Use Of Monte-Carlo Method Research Articles

Variance reduction in Monte Carlo for Integrals

Abstract. Nowadays, the extensive use of Monte Carlo methods in various fields has promoted the scientific decision-making, improved the efficiency of social operation, and enabled better management of many uncertain factors in daily life. However, in some cases, traditional Monte Carlo methods doesn't work so well because of the excessive variance. This paper aims to explore a new numerical integration method called splitting method to minimize intrinsic variance in Monte Carlo simulations. Through this innovative method, we found that the variance was reduced significantly. Despite some oscillating functions which are still difficult to estimate because they have too many turning points, this study provides new insights into variance reduction in Monte Carlo for integrals to optimize calculations in various fields when the modelling functions are not monotonic.

Pseudo-perplexity in One Fell Swoop for Protein Fitness Estimation.

Protein language models trained on the masked language modeling objective learn to predict the identity of hidden amino acid residues within a sequence using the remaining observable sequence as context. They do so by embedding the residues into a high dimensional space that encapsulates the relevant contextual cues. These embedding vectors serve as an informative context-sensitive representation that not only aids with the defined training objective, but can also be used for other tasks by downstream models. We propose a scheme to use the embeddings of an unmasked sequence to estimate the corresponding masked probability vectors for all the positions in a single forward pass through the language model. This One Fell Swoop (OFS) approach allows us to efficiently estimate the pseudo-perplexity of the sequence, a measure of the model's uncertainty in its predictions, that can also serve as a fitness estimate. We find that ESM2 OFS pseudo-perplexity performs nearly as well as the true pseudo-perplexity at fitness estimation, and more notably it defines a new state of the art on the ProteinGym Indels benchmark. The strong performance of the fitness measure prompted us to investigate if it could be used to detect the elevated stability reported in reconstructed ancestral sequences. We find that this measure ranks ancestral reconstructions as more fit than extant sequences. Finally, we show that the computational efficiency of the technique allows for the use of Monte Carlo methods that can rapidly explore functional sequence space.

OPTIMIZATION OF THE AUCTION DURATION IN THE PRESENSE OF TIME-DEPENDANT COSTS

This paper examines the influence of the duration of auctions or tenders on the expected gain of their organizer. Extending the duration of bidding affects auction results in two ways. On the one hand, it allows attracting a larger number of participants to the auction, and the competition between them increases the chances of the auctioneer to get a better price. On the other hand, delaying bids delays the receipt of money (for auctions) or required goods or services (for tenders), and time has value in itself. The influence of these two factors, which act in opposite directions, suggests the existence of an optimal duration of the bidding process. The paper develops a mathematical model of bidding, which formalizes these considerations and provides an algorithm to determine their optimal duration. The arrival of bidders willing to participate in the auction is modeled as a Poisson process. Each participant is characterized by his own assessment of the value of the object put up for auction. These estimates are assumed to be independent identically distributed random variables drawn from some parametric distribution. Under these assumptions, Myerson's revenue equivalence theorem makes it possible to predict the expected results of the auction as a function of the number of bidders, regardless of the auction rules. On this basis, it is possible to compare the benefits and costs associated with changing the duration of time for accepting applications for participation in bidding, which makes it possible to determine its optimal value. The obtained optimality conditions have a meaningful and intuitive economic interpretation. For practical applications, the use of Monte Carlo methods based on the empirical distribution of bid and ask prices is proposed. The practical implementation of the proposed algorithm can improve the economic performance of the auctioneer, which is especially relevant for the public sector of the economy.

K-th record estimator of the scale parameter of the α-stable distribution

Abstract Various techniques of scale parameter estimation have been proposed in the case of alpha stable distributions. In the paper, the authors present an estimation technique that involves the k-th record theory. Although this theory is over 40 years old, its implementation in the classical extreme value theory – being the other cornerstone of the presented approach – is quite new, and tempting. Several theoretical properties of the introduced scale parameter estimators are presented. With the use of Monte Carlo methods, a comparative analysis is performed between the approach based on k-th records and approaches based on Hill’s and Pickands’ estimators. Additionally, the paper uses a real-life data set to illustrate how to effectively apply the k-th record estimator of the scale parameter. The research indicates several advantages of the k-th record approach over its other counterparts, especially when dealing with incomplete information about the underlying sample.

