Monte Carlo Importance Sampling Research Articles

Maximum Likelihood Time Delay Estimation Based on Monte Carlo Importance Sampling in Multipath Environment

In multipath environment, the computation complexity of single snapshot maximum likelihood for time delay estimation is huge. In particular, the computational complexity of grid search method increases exponentially with the increase of dimension. For this reason, this paper presents a maximum likelihood estimation algorithm based on Monte Carlo importance sampling technique. Firstly, the algorithm takes advantage of the channel frequency response in order to build the likelihood function of time delay in multipath environment. The pseudoprobability density function is constructed by using exponential likelihood function. Then, it is crucial to choose the importance function. According to the characteristic of the Vandermonde matrix in likelihood function, the product of the conjugate transpose Vandermonde matrix and itself is approximated by the product of a constant and an identity matrix. The pseudoprobability density function can be decomposed into product of many probability density functions of single path time delay. The importance function is constructed. Finally, according to probability density function of multipath time delay decomposed by importance function, the time delay of the multipath is sampled by Monte Carlo method. The time delay is estimated via calculating weighted mean of sample. Simulation results show that the performance of proposed algorithm approaches the Cramér-Rao bound with reduced complexity.

A probabilistic bridge safety evaluation against floods.

To further capture the influences of uncertain factors on river bridge safety evaluation, a probabilistic approach is adopted. Because this is a systematic and nonlinear problem, MPP-based reliability analyses are not suitable. A sampling approach such as a Monte Carlo simulation (MCS) or importance sampling is often adopted. To enhance the efficiency of the sampling approach, this study utilizes Bayesian least squares support vector machines to construct a response surface followed by an MCS, providing a more precise safety index. Although there are several factors impacting the flood-resistant reliability of a bridge, previous experiences and studies show that the reliability of the bridge itself plays a key role. Thus, the goal of this study is to analyze the system reliability of a selected bridge that includes five limit states. The random variables considered here include the water surface elevation, water velocity, local scour depth, soil property and wind load. Because the first three variables are deeply affected by river hydraulics, a probabilistic HEC-RAS-based simulation is performed to capture the uncertainties in those random variables. The accuracy and variation of our solutions are confirmed by a direct MCS to ensure the applicability of the proposed approach. The results of a numerical example indicate that the proposed approach can efficiently provide an accurate bridge safety evaluation and maintain satisfactory variation.

Importance sampling and statistical Romberg method for Lévy processes

An important family of stochastic processes arising in many areas of applied probability is the class of Lévy processes. Generally, such processes are not simulatable especially for those with infinite activity. In practice, it is common to approximate them by truncating the jumps at some cut-off size ε (ε↘0). This procedure leads us to consider a simulatable compound Poisson process. This paper first introduces, for this setting, the statistical Romberg method to improve the complexity of the classical Monte Carlo method. Roughly speaking, we use many sample paths with a coarse cut-off εβ, β∈(0,1), and few additional sample paths with a fine cut-off ε. Central limit theorems of Lindeberg–Feller type for both Monte Carlo and statistical Romberg method for the inferred errors depending on the parameter ε are proved with explicit formulas for the limit variances. This leads to an accurate description of the optimal choice of parameters. Afterwards, the authors propose a stochastic approximation method in order to find the optimal measure change by Esscher transform for Lévy processes with Monte Carlo and statistical Romberg importance sampling variance reduction. Furthermore, we develop new adaptive Monte Carlo and statistical Romberg algorithms and prove the associated central limit theorems. Finally, numerical simulations are processed to illustrate the efficiency of the adaptive statistical Romberg method that reduces at the same time the variance and the computational effort associated to the effective computation of option prices when the underlying asset process follows an exponential pure jump CGMY model.

Extended saddlepoint methods for credit risk measurement

We propose a new method that extends the saddlepoint approximation to allocate credit risk. This method applies a Taylor expansion to the inverse Laplace transform around an arbitrary point to characterize the loss distribution of a portfolio. It is based on Hermite polynomials. From a computational point of view, our method is less demanding than other approximate methods. We also extend the current saddlepoint methods to deal with random recoveries and market valuation. Considering a portfolio that includes Spanish financial institutions, we show that these extensions can characterize the risk of the portfolio very well. The risk allocation method generates more accurate results than other approximate methods, with few calculations for default mode models and pure macroeconomy driven recoveries. We also find that modeling mixed idiosyncratic and macroeconomic random recoveries does not generate much greater risk than a pure macroeconomic random recoveries model. Finally, the results for the market valuation approximation are also very accurate, but this method requires a higher number of calculations. Other methods, such as the Monte Carlo importance sampling one, may be more suitable.

