Monte Carlo Estimation Research Articles

The Best Fit Bayesian Hierarchical Generalized Linear Model Selection Using Information Complexity Criteria in the MCMC Approach

Both frequentist and Bayesian statistics schools have improved statistical tools and model choices for the collected data or measurements. Model selection approaches have advanced due to the difficulty of comparing complicated hierarchical models in which linear predictors vary by grouping variables, and the number of model parameters is not distinct. Many regression model selection criteria are considered, including the maximum likelihood (ML) point estimation of the parameter and the logarithm of the likelihood of the dataset. This paper demonstrates the information complexity (ICOMP), Bayesian deviance information, or the widely applicable information criterion (WAIC) of the BRMS to hierarchical linear models fitted with repeated measures with a simulation and two real data examples. The Fisher information matrix for the Bayesian hierarchical model considering fixed and random parameters under maximizing a posterior estimation is derived. Using Gibbs sampling and Hybrid Hamiltonian Monte Carlo approaches, six different models were fitted for three distinct application datasets. The best-fitted candidate models were identified under each application dataset with the two MCMC approaches. In this case, the Bayesian hierarchical (mixed effect) linear model with random intercepts and random slopes estimated using the Hamiltonian Monte Carlo method best fits the two application datasets. Information complexity (ICOMP) is a better indicator of the best-fitted models than DIC and WAIC. In addition, the information complexity criterion showed that hierarchical models with gradient-based Hamiltonian Monte Carlo estimation are the best fit and have supper convergence relative to the gradient-free Gibbs sampling methods.

Experimental and computational study on removal of nitric oxide using NH2-MIL-125: Revisiting removal mechanism

The NH2-MIL-125 (NM-125) or modified NM-125 materials are used for photocatalytic removal of nitric oxide (NO). Most researchers attributed few NO2 emission during NO photocatalysis to high selectivity towards the formation of nitrate ions due to the neglect of the principle of electroneutrality and pore structure of NM-125. This may cause misleading photocatalytic mechanism of NO removal. Herein, this work proposes a new mechanism behind NO removal using NM-125 based on experimental investigations and theoretical calculations. First, experimentally, the highest NO removal efficiency of 88.54 % with negligible NO2 emission occurs at the anhydrous condition. In addition, in-situ diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) measurements verify the presence and accumulation of NO2 as product during photocatalytic conversion of NO. Furthermore, density functional theory (DFT) calculations and grand canonical Monte Carlo (GCMC) computations demonstrate that there exist strong interactions between NO2 and -NH2 group within pores. Few NO2 is detected during experiments is probably due to its subsequent adsorption in the pores of NM-125. The new NO removal mechanism including photocatalytic conversion NO into NO2 and subsequent NO2 adsorption in the pores of NM-125 is thus proposed. This work provides a deeper insight into photocatalytic NO removal over NM-125 and its variants.

A probabilistic peridynamic framework with an application to the study of the statistical size effect

The high computational expense of peridynamic models remains a major limitation, hindering ‘outer-loop’ applications that require a large number of simulations, for example, uncertainty quantification. This contribution presents a framework that makes such computations feasible. By employing a Multilevel Monte Carlo framework, where the majority of simulations are performed using a coarse mesh, and performing relatively few simulations using a fine mesh, a significant reduction in computational cost can be realised, and statistics of structural failure can be estimated. The maximum observed speed-up factor is 16 when compared to a standard Monte Carlo estimator, thus enabling the efficient forward propagation of uncertain parameters in a computationally expensive peridynamic model. Furthermore, the multilevel method provides an estimate of both the discretisation error and sampling error, thereby improving confidence in numerical predictions. The performance of the approach is demonstrated through an examination of the statistical size effect in quasi-brittle materials.

