Search

This paper focuses on approximating stochastic delay differential equations with delayed impulses using Euler-Maruyama-type approximations. One key difference from previous literature is that the impulsive perturbations considered in this paper are past-dependent. Additionally, both the time delays in the stochastic delay differential equations and in the impulsive functions are functions of time. We establish the mean square convergence of the Euler-Maruyama approximations under a local Lipschitz condition and a linear growth condition. Furthermore, we determine the order of convergence under a global Lipschitz condition and provide an illustrative example. [ABSTRACT FROM AUTHOR]

Estimating free energy differences, an important problem in computational drug discovery and in a wide range of other application areas, commonly involves a computationally intensive process of sampling a family of high-dimensional probability distributions and a procedure for computing estimates based on those samples. The variance of the free energy estimate of interest typically depends strongly on how the total computational resources available for sampling are divided among the distributions, but determining an efficient allocation is difficult without sampling the distributions. Here we introduce the Times Square sampling algorithm, a novel on-the-fly estimation method that dynamically allocates resources in such a way as to significantly accelerate the estimation of free energies and other observables, while providing rigorous convergence guarantees for the estimators. We also show that it is possible, surprisingly, for on-the-fly free energy estimation to achieve lower asymptotic variance than the maximum-likelihood estimator MBAR, raising the prospect that on-the-fly estimation could reduce variance in a variety of other statistical applications. for this article are available online. [ABSTRACT FROM AUTHOR]

In this study, we propose an approximation for a renewal reward process that describes a stochastic control model of type (s, S) based on the first three moments of demand random variables. Various asymptotic expansions for this model exist in the literature. All these studies rely on the condition of knowing the distribution function of demand random variables and require obtaining the asymptotic expansion of the renewal function produced by them. However, obtaining a renewal function can be challenging for certain distribution families, and in some cases, the mathematical structure of the renewal function is difficult to apply. Therefore, in this study, simple and compact approximations are presented for the stochastic control model of type (s, S). The findings of this study rely on Kambo's method, through which we obtain approximations for the ergodic distribution, and the nth order ergodic moments of this process. To conclude the study, the accuracy of the proposed approximate formulas are examined through a specialized illustrative example. Moreover, it has been noted that the proposed approximation is more accurate than the approximations existing in the literature. [ABSTRACT FROM AUTHOR]

In statistical process monitoring, control charts typically depend on a set of tuning parameters besides its control limit(s). Proper selection of these tuning parameters is crucial to their performance. In a specific application, a control chart is often designed for detecting a target process distributional shift. In such cases, the tuning parameters should be chosen such that some characteristic of the out-of-control (OC) run length of the chart, such as its average, is minimized for detecting the target shift, while the control limit is set to maintain a desired in-control (IC) performance. However, explicit solutions for such a design are unavailable for most control charts, and thus numerical optimization methods are needed. In such cases, Monte Carlo-based methods are often a viable alternative for finding suitable design constants. The computational cost associated with such scenarios is often substantial, and thus computational efficiency is a key requirement. To address this problem, a two-step design based on stochastic approximations is presented in this paper, which is shown to be much more computationally efficient than some representative existing methods. A detailed discussion about the new algorithm's implementation along with some examples are provided to demonstrate the broad applicability of the proposed methodology for the optimal design of univariate and multivariate control charts. Computer codes in the Julia programming language are also provided in the . [ABSTRACT FROM AUTHOR]

This article deals with the active redundancy allocation to coherent systems. We extend the optimal allocation policy uniformly maximizing the redundant system reliability function to that maximizing the mean lower semi-deviation of the redundant system lifetime, and then we propose a stochastic algorithm to approximate the optimal redundancy allocation policy through maximizing the mean lower semi-deviation of the system lifetime. Some numerical examples are presented to illustrate the algorithm as well. [ABSTRACT FROM AUTHOR]

It is shown that higher-order influence functions for M-estimators are mathematically equivalent to higher-order stochastic approximations to these estimators. The stochastic expansions are also shown to have corresponding higher-order U-statistic representations, providing an alternative approach for deriving and analyzing the approximate properties of M-estimators. [ABSTRACT FROM AUTHOR]