Comparison of GUM and Monte Carlo Methods for the Measurement Uncertainty Circular Runout Error of Shafts

Measurement uncertainty is one of the most important concepts. The ISO IEC 17025:2005 standard: describes harmonized policies and procedures for testing and calibration laboratories. Guide to the expression of uncertainty in measurement (GUM) is a direct uncertainty analysis method, which calculates the combined standard uncertainty and expanded uncertainty by law of propagation of uncertainty. Monte Carlo Method (MCM) as presented by the (GUM S1) involves the propagation of the distributions of the input sources of uncertainty by using a model to provide the distribution of the output. By random sampling, the probability density function of the input quantities. In this paper, present measurement uncertainty to circular runout error. By use shaft standard with a diameter of 32 mm., length 100 mm. From the experiment results, Comparison of GUM and MCM showed no differences. The cases the estimated uncertainty using the GUM approach slightly overestimated the results obtained with the MCM. However, the use of numerical methods such MCM as a valuable alternative to the GUM approach. The practical use of MCM it has proven to be a fundamental tool, being able to address more complex measurement problems that were limited by the GUM approximations.

On quadrature rules for solving Partial Differential Equations using Neural Networks

Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may arise in these applications and propose several alternatives to overcome them, namely: Monte Carlo methods, adaptive integration, polynomial approximations of the Neural Network output, and the inclusion of regularization terms in the loss. We also discuss the advantages and limitations of each proposed numerical integration scheme. We advocate the use of Monte Carlo methods for high dimensions (above 3 or 4), and adaptive integration or polynomial approximations for low dimensions (3 or below). The use of regularization terms is a mathematically elegant alternative that is valid for any spatial dimension; however, it requires certain regularity assumptions on the solution and complex mathematical analysis when dealing with sophisticated Neural Networks.

A parametric framework for multidimensional linear measurement error regression.

The ordinary linear regression method is limited to bivariate data because it is based on the Cartesian representation y = f(x). Using the chain rule, we transform the method to the parametric representation (x(t), y(t)) and obtain a linear regression framework in which the weighted average is used as a parameter for a multivariate linear relation for a set of linearly related variable vectors (LRVVs). We confirm the proposed approach by a Monte Carlo simulation, where the minimum coefficient of variation for error (CVE) provides the optimal weights when forming a weighted average of LRVVs. Then, we describe a parametric linear regression (PLR) algorithm in which the Moore-Penrose pseudoinverse is used to estimate measurement error regression (MER) parameters individually for the given variable vectors. We demonstrate that MER parameters from the PLR and nonlinear ODRPACK methods are quite similar for a wide range of reliability ratios, but ODRPACK is formulated only for bivariate data. We identify scale invariant quantities for the PLR and weighted orthogonal regression (WOR) methods and their correspondences with the partitioned residual effects between the variable vectors. Thus, the specification of an error model for the data is essential for MER and we discuss the use of Monte Carlo methods for estimating the distributions and confidence intervals for MER slope and correlation coefficient. We distinguish between elementary covariance for the y = f(x) representation and covariance vector for the (x(t), y(t)) representation. We also discuss the multivariate generalization of the Pearson correlation as the contraction between Cartesian polyad alignment tensors for the LRVVs and weighted average. Finally, we demonstrate the use of multidimensional PLR in estimating the MER parameters for replicate RNA-Seq data and quadratic regression for estimating the parameters of the conical dispersion of read count data about the MER line.