Monte Carlo simulations of a standing geometry whole body counter: Effects of skeletal sampling, age, sex and phantom size on calibration

International Commission on Radiological Protection (ICRP) adult and pediatric reference computational phantoms are widely employed to evaluate calibration of in-vivo monitoring systems using Monte Carlo codes. Quick Scan Whole Body Monitor (QSWBM) is an in-vivo monitoring system capable of fast screening subjects in standing linear geometry. In the present study, our objectives include: (1) Monte Carlo estimation of QSWBM counting efficiencies using age and sex specific ICRP computational reference phantoms, (2) understand the effect of skeletal sampling in counting efficiency, (3) comparison of efficiencies for multiple sized voxel phantoms of same age group and sex, and (4) comparison of experimental and numerical calibration. With this study, we have numerically estimated QSWBM counting efficiencies for three important gamma energies, 662 keV from 137Cs and 1173 keV and 1332 keV from 60Co using FLUKA code and a total of fifteen computational phantoms. The results obtained from the present work rule out the necessity of computationally complex skeletal soft tissue sampling in numerical calibration of standing geometry whole body counters for in-vivo detection of uniformly distributed sources in human body. It was also found that the efficiencies were greatly influenced by the physical size of the subjects while the deviation due to sex is not very great. Experimental calibration using Indian Reference Bottle Mannequin ABsorber (BOMAB-I) phantom was compared with modified adult male computational phantom of equivalent physical dimensions to understand the deviations. With this study, QSWBM was numerically calibrated to detect 137Cs and 60Co in diverse subjects of a population.

Multivariate nearest‐neighbors Gaussian processes with random covariance matrices

AbstractWe propose a non‐stationary spatial model based on a normal‐inverse‐Wishart framework, conditioning on a set of nearest‐neighbors. The model, called nearest‐neighbor Gaussian process with random covariance matrices is developed for both univariate and multivariate spatial settings and allows for fully flexible covariance structures that impose no stationarity or isotropic restrictions. In addition, the model can handle duplicate observations and missing data. We consider an approach based on integrating out the spatial random effects that allows fast inference for the model parameters. We also consider a full hierarchical approach that leverages the sparse structures induced by the model to perform fast Monte Carlo computations. Strong computational efficiency is achieved by leveraging the adaptive localized structure of the model that allows for a high level of parallelization. We illustrate the performance of the model with univariate and bivariate simulations, as well as with observations from two stationary satellites consisting of albedo measurements.

Investigation the generalized extreme value under liner distribution parameters for progressive type-Ⅱ censoring by using optimization algorithms

<abstract><p>Several random phenomena have been modeled by using extreme value distributions. Based on progressive type-Ⅱ censored data with three different distributions (i.e., fixed, discrete uniform, and binomial random removal), the statistical inference of the generalized extreme value distribution under liner normalization (GEVL distribution) parameters is investigated in this study. Since there is no analytical solution, determining the maximum likelihood parameters for the GEVL distribution is considered to be a problem. Standard numerical methods are frequently insufficient for this dilemma, requiring the use of artificial intelligence algorithms to address this difficulty. Here, nonlinear minimization and a genetic algorithm have been used to tackle that problem. In addition, Lindley approximation and Monte Carlo estimation were implemented via Metropolis-Hastings algorithms to carry out the Bayesian point estimation based on both the squared error loss function and LINEX loss functions. Moreover, the highest posterior density intervals were applied. The proposed theoretical inference techniques have been applied in a numerical simulation and a real-life example.</p></abstract>

Relative Entropy Regularized Sample-Efficient Reinforcement Learning With Continuous Actions.

In this article, a novel reinforcement learning (RL) approach, continuous dynamic policy programming (CDPP), is proposed to tackle the issues of both learning stability and sample efficiency in the current RL methods with continuous actions. The proposed method naturally extends the relative entropy regularization from the value function-based framework to the actor-critic (AC) framework of deep deterministic policy gradient (DDPG) to stabilize the learning process in continuous action space. It tackles the intractable softmax operation over continuous actions in the critic by Monte Carlo estimation and explores the practical advantages of the Mellowmax operator. A Boltzmann sampling policy is proposed to guide the exploration of actor following the relative entropy regularized critic for superior learning capability, exploration efficiency, and robustness. Evaluated by several benchmark and real-robot-based simulation tasks, the proposed method illustrates the positive impact of the relative entropy regularization including efficient exploration behavior and stable policy update in RL with continuous action space and successfully outperforms the related baseline approaches in both sample efficiency and learning stability.

