Monte Carlo Applications Research Articles

Variable selection in high dimensional linear regressions with parameter instability

This paper considers the problem of variable selection allowing for parameter instability. It distinguishes between signal and pseudo-signal variables that are correlated with the target variable, and noise variables that are not, and investigate the asymptotic properties of the One Covariate at a Time Multiple Testing (OCMT) method proposed by Chudik et al. (2018) under parameter insatiability. It is established that OCMT continues to asymptotically select an approximating model that includes all the signals and none of the noise variables. Properties of post selection regressions are also investigated, and in-sample fit of the selected regression is shown to have the oracle property. The theoretical results support the use of unweighted observations at the selection stage of OCMT, whilst applying down-weighting of observations only at the forecasting stage. Monte Carlo and empirical applications show that OCMT without down-weighting at the selection stage yields smaller mean squared forecast errors compared to Lasso, Adaptive Lasso, and boosting.

Multi-task learning regression via convex clustering

Multi-task learning (MTL) is a methodology that aims to improve the general performance of estimation and prediction by sharing common information among related tasks. In the MTL, there are several assumptions for the relationships and methods to incorporate them. One of the natural assumptions in the practical situation is that tasks are classified into some clusters with their characteristics. For this assumption, the group fused regularization approach performs clustering of the tasks by shrinking the difference among tasks. This enables the transfer of common information within the same cluster. However, this approach also transfers the information between different clusters, which worsens the estimation and prediction. To overcome this problem, an MTL method is proposed with a centroid parameter representing a cluster center of the task. Because this model separates parameters into the parameters for regression and the parameters for clustering, estimation and prediction accuracy for regression coefficient vectors are improved. The effectiveness of the proposed method is shown through Monte Carlo simulations and applications to real data.

15 years of Adjoint Algorithmic Differentiation (AAD) in finance

Following the seminal ‘Smoking Adjoint’ paper by Giles and Glasserman [Smoking adjoints: Fast monte carlo greeks. Risk, 2006, 19, 88–92], the development of Adjoint Algorithmic Differentiation (AAD) has revolutionized the way risk is computed in the financial industry. In this paper, we provide a tutorial of this technique, illustrate how it is immediately applicable for Monte Carlo and Partial Differential Equations applications, the two main numerical techniques used for option pricing, and review the most significant literature in quantitative finance of the past fifteen years.

Enhanced Twist-Averaging Technique for Magnetic Metals: Applications Using Quantum Monte Carlo.

We propose an improved twist-averaging (TA) scheme for quantum Monte Carlo methods that use converged Kohn-Sham or Hartree-Fock orbitals as the reference. This TA technique is tailored to sample the Brillouin zone of magnetic metals, although it naturally extends to nonmagnetic (NM) conducting systems. The proposed scheme aims to reproduce the reference magnetization and achieves charge neutrality by construction, thus avoiding the large energy fluctuations and the postprocessing needed to correct the energies. It shows the most robust convergence of total energy and magnetism to the thermodynamic limit (TDL) when compared to four other TA schemes. Diffusion Monte Carlo applications are shown on NM Al and ferromagnetic α-Fe. The cohesive energy of Al in the TDL shows an excellent agreement with the experimental result. Furthermore, the magnetic moments in α-Fe exhibit rapid convergence with an increasing number of twists.

Bayesian composite $$L^p$$-quantile regression

Abstract$$L^p$$Lp-quantiles are a class of generalized quantiles defined as minimizers of an asymmetric power function. They include both quantiles,$$p=1$$p=1, and expectiles,$$p=2$$p=2, as special cases. This paper studies composite$$L^p$$Lp-quantile regression, simultaneously extending single$$L^p$$Lp-quantile regression and composite quantile regression. A Bayesian approach is considered, where a novel parameterization of the skewed exponential power distribution is utilized. Further, a Laplace prior on the regression coefficients allows for variable selection. Through a Monte Carlo study and applications to empirical data, the proposed method is shown to outperform Bayesian composite quantile regression in most aspects.