We establish an almost sure convergence theorem of the stochastic approximation process of Oja for estimating eigenvectors of the Q-symmetric expectation of a random matrix, under a correlation model between the incoming random matrices. This theorem generalizes previous theorems and extends them to the case where the metric Q is unknown and estimated online in parallel. We apply it to streaming principal component analysis of a random vector Z, when a mini-batch of observations of Z is used at each step or all the observations up to the current step. We deal with the case of streaming generalized canonical correlation analysis, with a metric estimated online in parallel. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain convergence in mean in the uniform topology of piecewise linear approximations of stochastic differential equations (SDEs) with C1 drift and C2 diffusion coefficients with uniformly bounded derivatives. Convergence analyses for such Wong-Zakai approximations most often assume that the coefficients of the SDE are uniformly bounded. Almost sure convergence in the unbounded case can be obtained using now standard rough path techniques, although Lq convergence appears yet to be established and is of importance for several applications involving Monte-Carlo approximations. We consider L2 convergence in the unbounded case using a combination of traditional stochastic analysis and rough path techniques. We expect our proof technique extend to more general piecewise smooth approximations. [ABSTRACT FROM AUTHOR]

This article proposes an identification method of continuous-time fractional-order Hammerstein model using smoothed functional algorithm with a norm-limited update vector (NL-SFA). In particular, the standard smoothed functional algorithm (SFA) based method is modified by implementing a limit function in the update vector of the standard SFA based method to solve the issue of high tendency of divergence during the identification process. As a result of this, the proposed NL-SFA based method is applied to identify the variables of the linear and non-linear subsystems in the Hammerstein model. While most of the actual linear subsystems can be naturally expressed in a continuous-time domain, the implementation of the fractional-order could also reduce the computational complexity in finding a more accurate reduced-order model. Moreover, three experiments of the Hammerstein model identification based on a numerical example, an actual twin-rotor system, and an actual flexible manipulator system were carried out in this study to verify the effectiveness of the proposed NL-SFA-based method. The numerical and experimental results were analyzed to correspond to the measurement of the objective function and variable identification error and time-domain and frequency-domain responses. Conclusively, the proposed NL-SFA-based method can provide stable convergence and significantly better accuracy of the Hammerstein model in the numerical example, the actual twin-rotor system, and the flexible manipulator system compared to the standard SFA. Moreover, the proposed NL-SFA also provides slightly competitive identification accuracy with the existing norm-limited simultaneous perturbation stochastic approximation (NL-SPSA) and the average multi-verse optimizer sine cosine algorithm (AMVO-SCA) based methods. [ABSTRACT FROM AUTHOR]

This article discusses the importance of assessing the goodness-of-fit (GOF) of item response theory (IRT) models and proposes a method called the information matrix test (IMT) to address computational challenges. The IMT compares the cross-product form and the Hessian form of the information matrix to evaluate model specification. The study conducted a simulation to assess the effectiveness of the proposed method and found that the IMT effectively controlled the Type I error rate and demonstrated slightly higher power compared to other tests. Overall, the IMT shows promise as a method for GOF assessment in multidimensional IRT models. [Extracted from the article]

Finite-sum problems appear as the sample average approximation of a stochastic optimization problem and often arise in machine learning applications with large scale data sets. A very popular approach to face finite-sum problems is the stochastic gradient method. It is well known that a proper strategy to select the hyperparameters of this method (i.e. the set of a-priori selected parameters) and, in particular, the learning rate, is needed to guarantee convergence properties and good practical performance. In this paper, we analyse standard and line search based updating rules to fix the learning rate sequence, also in relation to the size of the mini batch chosen to compute the current stochastic gradient. An extensive numerical experimentation is carried out in order to evaluate the effectiveness of the discussed strategies for convex and non-convex finite-sum test problems, highlighting that the line search based methods avoid expensive initial setting of the hyperparameters. The line search based approaches have also been applied to train a Convolutional Neural Network, providing very promising results. [ABSTRACT FROM AUTHOR]

The recent emergence of reinforcement learning (RL) has created a demand for robust statistical inference methods for the parameter estimates computed using these algorithms. Existing methods for inference in online learning are restricted to settings involving independently sampled observations, while inference methods in RL have so far been limited to the batch setting. The bootstrap is a flexible and efficient approach for statistical inference in online learning algorithms, but its efficacy in settings involving Markov noise, such as RL, has yet to be explored. In this article, we study the use of the online bootstrap method for inference in RL policy evaluation. In particular, we focus on the temporal difference (TD) learning and Gradient TD (GTD) learning algorithms, which are themselves special instances of linear stochastic approximation under Markov noise. The method is shown to be distributionally consistent for statistical inference in policy evaluation, and numerical experiments are included to demonstrate the effectiveness of this algorithm across a range of real RL environments. for this article are available online. [ABSTRACT FROM AUTHOR]