An overview of last decade’s developments in RayXpert®, a 3D Monte Carlo code

This article provides an overview of the developments made over the last 10 years within RayXpert®, a CAD-based geometry 3D Monte Carlo software developed by TRAD – Tests & Radiations. The main features of RayXpert® are its 3D Monte Carlo engine and its CAD-based geometry. It is also possible to import STEP file, automatically detect overlaps, and perform parallel Monte Carlo computations. During the last 10 years, numerous new features were added to the software: TTB approximation, dose and flux mapping, computation resumption, radioactive decay computation, script support, MPI computation, advanced convergence indicators, etc. New features such as advanced biasing or neutron-induced activation simulation are under development. This article presents the past and future functionalities of RayXpert®.

A variance-reduction strategy for the sensitivity of βeff

The Monte Carlo computation of the GPT-based sensitivity of the effective delayed neutron fraction βeff to nuclear data proves to be quite difficult to converge due to the small amount of delayed neutrons that are sampled in k-eigenvalue calculations. This paper describes a variance-reduction method aimed at efficiently computing the sensitivity coefficients of βeff, reducing the associated Monte Carlo uncertainty and increasing the Figure Of Merit. This variance-reduction technique allows also computing the sensitivities of βj eff for a specific precursor family j. Verification and performance evaluation are achieved using simple configurations admitting analytical solutions and several continuousenergy benchmarks.

A weight window approach for dose rate calculations in Lead-cooled Fast Reactors with OpenMC

This paper presents the application of a variance reduction technique for radiation shielding calculations in Lead-cooled Fast Reactors (LFRs) using the OpenMC Monte Carlo code. The study focuses on assessing the computational efficiency of the Method of Automatic Generation of Importances by Calculation (MAGIC). This technique is employed to generate weight windows for Monte Carlo simulations, aiming at enhancing the efficiency of dose rate estimations for LFRs. Through a detailed study of a LFR mock-up model, the performance differences between a MAGIC-accelerated and a non-accelerated simulation are investigated in terms of both accuracy and computational cost. The results demonstrate the benefits of the variance reduction method, showing its effectiveness in spreading particles throughout the model while improving the accuracy of Monte Carlo estimates far from the core. In addition, this work demonstrates the performances of the MAGIC method in eigenvalue calculations. This work shows an interesting optimisation of Monte Carlo simulations for LFRs and can be considered as a first milestone for newcleo’s radiation shielding studies.

Comparison of distance-based spatial weight matrix in modeling Internet signal strengths in Tasikmalaya regency using logistic spatial autoregressive model

To ensure that national development objectives in rural areas are achieved evenly and sustainably, the Government of Indonesia applies the principles of Village Sustainable Development Goals (SDGs), which are derivative programs of SDGs. One of the indicators in measuring the progress and independence of villages in Indonesia is the availability of cellular phone signal access. Cellular phone signals have a vital role because most internet users in Indonesia rely on mobile data connections from cellular operators. However, the signal emitted by a provider tower has a limited range. According to the data of the Developing Villages Index in 2022, Tasikmalaya Regency is one of the regencies with the highest number of villages that have weak signal strength in West Java Province, Indonesia. To examine the effect of distance and height difference between the placement of the nearest provider tower and the location of the Village Office on the internet signal strength category in Tasikmalaya Regency, Logistic Spatial Autoregressive modeling is needed. In this study, the Bayesian Markov-Chain Monte Carlo estimation method was used, because it has advantages in flexibility and computational efficiency. In spatial modeling, there is a spatial weight matrix determined by the researcher’s understanding of the observed phenomenon. The variable observed in this study is signal strength, which has an orientation at a distance. However, there are several types of distance-based spatial weight matrices, such as K-nearest neighbor, radial distance, power distance, and exponential distance. To determine the most suitable distance-based spatial weight matrix in internet signal strength modeling, the four (4) weight matrices were compared based on the goodness of fit measure models, calculated from the confusion matrix. The results of the analysis showed that the radial distance weight matrix with a threshold distance of d = 1.7km is the most suitable use of distance-based spatial weight matrix in internet signal modeling in Tasikmalaya Regency. The weight matrix exerted a positive spatial autocorrelation effect of 57.141%. In addition, the height difference factor between the location of the provider tower with the location of the village office has a greater effect than the horizontal distance.