Quantifying uncertainty in land cover mappings: An adaptive approach to sampling reference data using Bayesian inference

AbstractMappings play an important role in environmental science applications by allowing practitioners to monitor changes at national and global scales. Over the last decade, it has become increasingly popular to use satellite imagery data and machine learning techniques (MLTs) to construct such maps. Given the black-box nature of many of these MLTs though, quantifying uncertainty in these maps often relies on sampling reference data under stricter conditions. However, practical constraints can sampling such data expensive, which forces stakeholders to make a trade-off between the degree of uncertainty in predictions and the costs of collecting appropriately sampled reference data. Furthermore, quantifying any trade-off is often difficult, as it will depend on many interdependent factors that cannot be fully understood until more data is collected. This paper investigates how a combination of Bayesian inference and an adaptive approach to sampling reference data can offer a generalizable way of managing such trade-offs. The approach is illustrated and evaluated using a woodland mapping of England as a case study in which reference data is collected under constraints motivated by COVID-19 travel restrictions. The key findings of this paper are as follows: (a) an adaptive approach to sampling reference data allows an informed approach when quantifying this trade-off; and (b) Bayesian inference is naturally suited to adaptive sampling and can make use of Monte Carlo methods when dealing with more advanced problems and analytical techniques.

Pre- and post-treatment image-based dosimetry in 90Y-microsphere radioembolization using the TOPAS Monte Carlo toolkit

Objective. To evaluate the pre-treatment and post-treatment imaging-based dosimetry of patients treated with 90Y-microspheres, including accurate estimations of dose to tumor, healthy liver and lung. To do so, the Monte Carlo (MC) TOPAS platform is in this work extended towards its utilization in radionuclide therapy. Approach. Five patients treated at the Massachusetts General Hospital were selected for this study. All patients had data for both pre-treatment SPECT-CT imaging using 99mTc-MAA as a surrogate of the 90Y-microspheres treatment and SPECT-CT imaging immediately after the 90Y activity administration. Pre- and post-treatment doses were computed with TOPAS using the SPECT images to localize the source positions and the CT images to account for tissue inhomoegeneities. We compared our results with analytical calculations following the voxel-based MIRD scheme. Main results. TOPAS results largely agreed with the MIRD-based calculations in soft tissue regions: the average difference in mean dose to the liver was 0.14 Gy GBq−1 (2.6%). However, dose distributions in the lung differed considerably: absolute differences in mean doses to the lung ranged from 1.2 to 6.3 Gy GBq−1 and relative differences from 153% to 231%. We also found large differences in the intra-hepatic dose distributions between pre- and post-treatment imaging, but only limited differences in the pulmonary dose. Significance. Doses to lung were found to be higher using TOPAS with respect to analytical calculations which may significantly underestimate dose to the lung, suggesting the use of MC methods for 90Y dosimetry. According to our results, pre-treatment imaging may still be representative of dose to lung in these treatments.

An efficient probabilistic framework for the long-term fatigue assessment of large diameter steel risers

Using recent advances in data analytics techniques and tools, this paper proposes a novel data-centric paradigm for riser fatigue analysis in which practitioners can efficiently make use of large hindcast and measured metocean datasets directly in the design process. In the conventional fatigue design method for offshore risers systems, in order to reduce the computational cost practitioners tend to condense large hindcast metocean datasets into small wave datasets, so-called wave scatter diagrams, to represent the long-term variation in significant wave height, Hs, and peak period, Tp, at a site of interest. These methods tend to predict rather conservative riser loading conditions and hence fatigue lives due to the information lost in the condensing method, which can limit the application of steel catenary and lazy wave risers (SCRs and SLWRs) with larger diameters (outside diameter, OD > 18") whose design is governed by fatigue. This paper proposes enhanced frameworks for more accurate prediction of the fatigue life of SCRs and SLWRs located in swell dominant regions by enabling the direct use of large measured and hindcast metocean datasets in the fatigue design process of risers. Firstly, we introduce a novel detailed framework that uses an “ANN-based technique” with a “representative (P50) year” concept to enable large metocean datasets to be directly used for accurate estimation of riser fatigue life that is suitable for detailed design stages. Secondly, we propose an alternative innovative framework based on the use of Monte Carlo methods for more efficient long-term fatigue assessment of risers. Finally, we demonstrate the usefulness of the proposed frameworks by calculating the riser fatigue lives and comparing them against those obtained via conventional wave-condensing strategies. For the case studied here, the results show that using the proposed framework can significantly increase the estimated riser fatigue life over the values estimated using conventional wave condensing methods.