Patient unpunctuality significantly disrupts the operations of healthcare facilities, reduces provider productivity, and increases healthcare costs. To alleviate the negative impact of unpunctual patients, this study addresses the appointment scheduling (AS) in the simultaneous presence of unpunctual patients, multiple servers, and no-shows. To determine the appointment schedule, we propose a two-stage stochastic mixed-integer programming model to minimise the total cost incurred by patient waiting and clinic overtime. It becomes challenging for a standard solver to solve this model due to the dynamic patient-to-server assignment decisions that are proactively anticipated in the determination of appointment times. To deal with this problem, a stochastic approximation algorithm is proposed under unbiased gradient estimators. The effectiveness and efficiency of this algorithm are validated in extensive numerical experiments that compare it with Benders decomposition and a heuristic algorithm. Further, the features of the optimal appointment schedule are analysed: (i) the shape of the appointment intervals relies on the number of servers; (ii) the length of intervals is sensitive to no-shows; (iii) the initial block size is greatly affected by patient unpunctuality. Managerial insights are also provided for hospital managers to schedule unpunctual patients in practice. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate a new kernel regression estimators based on the two-time-scale stochastic approximation algorithm in the case of independent functional data. We study the properties of the proposed recursive estimators and compare them with the recursive estimators based on single-time-scale stochastic algorithm proposed by Slaoui and to the non-recursive estimator proposed by Slaoui. It turns out that, with an adequate choice of the parameters, the proposed two-time-scale estimators perform better than the recursive estimators constructed using single-time-scale stochastic algorithm. We corroborate these theoretical results through some simulations and two real datasets. [ABSTRACT FROM AUTHOR]

Asymptotic residue expansions are proposed for inverting probability generating functions (PGFs) and approximating their associated mass and survival functions. The expansions are useful in the wide range of stochastic model applications in which a PGF admits poles in its analytic continuation. The error of such an expansion is a contour integral in the analytic continuation and saddlepoint approximations are developed for such errors using the method of steepest descents. These saddlepoint error estimates attain sufficient accuracy that they can be used to set the order of the expansion so it achieves a specified error. Numerical applications include a success run tutorial example, the discrete ruin model, the Pollaczek-Khintchine formula, and passage times for semi-Markov processes. The residue expansions apply more generally for inverting generating functions which arise in renewal theory and combinatorics and lead to a simple proof of the classic renewal theorem. They extend even further for determining Taylor coefficients of general meromorphic functions. [ABSTRACT FROM AUTHOR]

A decision-making process often involves selecting the best solution from a finite set of possible alternatives regarding some performance measure, which is known as Ranking-and-Selection (R&S) when the performance is not explicitly available and can only be estimated by taking samples. Many R&S procedures have been proposed considering different problem formulations. In this article, we adopt the classic fully sequential Indifference-Zone (IZ) formulation developed in the statistical literature, and take advantage of the control variates, a well-known variance reduction technique in the simulation literature, to investigate the potential benefits as well as the statistical guarantee by designing a new type of R&S procedure in an adaptive fashion. In particular, we propose a generic adaptive fully sequential procedure that can employ both linear and nonlinear control variates, in which both the control coefficient and sample variance can be sequentially updated as the sampling process progresses. We demonstrate that the proposed procedures provide the desired probability of correct selection in the asymptotic regime as the IZ parameter goes to zero. We then compare the proposed procedures with various existing procedures through the simulation experiments on practical illustrative examples, in which we observe several interesting findings and demonstrate the advantage of our proposed procedures. [ABSTRACT FROM AUTHOR]

Inference for high-dimensional, large scale and long series dynamic systems is a challenging task in modern data science. The existing algorithms, such as particle filter or sequential importance sampler, do not scale well to the dimension of the system and the sample size of the dataset, and often suffers from the sample degeneracy issue for long series data. The recently proposed Langevinized ensemble Kalman filter (LEnKF) addresses these difficulties in a coherent way. However, it cannot be applied to the case that the dynamic system contains unknown parameters. This article proposes the so-called stochastic approximation-LEnKF for jointly estimating the states and unknown parameters of the dynamic system, where the parameters are estimated on the fly based on the state variables simulated by the LEnKF under the framework of stochastic approximation Markov chain Monte Carlo (MCMC). Under mild conditions, we prove its consistency in parameter estimation and ergodicity in state variable simulations. The proposed algorithm can be used in uncertainty quantification for long series, large scale, and high-dimensional dynamic systems. Numerical results indicate its superiority over the existing algorithms. We employ the proposed algorithm in state-space modeling of the sea surface temperature with a long short term memory (LSTM) network, which indicates its great potential in statistical analysis of complex dynamic systems encountered in modern data science. for this article are available online. [ABSTRACT FROM AUTHOR]