Derivation and Evaluation of Monte Carlo Estimators of the Scattering Equation Using the Ward BRDF and Different Sample Allocation Strategies

Derivation and Evaluation of Monte Carlo Estimators of the Scattering Equation Using the Ward BRDF and Different Sample Allocation Strategies

DIFFUSION-MODEL-ASSISTED SUPERVISED LEARNING OF GENERATIVE MODELS FOR DENSITY ESTIMATION

We present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks (GANs), normalizing flows, and variational auto-encoders (VAEs), are usually considered as unsupervised learning models, because labeled data are usually unavailable for training. Despite the success of the generative models, there are several issues with the unsupervised training, e.g., requirement of reversible architectures, vanishing gradients, and training instability. To enable supervised learning in generative models, we utilize the score-based diffusion model to generate labeled data. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE), corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer both high accuracy and substantial time savings in neural network training. Once the labeled data are generated, we can train a simple, fully connected neural network to learn the generative model in the supervised manner. Compared with existing normalizing flow models, our method does not require the use of reversible neural networks and avoids the computation of the Jacobian matrix. Compared with existing diffusion models, our method does not need to solve the reverse-time SDE to generate new samples. As a result, the sampling efficiency is significantly improved. We demonstrate the performance of our method by applying it to a set of 2D datasets as well as real data from the University of California Irvine (UCI) repository.

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.

Nonlinearities in macroeconomic tail risk through the lens of big data quantile regressions

SummaryModeling and predicting extreme movements in GDP is notoriously difficult, and the selection of appropriate covariates and/or possible forms of nonlinearities are key in obtaining precise forecasts. In this paper, our focus is on using large datasets in quantile regression models to forecast the conditional distribution of US GDP growth. To capture possible nonlinearities, we include several nonlinear specifications. The resulting models will be huge dimensional, and we thus rely on a set of shrinkage priors. Since Markov chain Monte Carlo estimation becomes slow in these dimensions, we rely on fast variational Bayes approximations to the posterior distribution of the coefficients and the latent states. We find that our proposed set of models produces precise forecasts. These gains are especially pronounced in the tails. Using Gaussian processes to approximate the nonlinear component of the model further improves the good performance, in particular in the right tail.

PrOuD: Probabilistic Outlier Detection Solution for Time-Series Analysis of Real-World Photovoltaic Inverters

Anomaly detection methods applied to time series are mostly viewed as black boxes that solely provide a deterministic answer for the detected target. Without a convincing explanation, domain experts can hardly trust the detection results and must conduct further time-series diagnoses in real-world applications. To overcome this challenge, we mathematically analyzed the sources of anomalies and novelties in multivariate time series as well as their relationships from the perspective of Gaussian-distributed non-stationary noise. Furthermore, we proposed mathematical methods to generate artificial time series and synthetic anomalies, with the goal of solving the problem of it being difficult to train and evaluate models for real-world applications due to the lack of sufficient data. In addition, we designed Probabilistic Outlier Detection (PrOuD), which is a general solution to provide interpretable detection results to assist domain experts with time-series analysis. PrOuD can convert the predictive uncertainty of a time-series value from a trained model into the estimated uncertainty of the detected outlier through Monte Carlo estimation. The experimental results obtained on both artificial time series and real-world photovoltaic inverter data demonstrated that the proposed solution can detect emerging anomalies accurately and quickly. The implemented PrOuD demo case shows its potential to make the detection results of existing detection methods more convincing so that domain experts can more efficiently complete their tasks, such as time-series diagnosis and anomalous pattern clustering.

Evo‐Scope: Fully automated assessment of correlated evolution on phylogenetic trees

Abstract Correlated evolution describes how multiple biological traits evolve together. Recently developed methods provide increasingly detailed results of correlated evolution, sometimes at elevated computational costs. Here, we present evo‐scope, a fast and fully automated pipeline with minimal input requirements to compute correlation between discrete traits evolving on a phylogenetic tree. Notably, we improve two of our previously developed tools that efficiently compute statistics of correlated evolution to characterize the nature, such as synergy or antagonism, and the strength of the interdependence between the traits. Furthermore, we improved the running time and implemented several additional features, such as genetic mapping, Bayesian Markov Chain Monte Carlo estimation, consideration of missing data and phylogenetic uncertainty. As an application, we scan a publicly available penicillin resistance data set of Streptococcus pneumoniae and characterize genetic mutations that correlate with antibiotic resistance. The pipeline is accessible both as a self‐contained Github repository (https://github.com/Maxime5G/EvoScope) and through a graphical galaxy interface (https://galaxy.pasteur.fr/u/maximeg/w/evoscope).