Stochastic Approach to Phonon-Assisted Optical Absorption.

We develop a first-principles theory of phonon-assisted optical absorption in semiconductors and insulators which incorporates the temperature dependence of the electronic structure. We show that the Hall-Bardeen-Blatt theory of indirect optical absorption and the Allen-Heine theory of temperature-dependent band structures can be derived from the present formalism by retaining only one-phonon processes. We demonstrate this method by calculating the optical absorption coefficient of silicon using an importance sampling MonteCarlo scheme, and we obtain temperature-dependent line shapes and band gaps in good agreement with experiment. The present approach opens the way to predictive calculations of the optical properties of solids at finite temperature.

Modeling and Prediction of Criminal Activity Based on Spatio-Temporal Probabilistic Risk Functions


 
 
 Security forces need to model risk patterns associated with criminal activity to study cause-effect relationships and predict new crimes. In this regard, criminal risk models are important to obtain relevant information for better resource al- location and prevention of future crime activity. This paper proposes a method to model and predict future criminal activity based on spatial probabilistic risk functions and a characterization of their temporal evolution as new data become available. This method uses geo-referenced information of public services (e.g., shopping centers, banks) and criminal incidents to approximate the prior risk function as a Gaussian Mixture Model (GMM). Temporal evolution of crime activity is characterized using an algorithm that is based on Sequential Monte Carlo Methods and Importance Sampling. This algorithm incorporates information from new measurements, in a recursive manner, to approximate the posterior spatial probabilistic risk function by updating particle positions in the map. Finally, we propose a novel prediction scheme for criminal activity that uses Gaussian fields centered on hypothetical future criminal events, which are sampled from a GMM that characterizes the spatial distribution associated with recent crime activity. The optimum number of centroids for each Gaussian kernel is evaluated using Silhouette algorithm. The time index related to each hypothetical future crime event is probabilistically characterized using an exponential distribution. Results using real data show that the majority of future events occur within risk modeled zones, information which can be used for resource allocation and improvement of intervention plans.
 
 

Parallel software for lattice [formula omitted] supersymmetric Yang–Mills theory

We present new parallel software, SUSY LATTICE, for lattice studies of four-dimensional N=4 supersymmetric Yang–Mills theory with gauge group SU(N). The lattice action is constructed to exactly preserve a single supersymmetry charge at non-zero lattice spacing, up to additional potential terms included to stabilize numerical simulations. The software evolved from the MILC code for lattice QCD, and retains a similar large-scale framework despite the different target theory. Many routines are adapted from an existing serial code (Catterall and Joseph, 2012), which SUSY LATTICE supersedes. This paper provides an overview of the new parallel software, summarizing the lattice system, describing the applications that are currently provided and explaining their basic workflow for non-experts in lattice gauge theory. We discuss the parallel performance of the code, and highlight some notable aspects of the documentation for those interested in contributing to its future development. Program summaryProgram title: SUSY LATTICECatalogue identifier: AELS_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELS_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 72821No. of bytes in distributed program, including test data, etc.: 1294754Distribution format: tar.gzProgramming language: C.Operating system: Any, tested on Linux workstations and MPI clusters with InfiniBand.Has the code been vectorized or parallelized?: Code is parallelizedClassification: 11.5.Catalogue identifier of previous version: AELS_v1_0Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 1336.External routines: Lapack, Blas, Primme (optional)Does the new version supersede the previous version?: YesNature of problem: To carry out non-perturbative Monte Carlo importance sampling for maximally supersymmetric Yang–Mills theories in two and four dimensions, and thereby compute observables including Wilson loops, fermion bilinears, eigenvalues of D†D and the Pfaffian of the sparse fermion operator D.Solution method: The central application is a rational hybrid Monte Carlo algorithm with a two-level Omelyan molecular dynamics integrator. Gauge field configurations generated by this application may be saved to disk for subsequent measurements of additional observables. Input parameters for either configuration generation or analysis may be entered manually or read from a file.Reasons for new version: The code is parallelized to improve performance and scalability. In addition, several new features and measurements are provided.Summary of revisions: The program is completely rewritten on the basis of the MILC code for lattice QCD, and several new features and measurements are added.Restrictions: The code is currently restricted to two-dimensional N=(2,2) and four-dimensional N=4 supersymmetric Yang–Mills theories. The process of topological twisting on which it is based can also be applied to a few other systems, as discussed in Sections 1 and 5.Additional comments: Further documentation is provided in the distribution file, including a set of test runs with reference output in the testsuite directory.Running time: From seconds to hours depending on the computational task, lattice volume, gauge group, and desired statistics, as well as on the computing platform and number of cores used. For example, rational hybrid Monte Carlo generation of 50 molecular dynamics time units for a 163×32 lattice volume with gauge group U(2) takes approximately 16 hours on 512 cores of the USQCD bc cluster at Fermilab, while standard measurements on a saved 83×24 U(2) configuration require only 8 seconds on one eight-core workstation.