Sliced inverse regression (SIR) is a recommended method to identify and estimate the central dimension reduction (CDR) subspace. CDR subspace is at the base to describe the conditional distribution of the response Y given a d-dimensional predictor vector X. To estimate this space, two versions are very popular: the slice version and the kernel version. A recursive method of the slice version has already been the subject of a systematic study. In this paper, we propose to study the kernel version. It's a recursive method based on a stochastic approximation algorithm of the kernel version. The asymptotic normality of the proposed estimator is also proved. A simulation study that not only shows the good numerical performance of the proposed estimate and which also allows to evaluate its performance with respect to existing methods is presented. A real dataset is also used to illustrate the approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider a type of semidefinite programming problem (MSDP), which involves many (not necessarily finite) of semidefinite constraints. MSDP can be established in a wide range of applications, including covering ellipsoids problem and truss topology design. We propose a random method based on a stochastic approximation technique for solving MSDP, without calculating and storing the multiplier. Under mild conditions, we establish the almost sure convergence and expected convergence rates of the proposed method. A variety of simulation experiments are carried out to support our theoretical results. [ABSTRACT FROM AUTHOR]

We consider minimizing a class of nonconvex composite stochastic optimization problems, and deterministic optimization problems whose objective function consists of an expectation function (or an average of finitely many smooth functions) and a weakly convex but potentially nonsmooth function. And in this paper, we focus on the theoretical properties of two types of stochastic splitting methods for solving these nonconvex optimization problems: stochastic alternating direction method of multipliers and stochastic proximal gradient descent. In particular, several inexact versions of these two types of splitting methods are studied. At each iteration, the proposed schemes inexactly solve their subproblems by using relative error criteria instead of exogenous and diminishing error rules, which allows our approaches to handle some complex regularized problems in statistics and machine learning. Under mild conditions, we obtain the convergence of the schemes and their computational complexity related to the evaluations on the component gradient of the smooth function, and find that some conclusions of their exact counterparts can be recovered. [ABSTRACT FROM AUTHOR]

In this paper, we consider discrete time approximations for stochastic differential equations with the form: X t = X 0 + ∫ 0 t f (X s) d h s + ∫ 0 t g (X s) d Y s H , t > 0 , where h : R + → R is a continuous function with locally bounded variation, f , g : R → R are measurable functions, and the integral with respect to Y t H = ∫ 0 t σ s d S s H is the pathwise Riemann-Stieltjes integral, SH is a subfractional Brownian motion with H ∈ (1 2 , 1) , σ is a deterministic (possibly discontinuous) function. [ABSTRACT FROM AUTHOR]

We consider a symmetric system of conservation laws and its stochastic approximation with stochastic multiplicative noise. Using the vanishing viscosity with the zero-noise limit we obtain a deterministic weak solution for some time interval. [ABSTRACT FROM AUTHOR]

We consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model. In particular, the variance process is therefore not a Markov process or semimartingale, and has quite low Hölder-regularity. In practice, simulating such rough processes thus often results in high computational cost. To remedy this, we study approximations of stochastic Volterra equations using an N-dimensional diffusion process defined as solution to a system of ordinary stochastic differential equation. If the coefficients of the stochastic Volterra equation are Lipschitz continuous, we show that these approximations converge strongly with superpolynomial rate in N. Finally, we apply this approximation to compute the implied volatility smile of a European call option under the rough Bergomi and the rough Heston model. [ABSTRACT FROM AUTHOR]

In this paper, we consider an extension of the generalized class of recursive regression estimators to the case of strong mixing data. Then, we study the properties of these estimators and compare them with the well known Nadaraya-Watson estimator. The Bias, variance and Mean Integrated Square Error are computed explicitly. Using a selected bandwidth and a special stepsize, we showed that the proposed recursive estimators allowed us to obtain quite better results compared to the non-recursive regression estimator under α-mixing condition in terms of estimation error and much better in terms of computational costs. [ABSTRACT FROM AUTHOR]