Generalized Birnbaum–Saunders mixture cure frailty model: inferential method and an application to bone marrow transplant data

Cluster time data are commonly encountered in survival analysis due to unobservable factors such as shared environmental conditions and genetic similarity. In such cases, careful attention needs to be paid to model the possible correlation between the subjects within the same cluster. Moreover, some diseases are curable due to great advances on modern medical techniques and treatments. For tracking these issues, we consider here a mixture cure frailty model, with generalized Birnbaum–Saunders frailty distribution, and propose a marginal likelihood approach for the estimation of model parameter. We approximate the intractable integrals in the likelihood function by the use of Monte-Carlo method. Thereafter, the maximum likelihood estimates are numerically determined. A simulation study and model discrimination are then carried out for evaluating the performance of the proposed model. It is observed from this study that the proposed model provides more flexibility and the method of inference is quite robust. Finally, we conduct an analysis of the effects of allogeneic and autologous bone marrow transplant treatments on acute lymphoblastic leukemia patients to demonstrate the usefulness of the proposed model and the method of inference.

Comments regarding the use of Monte Carlo method in the analysis of maritime ship maintenance works

Elaboration of a mathematical structure, together with a list of correspondences between the mathematical symbols and the objects of the concrete situation considered, led to what is called the mathematical model. The Monte Carlo simulation method is increasingly applied to the analysis of stochastic problems or in conditions of risk, when the same direction of action can have several consequences, the probabilities of which can be estimated. The Monte Carlo simulation can be used to analyze the flow of processes involved in the maintenance works of a ship in a shipyard, because it represents a system characterized by both input and output variables that can interact and therefore the same course of action may have several consequences. Thus, the execution of a certain type of maintenance work on the ship may lead to an increase or decrease in the volume of work initially estimated depending on: class society inspections, limiting the budget for works due to the crisis on the maritime transport market, labor force resources of the shipyard (limited in certain periods with peak load). Consequently, a stochastic model is outlined in which randomness is present, and the states of the variables are not described by unique values, but rather by probability distributions. The paper highlights, through concrete examples, some applications of the Monte Carlo method for the analysis of maintenance works performed for seagoing vessels.

Novel use of the Monte-Carlo methods to visualize singularity configurations in serial manipulators

This paper analyses the problem of the kinematic singularity of 6 DOF serial robots by extending the use of Monte-Carlo numerical methods to visualize singularity configurations. To achieve this goal, first, forward kinematics and D-H parameters have been derived for the manipulator. Second, the derived equations are used to generate and visualize a workspace that gives a good intuition of the motion shape of the manipulator. Third, the Jacobian matrix is computed using graphical methods, aiming to locate positions that cause singularity. Finally, the data obtained are processed in order to visualize the singularity and to design a trajectory free of singularity. MATLAB robotics toolbox, Symbolic toolbox, and curve fitting toolbox are the MATLAB toolboxes used in the calculations. The results of the surface and contour plots of the determinate of the Jacobian matrix behavior lead to design a manipulator’s trajectory free of singularity and show the parameters that affect the manipulator’s singularity and its behavior in the workspace.

Calculation of stability reliability of soft base controlled unstable rock and parameter sensitivity analysis

There are a large number of unstable rocks whose stability are controlled by soft base layer in the mountainous areas of southwest China, and they have caused serious harm to people’s lives and local economic development. Therefore, it is of great practical significance to study the stability and failure mechanism of such unstable rock. Taking the in Wulong District, Chongqing as an example, this paper analyzes the failure probability and reliability index of the unstable rock under different conditions by use of Monte Carlo method and on this basis, the sensitivity of the stability of dangerous rock mass to the main influencing factors is analyzed. The results show that the stability coefficient, failure probability and reliability index of are equal to 1.151, 26.245% and 0.642 under natural condition. However, the stability coefficient of decreases rapidly and the reliability index and failure probability increase obviously when combined with other factors such as rainfall or earthquake. The sensitivities of the influencing factors of the unstable rock are from top to bottom internal friction angle of soft layer, the horizontal seismic force, the cohesion of soft layer, the water content in the crack and the weight of soft layer. The research results can provide some reference for the stability analysis and engineering prevention of such unstable rocks.