Option Pricing and Portfolio Optimization under a Multi-Asset Jump-Diffusion Model with Systemic Risk

We explore a multi-asset jump-diffusion pricing model, combining a systemic risk asset with several conditionally independent ordinary assets. Our approach allows for analyzing and modeling a portfolio that integrates high-activity security, such as an exchange trading fund (ETF) tracking a major market index (e.g., S&P500), along with several low-activity securities infrequently traded on financial markets. The model retains tractability even as the number of securities increases. The proposed framework allows for constructing models with common and asset-specific jumps with normally or exponentially distributed sizes. One of the main features of the model is the possibility of estimating parameters for each asset price process individually. We present the conditional maximum likelihood estimation (MLE) method for fitting asset price processes to empirical data. For the case with common jumps only, we derive a closed-form solution to the conditional MLE method for ordinary assets that works even if the data are incomplete and asynchronous. Alternatively, to find risk-neutral parameters, the least-square method calibrates the model to option values. The number of parameters grows linearly in the number of assets compared to the quadratic growth through the correlation matrix, which is typical for many other multi-asset models. We delve into the properties of the proposed model, its parameter estimation using the MLE method and least-squares technique, the evaluation of VaR and CVaR metrics, the identification of optimal portfolios, and the pricing of European-style basket options. We propose a Laplace-transform-based approach to computing Value at Risk (VaR) and conditional VaR (also known as the expected shortfall) of portfolio returns. Additionally, European-style basket options written on the extreme and average stock prices or returns can be evaluated semi-analytically. For numerical demonstration, we examine a combination of the SPDR S&P 500 ETF (as a systemic risk asset) with eight ordinary assets representing diverse industries. Using historical assets and options prices, we estimate the real-world and risk-neutral parameters of the model with common jumps, construct several optimal portfolios, and evaluate various basket options with the eight assets. The results affirm the robustness and efficiency of the estimation and evaluation methodologies. Computational results are compared with Monte Carlo estimates.

Amortizing Samples in Physics-Based Inverse Rendering Using ReSTIR

Recently, great progress has been made in physics-based differentiable rendering. Existing differentiable rendering techniques typically focus on static scenes, but during inverse rendering---a key application for differentiable rendering---the scene is updated dynamically by each gradient step. In this paper, we take a first step to leverage temporal data in the context of inverse direct illumination. By adopting reservoir-based spatiotemporal resampled importance resampling (ReSTIR), we introduce new Monte Carlo estimators for both interior and boundary components of differential direct illumination integrals. We also integrate ReSTIR with antithetic sampling to further improve its effectiveness. At equal frame time, our methods produce gradient estimates with up to 100× lower relative error than baseline methods. Additionally, we propose an inverse-rendering pipeline that incorporates these estimators and provides reconstructions with up to 20× lower error.

Doppler Time-of-Flight Rendering

We introduce Doppler time-of-flight (D-ToF) rendering, an extension of ToF rendering for dynamic scenes, with applications in simulating D-ToF cameras. D-ToF cameras use high-frequency modulation of illumination and exposure, and measure the Doppler frequency shift to compute the radial velocity of dynamic objects. The time-varying scene geometry and high-frequency modulation functions used in such cameras make it challenging to accurately and efficiently simulate their measurements with existing ToF rendering algorithms. We overcome these challenges in a twofold manner: To achieve accuracy, we derive path integral expressions for D-ToF measurements under global illumination and form unbiased Monte Carlo estimates of these integrals. To achieve efficiency, we develop a tailored time-path sampling technique that combines antithetic time sampling with correlated path sampling. We show experimentally that our sampling technique achieves up to two orders of magnitude lower variance compared to naive time-path sampling. We provide an open-source simulator that serves as a digital twin for D-ToF imaging systems, allowing imaging researchers, for the first time, to investigate the impact of modulation functions, material properties, and global illumination on D-ToF imaging performance.