We introduce computational methods that allow for effective estimation of a flexible nonstationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field is defined as a weighted spatially varying linear combination of a globally stationary process and locally stationary processes. Often in such a model, the difficulty in its practical use is in the definition of the boundaries for the local processes, and therefore, we describe one such selection procedure that generally captures complex nonstationary relationships. We generalize the use of a stochastic approximation to the score equations in this nonstationary case and provide tools for evaluating the approximate score in O (n log ⁡ n) operations and O(n) storage for data on a subset of a grid. We perform various simulations to explore the effectiveness and speed of the proposed methods and conclude by predicting average daily temperature. for this article are available online. [ABSTRACT FROM AUTHOR]

In the machine learning and optimization community, there are two main approaches for the convex risk minimization problem, namely the Stochastic Approximation (SA) and the Sample Average Approximation (SAA). In terms of the oracle complexity (required number of stochastic gradient evaluations), both approaches are considered equivalent on average (up to a logarithmic factor). The total complexity depends on a specific problem, however, starting from the work [A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro, Robust stochastic approximation approach to stochastic programming, SIAM. J. Opt. 19 (2009), pp. 1574–1609] it was generally accepted that the SA is better than the SAA. We show that for the Wasserstein barycenter problem, this superiority can be inverted. We provide a detailed comparison by stating the complexity bounds for the SA and SAA implementations calculating barycenters defined with respect to optimal transport distances and entropy-regularized optimal transport distances. As a byproduct, we also construct confidence intervals for the barycenter defined with respect to entropy-regularized optimal transport distances in the ℓ 2 -norm. The preliminary results are derived for a general convex optimization problem given by the expectation to have other applications besides the Wasserstein barycenter problem. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of the regression estimation near the edges under censoring. For this purpose, we consider a new recursive estimator based on the stochastic approximation algorithm and Bernstein polynomials of the regression function when the response random variable is subject to random right censoring. We give the central limit theorem and the strong pointwise convergence rate for our proposed nonparametric recursive estimators under some mild conditions. Finally, we provide pointwise moderate deviation principles (MDP) for the proposed estimators. We corroborate these theoretical results through simulations as well as the analysis of a real data set. [ABSTRACT FROM AUTHOR]

We propose a tamed-adaptive Euler-Maruyama approximation scheme for stochastic differential equations with locally Lipschitz continuous, polynomial growth drift, and locally Hölder continuous, polynomial growth diffusion coefficients. We consider the strong convergence and the stability of the new scheme. In particular, we show that under some sufficient conditions for the stability of the exact solution, the tamed-adaptive scheme converges strongly in both finite and infinite time intervals. [ABSTRACT FROM AUTHOR]

A safe experimentation dynamics (SED) is a game theoretic method that randomly perturbs several elements of its design parameter to search for the optimal design parameter. However, the accuracy of the standard SED can be further improved by proposing an adaptive SED method. This paper aims to develop a method based on adaptive safe experimentation dynamics (ASED) where the updated design parameter is modified to adapt to the change of the objective function. The proposed ASED is then used to tune the parameters of the neuroendocrine-PID controller. The neuroendocrine-PID controller, which is based on the secretion rule of hormone regulation in the human body and well known for its high control accuracy, is chosen to improve the conventional PID controller structure for the MIMO systems. Moreover, it is shown that the proposed neuroendocrine-PID based ASED can solve an unstable convergence problem in the existing neuroendocrine-PID based Simultaneous Perturbation Stochastic Approximation (SPSA). The performance of the proposed neuroendocrine-PID based on the ASED method is evaluated by tracking its performances and computational time. Additionally, the performance of the ASED based method is compared to the standard SED and SPSA based methods. The results of the simulation showed that the ASED method could provide stable convergence by minimizing the function of the given objective. The ASED also obtains a value for the objective function and the total norm error for tracking performance accuracy that is lower compared to other methods. [ABSTRACT FROM AUTHOR]

Online learning is a method for analyzing very large datasets ('big data') as well as data streams. In this article, we consider the case of constrained binary logistic regression and show the interest of using processes with an online standardization of the data, in particular to avoid numerical explosions or to allow the use of shrinkage methods. We prove the almost sure convergence of such a process and propose using a piecewise constant step-size such that the latter does not decrease too quickly and does not reduce the speed of convergence. We compare twenty-four stochastic approximation processes with raw or online standardized data on five real or simulated data sets. Results show that, unlike processes with raw data, processes with online standardized data can prevent numerical explosions and yield the best results. [ABSTRACT FROM AUTHOR]