Statistical exploration of halo anisotropic clustering and intrinsic alignments with the mass-Peak Patch algorithm

ABSTRACT The anisotropy or triaxiality of massive dark matter haloes largely defines the structure of the cosmic web, in particular the filaments that join the haloes together. Here, we investigate such oriented correlations in mass-Peak Patch halo catalogues by using the initial strain tensor of spherical proto-halo regions to orient the haloes. To go beyond the spherically averaged two-point correlation function of haloes, we use oriented stacks to compute oriented two-point correlations: we explicitly break isotropy by imposing a local frame set by the strain tensor of the reference halo before stacking neighbouring haloes. Beyond the exclusion zone of the reference halo, clustering is found to be strongly enhanced along the major direction of the strain tensor as expected. This anisotropic clustering of haloes along filaments is further quantified by using a spherical harmonics decomposition. Furthermore, we compute the evolution of cluster-scale halo principal directions relative to those of their neighbours and show that there are strong correlations extending up to very large scales. In order to provide calculations more suitable to observational confrontations, we also utilize 2D projected versions of some equivalent correlation functions. Finally, we show that the multipole structure of the mass-peak patch halo’s anisotropic clustering can be qualitatively captured in an analytic treatment based on peak theory. Though highly informative, giving the same qualitative features as the oriented correlations found from the simulation catalogue, analytic evaluation involves extensive use of Monte Carlo methods, which is also what the simulated catalogue uses, taking into account as they do the adaptive nature of the mass-peak patch mass hierarchy and all non-local complexities associated with the exclusion of smaller haloes overlapping with larger ones: there is no substitute for the mass-Peak Patch simulation-based determination of oriented and anisotropic correlations.

Ring oscillators yield analysis: Improving Monte Carlo models with optimized clustering methods

SummaryThe aim of this article is to demonstrate the interest of the optimized clustering method (OCM) when dealing with the yield analysis of ring oscillators, given uncertain assumptions over inputs. Indeed, the complementary metal–oxide semiconductor (CMOS) integrated circuit domain is facing a major challenge since these devices are subjected to noticeable fluctuations (mostly due to transistor constant scaling down at sub‐micron sizes), with utmost expectations regarding their performances (e.g., for digital circuits). Whether the classical approach requires use of Monte Carlo methods coupled with classical circuit solver (e.g., Spice and/or transistor model), the natural complexity of systems and varying inputs needs to provide alternative techniques, such as OCM. The foundations of the method and its efficiency will be presented and illustrated through ring oscillator applications.

Monte-Carlo Simulations of Soft Matter Using SIMONA: A Review of Recent Applications

Molecular simulations such as Molecular Dynamics (MD) and Monte Carlo (MC) have gained increasing importance in the explanation of various physicochemical and biochemical phenomena in soft matter and help elucidate processes that often cannot be understood by experimental techniques alone. While there is a large number of computational studies and developments in MD, MC simulations are less widely used, but they offer a powerful alternative approach to explore the potential energy surface of complex systems in a way that is not feasible for atomistic MD, which still remains fundamentally constrained by the femtosecond timestep, limiting investigations of many essential processes. This paper provides a review of the current developments of a MC based code, SIMONA, which is an efficient and versatile tool to perform large-scale conformational sampling of different kinds of (macro)molecules. We provide an overview of the approach, and an application to soft-matter problems, such as protocols for protein and polymer folding, physical vapor deposition of functional organic molecules and complex oligomer modeling. SIMONA offers solutions to different levels of programming expertise (basic, expert and developer level) through the usage of a designed Graphical Interface pre-processor, a convenient coding environment using XML and the development of new algorithms using Python/C++. We believe that the development of versatile codes which can be used in different fields, along with related protocols and data analysis, paves the way for wider use of MC methods. SIMONA is available for download under http://int.kit.edu/nanosim/simona.

