drawing on social cognitive theory, we propose a novel theoretical framework to analyze peer effects on individual decision-making in DPM. Using data gathered from 536 respondents in Sichuan Province, China, this paper adopts the Bayes Markov chain Monte Carlo estimation method to perform a regression of the spatial probit model. Further, the propensity score matching model was used to explore peer effects on the transformation between residents’ willingness to actual behaviour. Results indicate significant and robust peer effects on DPM behaviour among residents. A heterogeneity test indicated that peer effects are predominantly observed among residents with low and medium social status perception and not in those with high social status perception. Peer effects have a significant and positive influence on the transformation from residents’ willingness to their behaviour. Residents are not completely independent in their decision-making, and complex social mechanisms dictate rational and irrational choices of behaviour. Therefore, it is necessary to fully consider positive peer effects on residents in the formulation of policies. Key policy insights Focusing on the adaptation behaviours and peer effects of rural residents is conducive to improving the public's acceptance of disaster reduction policies. It is difficult for homogenization policies to accurately meet the needs of rural residents in China, and the response to geohazard events requires diversified local policies. Through peer effect, the government can create a kind of environmental soft pressure and promote the transformation of residents’ willingness into behaviour. Due to peer effects, the government can utilize the leading role of a small number of target groups to reduce the cost of implementing disaster reduction policies.