Evaluation of the Reliability of a System: Approach by Monte Carlo Simulation and Application

Evaluation of the Reliability of a System: Approach by Monte Carlo Simulation and Application

Beyond games: a systematic review of neural Monte Carlo tree search applications

The advent of AlphaGo and its successors marked the beginning of a new paradigm in playing games using artificial intelligence. This was achieved by combining Monte Carlo tree search, a planning procedure, and deep learning. While the impact on the domain of games has been undeniable, it is less clear how useful similar approaches are in applications beyond games and how they need to be adapted from the original methodology. We perform a systematic literature review of peer-reviewed articles detailing the application of neural Monte Carlo tree search methods in domains other than games. Our goal is to systematically assess how such methods are structured in practice and if their success can be extended to other domains. We find applications in a variety of domains, many distinct ways of guiding the tree search using learned policy and value functions, and various training methods. Our review maps the current landscape of algorithms in the family of neural monte carlo tree search as they are applied to practical problems, which is a first step towards a more principled way of designing such algorithms for specific problems and their requirements.

Inequality restricted estimator for gamma regression: Bayesian approach as a solution to the multicollinearity

In this article, we consider the multicollinearity problem in the gamma regression model when model parameters are bounded linearly restricted. The linear restrictions are available from prior information to ensure the validity of scientific theories or structural consistency based on physical phenomena. To make relevant statistical inference for a model, any available knowledge and prior information on the model parameters should be taken into account. This article proposes therefore an algorithm to acquire Bayesian estimator for the parameters of a gamma regression model subjected to some linear inequality restrictions. We then show that the proposed estimator outperforms the ordinary estimators such as the maximum likelihood and ridge estimators in terms of pertinence and accuracy through Monte Carlo simulations and application to a real dataset.

Montecarlo Application on Nucleon Dynamics in Calculating Fission Yield at 14 MeV Neutron Energy

Nuclear data is a completeness that must be present in every activity related to nuclear technology. So high is the role of nuclear data, it is necessary to have very complete nuclear data. The need for nuclear data is not in line with the resulting experimental products. The amount of experimental data needs to be completed. This is because the operational costs for these experiments are costly. Thus, theoretical modeling calculations are inevitably the right choice to replace experimental results. Many theoretical models have been developed to obtain satisfactory results. They were starting from microscopic models to macroscopic models. A common obstacle is that microscopic models must be simplified and efficient to produce massive nuclear data. Meanwhile, the constraints on the macroscopic model could be more accurate. This paper will present a calculation that tries to produce accurate but uncomplicated and economical data. This technique uses the basic principles of random numbers and classical nucleon dynamics in the nucleus. At the end of the paper, the results of calculations are presented, which are very accurate and, at the same time, show the dynamics of the nucleons that occur.

Development of Monte Carlo hybrid parallel algorithm and application in high resolution spatial-energy flux distribution calculation

Monte Carlo transport calculations for fusion reactors are very challenging due to factors such as large radiation decay gradients, complex geometric structures, and strong neutron anisotropy. For such deep penetration shielding calculation problems, in order to obtain accurate global flux distribution, variance reduction methods and parallel computing are necessary means. When using the global weight window variance reduction technique, the huge deviation of the particle arrival weight and the weight window can lead to an extreme number of splits, which is the long history problem. If a process encounters the long history problem in parallel computing and takes a lot of time to complete, other processes will stop computing because the histories allocated in the computing cycle have been completed, seriously degrading computing efficiency. In addition, the calculation of the shutdown dose rate, a key issue in fusion neutronics calculations, requires a high “space-energy” resolution, which brings huge challenges to computational memory, especially in parallel computing. In order to overcome the degradation of parallel efficiency caused by the long history problem and the memory limitation in large-scale shutdown dose rate calculation, a hybrid parallel algorithm based on shared memory was researched. Finally, the hybrid parallel architecture was built in the Monte Carlo code cosRMC to realize dynamic load balancing between threads. Through the memory sharing among all threads of a single node, the pressure of memory consumption can be effectively relieved. In order to verify the effectiveness of the hybrid parallel algorithm developed in this paper, it was applied to the calculation of CFETR. The results showed that the hybrid parallel algorithm can effectively alleviate the impact of the long history problem on the parallel efficiency. In terms of saving memory, the hybrid parallel algorithm also showed a significant effect, which provides a guarantee for large-scale shutdown dose rate calculation.