THE McSAFE PROJECT - HIGH-PERFORMANCE MONTE CARLO BASED METHODS FOR SAFETY DEMONSTRATION: FROM PROOF OF CONCEPT TO INDUSTRY APPLICATIONS

The increasing use of Monte Carlo methods for core analysis is fostered by the huge and cheap computer power available nowadays e.g. in large HPC. Apart from the classical criticality calculations, the application of Monte Carlo methods for depletion analysis and cross section generation for diffusion and transport core simulators is also expanding. In addition, the development of multi-physics codes by coupling Monte Carlo solvers with thermal hydraulic codes (CFD, subchannel and system thermal hydraulics) to perform full core static core analysis at fuel assembly or pin level has progressed in the last decades. Finally, the extensions of the Monte Carlo codes to describe the behavior of prompt and delay neutrons, control rod movements, etc. has been started some years ago. Recent coupling of dynamic versions of Monte Carlo codes with subchannel codes make possible the analysis of transient e.g. rod ejection accidents and it paves the way for the simulation of any kind of design basis accidents as an alternative option to the use of diffusion and transport based deterministic solvers. The H2020 McSAFE Project is focused on the improvement of methods for depletion considering thermal hydraulic feedbacks, extension of the coupled neutronic/thermal hydraulic codes by the incorporation of a fuel performance solver, the development of dynamic Monte Carlo codes and the development of methods to handle large depletion problems and to reduce the statistical uncertainty. The validation of the multi-physics tools developed within McSAFE will be performed using plant data and unique tests e.g. the SPERT III E REA test. This paper will describe the main developments, solution approaches, and selected results.

Исследование межступенчатого канала комбинированного турбомолекулярного насоса

The calculation is based on the use of Monte Carlo method (method of test particle), which consists in the statistical modeling of processes. The article describes an algorithm to construct a mathematical model step by step. The article defines both a probability for gas molecules to pass through the interstage channel of a hybrid turbomolecular pump in forward and backward direction. The effect of the movable walls limiting the channel is taken into account. Results and, accordingly, recommendations, given in the article, can be used in designing a flow passage of the hybrid turbomolecular pumps. The dependencies of a probability for gas molecules to pass through the interstage canal on the relative parameters determining the geometry and dynamics of the channel walls are given

The use of Monte Carlo method to assess the uncertainty of thermal comfort indices PMV and PPD: Benefits of using a measuring set with an operative temperature probe

The Predicted Mean Vote (PMV) and Predicted Percentage of Dissatisfied (PPD) are the most used indices for the assessment of thermal conditions in indoor environments. However, many times, the uncertainties associated with the calculation of both indices are not reported, may be because direct methods are not easily applicable to calculate it. The present study applies Monte Carlo method to assess the uncertainties on the calculation of PMV and PPD, as a function of values and the uncertainties of four environmental (air temperature, mean radiant temperature, air velocity, and partial vapour pressure) and two individual related input parameters (metabolic rate and clothing insulation), used in Fanger's model, to calculate it. The metrological quality of the measuring probes was assumed through the scenarios established by ISO 7726 (1998) (required and desirable conditions). The use of uncertainties values for metabolic rate, clothing insulation and operative temperature were also considered. The main findings of this research are: (i) condition defined as required is not suitable for implementation of the classification scheme of thermal environments proposed by ISO 7730 (2005); (ii) in desirable condition, it is unrealistic obtaining an uncertainty of 0.2 °C for mean radiant temperature, if a 0.2 °C uncertainty temperature probe is used; (iii) the use of an operative temperature probe is a good strategy to decrease the overall level of uncertainty in the indices.