Condition-based maintenance (CBM) is becoming increasingly prevalent because of its capability to continuously track equipment health degradation and accurately predict unscheduled equipment failure. CBM helps to improve the business bottom line by preventing costly station failure. However, it is not uncommon that CBM needs to stop stations for maintenance during operation, which can severely impede the normal production. The objective of this paper is to develop a systematic method to predict the negative impact of CBM stoppage events on production in a multistage manufacturing system. The research helps to predict the real expense of applying CBM, which is the foundation to establish a comprehensive real-time CBM decision-making model. We start from the event-based analysis of system dynamics and develop a stochastic estimation method to predict the permanent production loss caused by a CBM stoppage event. The monotonicity property of permanent production loss is investigated. Simulation case studies are performed to illustrate the theoretical results and demonstrate their potential in facilitating CBM decision-making. [ABSTRACT FROM PUBLISHER]

This paper deals with the selective maintenance problem for a multi-component system performing consecutive missions separated by scheduled breaks. To increase the probability of successfully completing its next mission, the system components are maintained during the break.Alist of potential imperfect maintenance actions on each component, ranging from minimal repair to replacement is available. The general hybrid hazard rate approach is used to model the reliability improvement of the system components. Durations of the maintenance actions, the mission and the breaks are stochastic with known probability distributions. The resulting optimisation problem is modelled as a non-linear stochastic programme. Its objective is to determine a cost-optimal subset of maintenance actions to be performed on the components given the limited stochastic duration of the break and the minimum system reliability level required to complete the next mission. The fundamental concepts and relevant parameters of this decision-making problem are developed and discussed. Numerical experiments are provided to demonstrate the added value of solving this selective maintenance problem as a stochastic optimisation programme. [ABSTRACT FROM AUTHOR]

We consider a two-echelon production-inventory system with a central supplier connected to production systems (servers) at several locations, each with a local inventory. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted. To satisfy a customer’s demand, a server at the production system takes exactly one unit of raw material from the associated local inventory. The central supplier manufactures raw material to replenish the local inventories, which are controlled by a continuous review base stock policy. We derive stationary distributions of joint queue length and inventory processes in explicit product form. After performing a cost analysis, we find out that the global search for the vector of optimal base stock levels can be reduced to a set of independent optimisation problems. The explicit form of the stationary distribution enables us to get additional structural insights, e.g. about monotonicity properties and stability conditions. Obtaining the product form relies on some simplifying assumptions. The results are therefore compared with simulations of a more realistic system, which supports to use it as approximation. [ABSTRACT FROM AUTHOR]

One of the fundamental problems in Bayesian statistics is the approximation of the posterior distribution. Gibbs sampler and coordinate ascent variational inference are renownedly utilized approximation techniques that rely on stochastic and deterministic approximations. In this paper, we define fundamental sets of densities frequently used in Bayesian inference. We shall be concerned with the clarification of the two schemes from the set-theoretical point of view. This new way provides an alternative mechanism for analyzing the two schemes endowed with pedagogical insights. [ABSTRACT FROM AUTHOR]

The linear regression model is a popular tool used by almost all in different areas of research. The model relies mainly on the assumption of uncorrelated errors from a Gaussian distribution. However, many datasets in practice violate this basic assumption, making inference in such cases invalid. Therefore, the linear regression model with structured errors driven by heavy-tailed innovations are preferred in practice. Another issue that occur frequently with real-life data is missing values, due to some reasons such as system breakdown and labor unrest. Despite the challenge these two issues pose to practitioners, there is scarcity of literature where they have jointly been studied. Hence, this article considers these two issues jointly, for the first time, and develops an efficient parameter estimation procedure for Student's-t autoregressive regression model for time series with missing values of the response variable. The procedure is based on a stochastic approximation expectation–maximization algorithm coupled with a Markov chain Monte Carlo technique. The procedure gives efficient closed-form expressions for the parameters of the model, which are very easy to compute. Simulations and real-life data analysis show that the method is efficient for use with incomplete time series data. [ABSTRACT FROM AUTHOR]