A new modification of the flexible Weibull distribution based on power transformation: Monte Carlo simulation and applications

Statistical modeling is a crucial phase for decision-making and predicting future events. Data arising from engineering-related fields have most often complex structures whose failure rate possesses mixed state behaviors (i.e., non-monotonic shapes). For the data sets whose failure rates are in the mixed state, the utilization of the traditional probability models is not a suitable choice. Therefore, searching for more flexible probability models that are capable of adequately describing the mixed state failure data sets is an interesting research topic for researchers. In this paper, we propose and study a new statistical model to achieve the above goal. The proposed model is called a new beta power very flexible Weibull distribution and is capable of capturing five different patterns of the failure rate such as uni-modal, decreasing-increasing-decreasing, bathtub, decreasing, increasing-decreasing-increasing shapes. The estimators of the new beta power very flexible Weibull distribution are obtained using the maximum likelihood method. The evaluation of the estimators is assessed by conducting a simulation study. Finally, the usefulness and applicability of the new beta power very flexible Weibull distribution are shown by analyzing two engineering data sets. Using four information criteria, it is observed that the new beta power very flexible Weibull distribution is the best-suited model for dealing with failure times data sets.

Validation of HDR brachytherapy doses in the treatment of keloid scars using the egs_brachy Monte Carlo application

Objective. Radiotherapy is a well-known alternative in the treatment of keloid scars to reduce the recurrence of scars. The purpose of this study was to investigate the feasibility and accuracy of dose delivered from a high-dose-rate (HDR) afterloaders in keloid scar brachytherapy using Monte Carlo (MC) simulations and measurements. Approach. Treatment doses and central axis dose profiles were measured using radiophotoluminescence dosimeters and radiochromic films, respectively, with two HDR afterloaders, both using an Ir-192 source, in a phantom made of solid water and polycarbonate sheets. The nominal treatment dose calculated by the AAPM Task Group No. 43 (TG-43) dose model was set to 8.5 Gy at a distance of 0.5 cm laterally from the middle of the source line located in a plastic applicator simulating a 15 cm long surgically removed scar treatment with 30 equally spaced (0.5 cm) source positions. The dose profiles were measured at three different distances from the applicator and the absolute doses at four points at different distances. MC simulations were performed using the egs_brachy, which is based on EGSnrc code system. Main results. The measured and simulated dose profiles match well, especially at 10.0 mm (difference <1%) and 15.0 mm depths (difference <4%), and with a small dose difference at 5.0 mm depth (difference <4%). Point dose measurements agreed well in the dose maximum area (difference <7%) with the simulated dose profiles, although the largest difference near the edge of the profile was <30%. The dose differences between the TG-43 dose model and the MC simulation were small (differences <4%). Significance. Simulated and measured dose levels at a depth of 0.5 cm showed that the nominal treatment dose can be achieved with the utilized setup. The measurement results of the absolute dose agree well with the corresponding simulation results.

Determining Dimensionality with Dichotomous Variables: A Monte Carlo Simulation Study and Applications to Missing Data in Longitudinal Research

Dichotomous data correspond with various types of commonly encountered data, e.g., positive/negative, case/control, missing/observed, in many fields, including medicine, health, and social sciences. Despite their ubiquity, criteria for determining dimensionality from dichotomous variables are not yet established. We conducted a large-scale simulation (Study 1) to evaluate four criteria—Kaiser, empirical Kaiser, parallel analysis, and profile likelihood—to determine the dimensionality of dichotomous data across combinations of correlation matrices (Pearson r or tetrachoric ρ) and analysis methods (principal component analysis or exploratory factor analysis), and combinations of study characteristics: sample sizes (100, 250, and 1000), variable splits (10%/90%, 25%/75%, and 50%/50%), dimensions (1, 3, 5, and 10), and items per dimension (3, 5, and 10) with 1000 replications per condition. Parallel analysis performed best, recovering dimensionality in 87.9% of replications when using principal component analysis with Pearson correlations. Guidance for selecting criteria is provided. In Study 2, we applied this dimensionality reduction approach to two different longitudinal data sets where missing data posed difficulty for multivariate data analysis. The applications of this approach to longitudinal data suggest that the exploration of resulting missing data meta-patterns is useful in practice.