Modeling zoned shock effects on stochastic degradation in dependent failure processes

This article studies a system that experiences two dependent competing failure processes, in which shocks are categorized into different shock zones. These two failure processes, a stochastic degradation process and a random shock process, are dependent because arriving shocks can cause instantaneous damage on the degradation process. In existing studies, every shock causes an abrupt damage on degradation. However, this may not be the case when shock loads are small and within the tolerance of system resistance. In the proposed model, only shock loads that are larger than a certain level are considered to cause abrupt damage on degradation, which makes this new model realistic and challenging. Shocks are divided into three zones based on their magnitudes: safety zone, damage zone, and fatal zone. The abrupt damage is modeled using an explicit function of shock load exceedances (differences between load magnitudes and a given threshold). Due to the complexity in modeling these two dependent stochastic failure processes, no closed form of the reliability function can be derived. Monte Carlo importance sampling is used to estimate the system reliability. Finally, two application examples with sensitivity analyses are presented to demonstrate the models.

Quenched large deviations for multiscale diffusion processes in random environments

We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium is assumed to be stationary and ergodic. In the course of the proof we also prove related quenched ergodic theorems for controlled diffusion processes in random environments that are of independent interest. The proof relies entirely on probabilistic arguments, allowing to obtain detailed information on how the rare event occurs. We derive a control, equivalently a change of measure, that leads to the large deviations lower bound. This information on the change of measure can motivate the design of asymptotically efficient Monte Carlo importance sampling schemes for multiscale systems in random environments

Reliability assessment on prediction of pile bearing capacity

There are many prediction methods that can be used to determine the bearing capacity of pipe pile. However, most of these methods are highly sensitive to specific in situ conditions and hence usually result in significant error. Therefore, it is important to evaluate the reliability of different pile bearing capacity prediction methods. Based on reliability theory, a computer code is developed in this paper to calculate reliability. Random variable statistic properties and corresponding reliabilities for different prediction methods are investigated and analysed. Results show that the reliability index for logarithmic normal distribution is higher than normal distribution. Analysis results demonstrate that the checking point method (JC method) method has a slightly lower efficiency than the Monte-Carlo importance sampling method and the Monte-Carlo direct sampling method. The Monte-Carlo importance sampling method has a higher efficiency than the Monte-Carlo direct sampling method. The Monte-Carlo importance sampling method can be used in major engineering projects. It is concluded that the clustering centre method has higher reliability in predicting pile bearing capacity than the Eslami and Fellenius method, Almeida method and Powell method.

Stochastic cost optimization of ground improvement with prefabricated vertical drains and surcharge preloading

The typical design of ground improvement with prefabricated vertical drains (PVD) and surcharge preloading involves a series of deterministic analyses using averaged or mean soil properties for the various combination of the PVD spacing and surcharge preloading height that would meet the criteria for minimum consolidation time and required degree of consolidation. The optimum design combination is then selected in which the total cost of ground improvement is a minimum. Considering the variability and uncertainties of the soil consolidation parameters, as well as considering the effects of soil disturbance (smear zone) and drain resistance in the analysis, this study presents a stochastic cost optimization of ground improvement with PVD and surcharge preloading. Direct Monte Carlo (MC) simulation and importance sampling (IS) technique is used in the stochastic analysis by limiting the sampled random soil parameters within the range from a minimum to maximum value while considering their statistical distribution. The method has been verified in a case study of PVD improved ground with preloading, in which average results of the stochastic analysis showed a good agreement with field monitoring data.