We consider the problem of variable selection in high-dimensional settings with missing observations among the covariates. To address this relatively understudied problem, we propose a new synergistic procedure—adaptive Bayesian SLOPE with missing values—which effectively combines SLOPE (sorted l1 regularization) with the spike-and-slab LASSO (SSL) and is accompanied by an efficient stochastic approximation of expected maximization (SAEM) algorithm to handle missing data. Similarly as in SSL, the regression coefficients are regarded as arising from a hierarchical model consisting of two groups: the spike for the inactive and the slab for the active. However, instead of assigning independent spike and slab Laplace priors for each covariate, here we deploy a joint SLOPE "spike-and-slab" prior which takes into account the ordering of coefficient magnitudes in order to control for false discoveries. We position our approach within a Bayesian framework which allows for simultaneous variable selection and parameter estimation while handling missing data. Through extensive simulations, we demonstrate satisfactory performance in terms of power, false discovery rate (FDR) and estimation bias under a wide range of scenarios including complete data and existence of missingness. Finally, we analyze a real dataset consisting of patients from Paris hospitals who underwent severe trauma, where we show competitive performance in predicting platelet levels. Our methodology has been implemented in C++ and wrapped into open source R programs for public use. Supplemental files for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper we study the discrete approximation of backward stochastic differential equations. Under a kind of non-Lipschitz assumption we prove the convergence of the proposed discrete scheme to the solution of backward stochastic differential equation. [ABSTRACT FROM AUTHOR]

We develop a Bayesian approach called the Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from an unknown complex physical system. The calibration parameter and the physical system are parameterized in an identifiable fashion via the L2-projection. The physical system is imposed a Gaussian process prior distribution, which naturally induces a prior distribution on the calibration parameter through the L2-projection constraint. The calibration parameter is estimated through its posterior distribution, serving as a natural and nonasymptotic approach for the uncertainty quantification. We provide rigorous large sample justifications of the proposed approach by establishing the asymptotic normality of the posterior of the calibration parameter with the efficient covariance matrix. In addition to the theoretical analysis, two convenient computational algorithms based on stochastic approximation are designed with strong theoretical support. Through extensive simulation studies and the analyses of two real-world datasets, we show that the proposed Bayesian projected calibration can accurately estimate the calibration parameters, calibrate the computer models well, and compare favorably to alternative approaches. for this article are available online. [ABSTRACT FROM AUTHOR]

In a Covid-19 susceptible-infected-recovered-dead model with time-varying rates of transmission, recovery, and death, the parameters are constant in small time intervals. A posteriori parameters result from the Euler-Maruyama approximation for stochastic differential equations and from Bayes' theorem. Parameter estimates and 10-day predictions are performed based on Moroccan and Italian Covid-19 data. Mean absolute errors and mean square errors indicate that predictions are of good quality. [ABSTRACT FROM AUTHOR]

In this article, we aim to solve Bayesian Risk Optimization (BRO), which is a recently proposed framework that formulates simulation optimization under input uncertainty. In order to efficiently solve the BRO problem, we derive nested stochastic gradient estimators and propose corresponding stochastic approximation algorithms. We show that our gradient estimators are asymptotically unbiased and consistent, and that the algorithms converge asymptotically. We demonstrate the empirical performance of the algorithms on a two-sided market model. Our estimators are of independent interest in extending the literature of stochastic gradient estimation to the case of nested risk measures. [ABSTRACT FROM AUTHOR]

In this paper, we propose two kernel distribution estimators based on a data transformation. We study the properties of these estimators and we compare them with two conventional estimators. It appears that with an appropriate choice of the parameters of the two proposed estimators, the convergence rate of two estimators will be faster than that of the two conventional estimators and the Mean Integrated Square Error will be smaller than the two conventional estimators. We corroborate these theoretical results through simulations as well as a real data set. [ABSTRACT FROM AUTHOR]

This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious representation of spectral matrices from a large number of simultaneously observed time series. Real and imaginary parts of the factor loading matrices are modeled independently using a prior that is formulated from the tensor product of penalized splines and multiplicative gamma process shrinkage priors, allowing for infinitely many factors with loadings increasingly shrunk toward zero as the column index increases. Formulated in a fully Bayesian framework, the time series is adaptively partitioned into approximately stationary segments, where both the number and locations of partition points are assumed unknown. Stochastic approximation Monte Carlo techniques are used to accommodate the unknown number of segments, and a conditional Whittle likelihood-based Gibbs sampler is developed for efficient sampling within segments. By averaging over the distribution of partitions, the proposed method can approximate both abrupt and slowly varying changes in spectral matrices. Performance of the proposed model is evaluated by extensive simulations and demonstrated through the analysis of high-density electroencephalography. for this article are available online. [ABSTRACT FROM AUTHOR]