Development of anthropomorphic computational phantoms at the UFPE

To evaluate the amount of energy deposited in radiosensitive organs and tissues of the human body, when an anthropomorphic phantom is irradiated, researchers in numerical dosimetry use the so-called exposure computational models (ECMs). One can imagine an ECM as a virtual scene composed of a phantom in a mathematically defined position in relation to a radioactive source. The source in these ECMs produces the initial state of the simulation: the position, direction, and energy with which each particle enters the phantom are essential variables. For subsequent states of a particle history, robust Monte Carlo (MC) codes are used. For the subsequent states of a particle's history, robust Monte Carlo (MC) codes are used, which simulate the average free path that the particle performs without interacting, its interaction with the atoms in the medium and the amount of energy deposited per interaction. MC codes also evaluate normalization quantities, so the results are printed in text files in the form of conversion coefficients between the absorbed dose and the selected normalization quantity. From the 2000s, the authors have published ECMs where a voxel phantom is irradiated by photons in the environment of the MC code EGSnrc (EGS = Electron Gamma Shower; nrc = National Research Council Canada). The production of articles, dissertations and theses required the use of specific computational tools, such as the FANTOMAS, DIP (Digital Image Processing) and Monte Carlo applications, for the various steps of numerical dosimetry, which ranges from the preparation of input files to the execution from the ECM to the organization and graphical and numerical analysis of the results. This article reviews computational phantoms for dosimetry mainly those produced in DEN-UFPE dissertations and thesis.

G4XRTube: A Geant4-based Monte Carlo application for X-ray tube simulation

This paper focuses mainly on the generation of X-rays in the X-ray tubes and their utilization in imaging applications. In this work, the Geant4 Monte Carlo simulation toolkit was used to develop an application for simulating the production of X-rays in X-ray tubes. This Geant4-based Monte Carlo application generates X-ray spectra depending on anode angle, tube voltage, filter and anode material. In addition to X-ray spectra, G4XRTube can be used, for instance, for the prediction of half-value layer (HVL) and investigation of anode heel effect. The utilization of G4XRTube can also be extended to include other fields such as radiation protection, shielding, dosimetry and investigation of the performance of X-ray tubes and detectors. The results obtained in this work with G4XRTube were validated against existing data in the literature. Specifically, we compared our results with experimental literature data and TASMICS, SpekCalc, and SpekPy codes. The comparison shows a good agreement between G4XRTube results and other data.

Reverse Monte Carlo applications in disordered systems

晶体学只能够给出有关晶体平均原子结构的信息，而结合逆向蒙特卡洛(Reverse Monte Carlo，RMC)模拟的全散射方法将同时包含原子的平均结构和局部尺度上原子间距、键角以及结构多面体的取向和形变等方面的信息，这也是 RMC方法一个独特的优势。近年来，借助第三代同步辐射加速器和散裂中子源，RMC方法在实验和理论上都有了较快的发展，同时数据质量高，保证了该方法在材料的局域波动和无序的精细结构研究中的适用性。本文从RMC基本原理和分析方法两个方面介绍了无序体系中的逆向蒙特卡洛方法，同时给出了一系列有助于理解的RMC模型案例。最后，我们对RMC方法的发展进行了展望。近年来我国对大学科装置的投入迅速增长，相信RMC方法搭载第四代高能量光源，在我国新材料的设计与开发中发挥重要的作用。

Monte Carlo-derived 99m Tc uptake quantification with commercial planar MBI: Tumor and breast activity concentrations.