Estimating the distribution of total default losses on the Spanish financial system

This paper quantifies the credit risk loss distribution of the Spanish financial system by introducing a general Monte Carlo importance sampling (IS) approach. We start obtaining all the required information for the standard credit risk model. Then we quantify the loss distribution under the standard IS method and allocate the total risk over the different institutions in the Spanish financial system. We extend the current IS framework to deal with more general assumptions like random recoveries and market valuation. We also study the variability of the risk measures over the business cycle and the possible variability due to the model parameters uncertainty. Our results show that this approach can be very useful for banking supervisors from a macroprudential point of view and that the risk allocation can vary considerably depending on the valuation model under analysis.

Reduced Complexity HMM Filtering With Stochastic Dominance Bounds: A Convex Optimization Approach

This paper uses stochastic dominance principles to construct upper and lower sample path bounds for Hidden Markov Model (HMM) filters. We consider an HMM consisting of an X-state Markov chain with transition matrix P. By using convex optimization methods for nuclear norm minimization with copositive constraints, we construct low rank stochastic matrices P and P̅ so that the optimal filters using P,P̅ provably lower and upper bound (with respect to a partially ordered set) the true filtered distribution at each time instant. Since P and P̅ are low rank (say R), the computational cost of evaluating the filtering bounds is O(X R) instead of O(X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). A Monte-Carlo importance sampling filter is presented that exploits these upper and lower bounds to estimate the optimal posterior. Finally, explicit bounds are given on the variational norm between the true posterior and the upper and lower bounds in terms of the Dobrushin coefficient.

Structure and solid solution properties of Cu–Ag nanoalloys

The nanoparticle phase diagram of an immiscible system is studied at the atomic level. Cu–Ag clusters with sizes 1000 and 2000 atoms, resulting from a global minimum search and belonging to icosahedral and crystalline structural motifs, are considered. We present the statistical analysis of the effect of temperature on the solubility of the two elements based on Metropolis Monte Carlo importance sampling. Our results suggest that the relevance of bulk phase diagrams to nanoparticles is limited to cases where the internal stress distribution does not deviate very much from uniform (e.g. sufficiently large crystalline clusters). In the general case, the principal interdependence between partial phase compositions and the overall cluster composition in nanoparticle phase diagrams need to be taken into account.

Multiview feature distributions for object detection and continuous pose estimation

This paper presents a multiview model of object categories, generally applicable to virtually any type of image features, and methods to efficiently perform, in a unified manner, detection, localization and continuous pose estimation in novel scenes. We represent appearance as distributions of low-level, fine-grained image features. Multiview models encode the appearance of objects at discrete viewpoints, and, in addition, how these viewpoints deform into one another as the viewpoint continuously varies (as detected from optical flow between training examples). Using a measure of similarity between an arbitrary test image and such a model at chosen viewpoints, we perform all tasks mentioned above with a common method. We leverage the simplicity of low-level image features, such as points extracted along edges, or coarse-scale gradients extracted densely over the images, by building probabilistic templates, i.e. distributions of features, learned from one or several training examples. We efficiently handle these distributions with probabilistic techniques such as kernel density estimation, Monte Carlo integration and importance sampling. We provide an extensive evaluation on a wide variety of benchmark datasets. We demonstrate performance on the “ETHZ Shape” dataset, with single (hand-drawn) and multiple training examples, well above baseline methods, on par with a number of more task-specific methods. We obtain remarkable performance on the recognition of more complex objects, notably the cars of the “3D Object” dataset of Savarese et al. with detection rates of 92.5% and an accuracy in pose estimation of 91%. We perform better than the state-of-the-art on continuous pose estimation with the “rotating cars” dataset of Ozuysal et al. We also demonstrate particular capabilities with a novel dataset featuring non-textured objects of undistinctive shapes, the pose of which can only be determined from shading, captured here by coarse scale intensity gradients.