This paper considers computational challenges to practically important problems related to pricing exotic interest rate derivatives, using the Kusuoka–Lyons–Ninomiya–Victoir scheme (KLNV-scheme) which is a higher-order discretization framework for performing weak approximations of stochastic differential equations. The author demonstrates the KLNV-scheme is even more effective for some types of practical high-dimensional problems, especially when close or approximate solutions to the involved ordinary differential equations can be found. Moreover, the numerical results show the proposed methods are 500 to more than 6000 times faster compared to the conventional methods. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the topological support in Hölder norm of the law of the solution to a stochastic wave equation with three-dimensional space variable. This note is an extension of Delgado-Vences and Sanz-Solé [Approximation of a stochastic wave equation in dimension three, with applications to a support theorem in Hölder norm, Bernoulli 20(4) (2014), pp. 2169–2216; Approximation of a stochastic wave equation in dimension three, with application to a support theorem in Hölder norm: The non-stationary case, Bernoulli 22(3) (2016), pp. 1572–1597]. The result presented here characterize a more general type of stochastic wave equations in 3-d space variable than those considered in Delgado-Vences and Sanz-Solé [Approximation of a stochastic wave equation in dimension three, with applications to a support theorem in Hölder norm, Bernoulli 20(4) (2014), pp. 2169–2216; Approximation of a stochastic wave equation in dimension three, with application to a support theorem in Hölder norm: The non-stationary case, Bernoulli 22(3) (2016), pp. 1572–1597]. Here we extend these two previous results in the folowing sense. The first extension is that we cover the case of multiplicative noise and non-zero initial conditions. The second extension is related to the covariance function associated with the noise, here we follow the approach of Hu, Huang and Nualart and ask conditions in terms of the mean Hölder continuity of such covariance function. As in Delgado-Vences and Sanz-Solé [Approximation of a stochastic wave equation in dimension three, with applications to a support theorem in Hölder norm, Bernoulli 20(4) (2014), pp. 2169–2216; Approximation of a stochastic wave equation in dimension three, with application to a support theorem in Hölder norm: The non-stationary case, Bernoulli 22(3) (2016), pp. 1572–1597] the result is a consequence of an approximation theorem, in the convergence of probability, for a sequence of evolution equations driven by a family of regularizations of the driving noise. [ABSTRACT FROM AUTHOR]

Recursive marginal quantization has a high convergence rate in numerical approximation of stochastic volatility option pricing models [ABSTRACT FROM AUTHOR]

We prove the applicability of the Weighted Energy-Dissipation (WED) variational principle to nonlinear parabolic stochastic partial differential equations in abstract form. The WED principle consists in the minimization of a parameter-dependent convex functional on entire trajectories. Its unique minimizers correspond to elliptic-in-time regularizations of the stochastic differential problem. As the regularization parameter tends to zero, solutions of the limiting problem are recovered. This in particular provides a direct approach via convex optimization to the approximation of nonlinear stochastic partial differential equations. [ABSTRACT FROM AUTHOR]

Recently, the Hamilton Monte Carlo (HMC) has become widespread as one of the more reliable approaches to efficient sample generation processes. However, HMC is difficult to sample in a multimodal posterior distribution because the HMC chain cannot cross energy barrier between modes due to the energy conservation property. In this paper, we propose a Stochastic Approximate Hamilton Monte Carlo (SAHMC) algorithm for generating samples from multimodal density under the Hamiltonian Monte Carlo (HMC) framework. SAHMC can adaptively lower the energy barrier to move the Hamiltonian trajectory more frequently and more easily between modes. Our simulation studies show that the potential for SAHMC to explore a multimodal target distribution is more efficient than HMC-based implementations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a relative recursive regression estimator for censored data defined by the stochastic approximation algorithm to deal with the presence of outliers or when the response is usually positive. We give the central limit theorem and the strong pointwise convergence rate for our proposed nonparametric relative recursive estimators under some mild conditions. We finally developed a second generation plug-in bandwidth selection procedure. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with strong convergence rate of Euler scheme for time-inhomogeneous one-dimensional stochastic differential equations involving the local time (SDELT) of the unknown process at point zero. We use a space transform in order to remove the local time from this class of stochastic differential equations. We provide the approximation of Euler for the stochastic differential equation without local time. After that the approximation can be transformed back, giving an approximation of Euler to the solution of the original SDELT, and we provide the rate of strong convergence. [ABSTRACT FROM AUTHOR]

In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise. [ABSTRACT FROM AUTHOR]