Current molecular breast imaging (MBI) images are limited to qualitative evaluation, not absolute measurement, of 99m Tc uptake in benign and malignant breast tissues. This work assesses the accuracy of previously-published and newly-proposed tumor and normal breast tissue 99m Tc uptake MBI measurements using simulations of a commercial dual-headed planar MBI system under typical clinical and acquisition protocols. Quantification techniques were tested in over 4000 simulated acquisitions of spherical and ellipsoid tumors with clinically relevant uptake conditions using a validated Monte Carlo application of the GE Discovery NM750b system. The evaluated techniques consisted of four tumor total activity methodologies (two single-detector-based and two geometric-mean-based), two tumor MBI volume methodologies (diameter-based and ROI-based), and two normal tissue activity concentration methodologies (single-detector-based and geometric-mean-based). The most accurate of these techniques were then used to estimate tumor activity concentrations and tumor to normal tissue relative activity concentrations (RC). Single-detector techniques for tumor total activity quantification achieved mean (standard deviation) relative errors of 0.2% (4.3%) and 1.6% (4.4%) when using the near and far detector images, respectively and were more accurate and precise than the measured 8.1% (5.8%) errors of a previously published geometric-mean technique. Using these activity estimates and the true tumor volumes resulted in tumor activity concentration and RC errors within 10% of simulated values. The precision of tumor activity concentration and RC when using only MBI measurements were largely driven by the errors in estimating tumor MBI volume using planar images (±30% inter-quartile range). Planar MBI images were shown to accurately and reliably be used to estimate tumor total activities and normal tissue activity concentrations in this simulation study. However, volumetric tumor uptake measurements (i.e., absolute and relative concentrations) are limited by inaccuracies in MBI volume estimation using two-dimensional images, highlighting the need for either tomographic MBI acquisitions or anatomical volume estimates for accurate three-dimensional tumor uptake estimates.

Monte Carlo-derived 99m Tc uptake quantification with commercial planar MBI: Absolute tumor activity.

Molecular breast imaging (MBI) of 99m Tc-sestamibi is an emerging adjunct qualitative tool in the detection and diagnosis of breast cancer. This work outlines the development and performance evaluation of a methodology to absolutely quantify tumor 99m Tc activity uptake using a commercially available dual-headed MBI system by implementing corrections for background, scatter, attenuation, and detector characteristics. A validated Monte Carlo application of a commercial MBI system was used to simulate over 7000 unique acquisitions of spherical and ellipsoidal tumors in breast tissue. Tumor absolute activity was calculated following background, scatter, and attenuation corrections of tumor region of interest counts. The methodology was first optimized using a set of high-uptake spherical tumors, and its accuracy and precision was then assessed in a set of spherical tumors with clinical uptake conditions. Finally, the performance of the activity methodology was evaluated under various bias and uncertainty conditions to better characterize the technique under expected clinical measurement conditions. In a test set of images with clinically relevant contrast and noise conditions, the mean ± standard deviation relative error in total tumor activity was 0.5% ± 6.5% (n = 2363) under ideal measurement conditions. Allowing for variability in tumor and background contours and in estimated tumor depths, the expected accuracy of the methodology in clinical practice was 0.5% ± 11.1% (n = 2363), with minimal loss of accuracy for ellipsoidal tumors. Planar MBI photopeak images acquired with standard-of-care protocols can be used to accurately quantify absolute tumor 99m Tc activity with an accuracy and precision of 0.5% ± 11.1%. The reported precision was based on a comprehensive evaluation of random errors and systematic biases.

A note on the posterior risk of the entropy loss function

Scholars have discussed the Bayesian estimation and their corresponding posterior risks for the Lindley distribution parameter, respectively, using seven different loss functions, where the posterior risk under entropy loss function (ELF) is not correct. In this paper, we will derive the Bayesian estimation and its corrected posterior risk under the entropy loss function. Moreover, the Bayesian estimations and their posterior risks of binomial distribution parameter under the entropy loss function and squared error loss function are respectively developed. Monte Carlo simulation example and application example are provided for illustrative purposes, and results are compared based on posterior risk.

A new distributional approach: estimation, Monte Carlo simulation and applications to the biomedical data sets

&lt;abstract&gt;&lt;p&gt;This paper introduces the generalized exponential-$ U $ family of distributions as a novel methodological approach to enhance the distributional flexibility of existing classical and modified distributions. The new family is derived by combining the T-$ X $ family method with the exponential model. The paper presents the generalized exponential-Weibull model, an updated version of the Weibull model. Estimators and heavy-tailed characteristics of the proposed method are derived. The new model is applied to three healthcare data sets, including COVID-19 patient survival times and mortality rate data set from Mexico and Holland. The proposed model outperforms other models in terms of analyzing healthcare data sets by evaluating the best model selection measures. The findings suggest that the proposed model holds promise for broader utilization in the area of predicting and modeling healthcare phenomena.&lt;/p&gt;&lt;/abstract&gt;