Reliability analysis of marine risers with narrow and long corrosion defects under combined loads

A marine riser, one of the most important components of offshore oil/gas transportation, needs to be designed to eliminate the risks caused by complex ocean environments, platform displacement and internal corrosion, etc. In this study, a new analytical-numerical assessment approach is proposed in order to quantitatively investigate the reliability of internally corroded risers under combined loads including axial tension and internal pressure. First, an analytical solution of the limit state function of intact risers under combined loads is obtained, which is further modified by the non-dimensional corrosion depth (d/t) for the risers with a narrow and long corrosion defect. The relationship between d/t and limited internal pressure is obtained by finite element analysis and nonlinear regression. Through an advanced first-order reliability method (HL-RF) algorithm, reliability analysis is performed to obtain the failure probability, the reliability index and the sensitivity. These results are further verified by Monte-Carlo importance sampling. The proposed approach of reliability analysis provides an accurate and effective way to estimate the reliability of marine risers with narrow and long corrosion defects under combined loads.

오류 마루 현상이 완화된 비이진 LDPC 부호의 설계 및 성능 분석 연구

본 논문은 오류 마루 영역에서 우수한 성능을 가지는 비이진 LDPC (low-density parity-check) 부호의 설계 방법을 제안하고 성능을 검증한다. 제안된 설계 방법은 비이진 LDPC 부호의 이진 최소 거리(binary minimum distance)를 최대화하도록 패리티 검사 행렬의 비이진 원소 값들을 결정한다. BPSK (binary phase-shift keying) 변조 방식 하에서 제안된 방법으로 설계된 비이진 LDPC 부호가 오류 마루(error floor) 영역에서 우수한 성능을 가지는 것을 Monte Carlo 시뮬레이션과 중요도 표본 추출(importance sampling) 기법을 사용하여 검증한다. In this paper we propose a design algorithm for nonbinary LDPC (low-density parity-check) codes with low error-floors. The proposed algorithm determines the nonbinary values of the nonzero entries in the parity-check matrix in order to maximize the binary minimum distance of the designed nonbinary LDPC codes. We verify the performance of the designed nonbinary LDPC codes in the error-floor region by Monte Carlo simulation and importance sampling over BPSK (binary phase-shift keying) modulation.

Importance Sampling and the Spanish Financial System

This paper quantifies the credit risk loss distribution of the Spanish financial system by introducing a general Monte Carlo importance sampling (IS) approach. We start obtaining all the required information for the Vasicek (1987) model. Then we quantify the loss distribution under the standard IS method introduced by Glasserman and Li (2005) and allocate the total risk over the different institutions in the Spanish financial system. We also extend the current IS framework to deal with more general assumptions like random recoveries and market valuation. Our results show that this approach can be very useful for banking supervisors from a macroprudential point of view and that the risk allocation can vary considerably depending on the valuation model under analysis.

Exact Enumeration of the Phase Space of an Ising Model of Ni$_{2}$MnGa

Exact evaluations of partition functions are generally prohibitively expensive due to exponential growth of phase space with the number of degrees of freedom. For an 'sing model with sites the number of possible states is requiring the use of better scaling methods such as importance sampling Monte-Carlo calculations for all but the smallest systems. Yet the ability to obtain exact solutions for as large as possible systems can provide important benchmark results and opportunities for unobscured insight into the underlying physics of the system. Here we present an 'sing model for the magnetic sublattices of the important magneto-caloric material Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> MnGa and use an exact enumeration algorithm to calculate the number of states for each energy and sublattice magnetizations M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ni</sub> and M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Mn</sub> . This allows the efficient calculation of the partition function and derived thermodynamic quantities such as specific heat and susceptibility. Utilizing the jaguarpf system at Oak Ridge we are able to calculate for systems of up to 48 sites, which provides important insight into the mechanism for the large magnet-caloric effect in Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> MnGa as well as an important benchmark for Monte-Carlo (esp. Wang-Landau method).

Local estimation of failure probability function by weighted approach

In the reliability-based design of engineering systems, it is often required to evaluate the failure probability for different values of distribution parameters involved in the specification of design configuration. The failure probability as a function of the distribution parameters is referred as the ‘failure probability function (FPF)’ in this work. From first principles, this problem requires repeated reliability analyses to estimate the failure probability for different distribution parameter values, which is a computationally expensive task. A “weighted approach” is proposed in this work to locally evaluate the FPF efficiently by means of a single simulation. The basic idea is to rewrite the failure probability estimate for a given set of random samples in simulation as a function of the distribution parameters. It is shown that the FPF can be written as a weighted sum of sample values. The latter must be evaluated by system analysis (the most time-consuming task) but they do not depend on the distribution. Direct Monte Carlo simulation, importance sampling and Subset Simulation are incorporated under the proposed approach. Examples are given to illustrate their application.