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Through the Bayesian lens of four-dimensional variational (4D-Var) data assimilation, uncertainty in model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive forward models, posterior covariance knowledge must be relaxed to deterministic or stochastic approximations. In the carbon flux inversion literature, proposed a stochastic method capable of approximating posterior variances of linear functionals of the model parameters that is particularly well suited for large-scale Earth-system 4D-Var data assimilation tasks. This note formalizes this algorithm and clarifies its properties. We provide a formal statement of the algorithm, demonstrate why it converges to the desired posterior variance quantity of interest, and provide additional uncertainty quantification allowing incorporation of the Monte Carlo sampling uncertainty into the method's Bayesian credible intervals. The methodology is demonstrated using toy simulations and a realistic carbon flux inversion observing system simulation experiment. [ABSTRACT FROM AUTHOR]

Aims Methods Results Conclusions To develop a non‐linear mixed‐effects population pharmacokinetic and pharmacodynamic (PK‐PD) model describing the change in the concentration of methotrexate polyglutamates in erythrocytes (ery‐MTX‐PGn with “n” number of glutamate, representing PK component) and how this relates to modified 28‐joint Disease Activity Score incorporating erythrocyte sedimentation rate (DAS‐28‐3) for rheumatoid arthritis (RA), representing PD component.An existing PK model was fitted to data from a study consisting of 117 RA patients. The estimation of population PK‐PD parameters was performed using stochastic approximation expectation maximisation algorithm in Monolix 2021R2. The model was used to perform Monte Carlo simulations of a loading dose regimen (50mg subcutaneous methotrexate as loading doses, then 20mg weekly oral methotrexate) compared to a standard dosing regimen (10mg weekly oral methotrexate for 2 weeks, then 20mg weekly oral methotrexate).Every 40 nmol/L increase in ery‐MTX‐PG3‐5 total concentration correlated with 1‐unit reduction in DAS‐28‐3. Significant covariate effects on the therapeutic response of methotrexate included the use of prednisolone in the first 4 weeks (positive use correlated with 25% reduction in DAS‐28‐3 when other variables were constant) and patient age (every 10‐year increase in age correlated with 3.4% increase in DAS‐28‐3 when other variables were constant). 4 methotrexate loading doses led to a higher percentage of patients achieving a good/moderate response compared to the standard regimen (Week 4: 87.6% vs. 39.8%; Week 10: 64.7% vs. 57.0%).A loading dose regimen was more likely to achieve higher ery‐MTX‐PG concentration and better therapeutic response after 4 weeks of methotrexate treatment. [ABSTRACT FROM AUTHOR]

We establish theoretical properties of the solution to a two-variance-driven interest rate model with super-linear coefficient terms. Since this model is not tractable analytically, we construct an implementable numerical method to approximate it and prove the finite-time strong convergence theory under the local Lipschitz condition. Finally, we provide simulation examples to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

A popular approach to the simulation of multivariate, non-normal data in the social sciences is to define a multivariate normal distribution first, and then alter its lower-dimensional marginals to achieve the shape of the distribution intended by the researchers. A consequence of this process is that the correlation structure is altered, so further methods are needed to specify an intermediate correlation matrix in the multivariate normal distribution step. Most of the techniques available in the literature estimate this intermediate correlation matrix bivariately (i.e., correlation by correlation), risking the possibility of generating a non-positive definite matrix. The present article addresses this issue by offering an algorithm that estimates all elements of the intermediate correlation matrix simultaneously, through stochastic approximation. A small simulation study demonstrates the feasibility of the present method to induce the correlation structure both in simulated and empirical data. [ABSTRACT FROM AUTHOR]

The paper provides a precise error estimate for an asymptotic expansion of a certain stochastic control problem related to relative entropy minimization. In particular, it is shown that the expansion error depends on the regularity of functionals on path space. An efficient numerical scheme based on a weak approximation with Monte Carlo simulation is employed to implement the asymptotic expansion in multidimensional settings. Throughout numerical experiments, it is confirmed that the approximation error of the proposed scheme is consistent with the theoretical rate of convergence. [ABSTRACT FROM AUTHOR]

Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive forward models, posterior covariance knowledge must be relaxed to deterministic or stochastic approximations. In the carbon flux inversion literature, Chevallier et al. (2007) proposed a stochastic method capable of approximating posterior variances of linear functionals of the model parameters that is particularly well-suited for large-scale Earth-system data assimilation tasks. This note formalizes this algorithm and clarifies its properties. We provide a formal statement of the algorithm, demonstrate why it converges to the desired posterior variance quantity of interest, and provide additional uncertainty quantification allowing incorporation of the Monte Carlo sampling uncertainty into the method's Bayesian credible intervals. The methodology is demonstrated using toy simulations and a realistic carbon flux inversion observing system simulation experiment. [ABSTRACT FROM AUTHOR]

The article summarizes a thesis which examined the theory and application of Monte Carlo methods and variance reduction techniques in structural reliability analysis. The study investigated sampling and change of measure on simplices, batching adaptive variance reduction, dynamic finite-budget allocation of stratified sampling with adaptive variance reduction by strata, adaptive stratified sampling for structural reliability analysis, and adaptive stratified directional importance sampling.

This study presents a numerical investigation of the dimerization of polyglutamine homo‐peptides of varying length. It employs the PRIME20 intermediate resolution protein model and studies it with a flat‐histogram type Monte Carlo simulation that gives access to the thermodynamic equilibrium of this model over the complete control parameter range (for the simulations this is temperature). For densities comparable to typical in vitro experimental conditions, this study finds that the aggregation and folding of the polyglutamine chains occur concurrently. However, as a function of chain length the sequence of establishment of intra‐ and intermolecular hydrogen bonding contacts changes. Chains longer than about N = 24 polyglutamine repeat units fold first and then aggregate. This agrees well with the experimental finding that, beyond N = 24 the single polyglutamine chain is the critical nucleus for the aggregation of amyloid fibrils. A finite size scaling of the ordering temperatures reveals that for this chain length (and longer chains) folding occurs at physiological (respectively larger) temperatures, whereas shorter chains are disordered at physiological conditions. [ABSTRACT FROM AUTHOR]

We consider the computation of free energy-like quantities for diffusions when resorting to Monte Carlo simulation is necessary, for instance in high dimension. Such stochastic computations typically suffer from high variance, in particular in a low noise regime, because the expectation is dominated by rare trajectories for which the observable reaches large values. Although importance sampling, or tilting of trajectories, is now a standard technique for reducing the variance of such estimators, quantitative criteria for proving that a given control reduces variance are scarce, and often do not apply to practical situations. The goal of this work is to provide a quantitative criterion for assessing whether a given bias reduces variance, and at which scale. We rely for this on a recently introduced notion of stochastic solution for Hamilton–Jacobi–Bellman (HJB) equations. Based on this tool, we introduce the notion of k-stochastic viscosity approximation (SVA) of a HJB equation. We next prove that such approximate solutions are associated with estimators having a relative variance of order k − 1 at log-scale. In particular, a sampling scheme built from a 1-SVA has bounded variance as noise goes to zero. Finally, in order to show that our definition is relevant, we provide examples of stochastic viscosity approximations of order one and two, with a numerical illustration confirming our theoretical findings. [ABSTRACT FROM AUTHOR]

In this article, we establish a cluster‐based gradient method (CGM) by combining K‐means clustering algorithm and stochastic gradient descent (SGD). By clustering the sampling solutions, we use the cluster centroids to represent sampling data and give an estimate to the full gradient. It is well known that the full gradient descent (FGD) can provide the steepest descent direction for finding a local minimum of the desired stochastic control problems. However, the huge computational requirements, which is proportional to the product of sample size and the numerical cost for each sample, often makes FGD cost prohibitive for large scale optimization problems. To reduce the formidable cost and the risks of getting stuck in a local minimum, SGD is proposed and can be regarded as a stochastic approximation of FGD. This, however, would result in a slow convergence due to the incorrect approximation of the iteratively update parameters. Our study shows that CGM could provide a good stochastic approximation to the full gradient with small sample size while has a more stable and faster convergence than SGD. To verify our algorithm, a stochastic elliptic control problem is selected and tested. The numerical results validate our method as a reliable gradient descent method with great potential applications in optimization problems. [ABSTRACT FROM AUTHOR]

Model space quantum Monte Carlo (MSQMC) is an extension of full configuration interaction QMC that allows us to calculate quasi-degenerate and excited electronic states by sampling the effective Hamiltonian in the model space. We introduce a novel algorithm based on the state-selective partitioning for the effective Hamiltonian using left eigenvectors to calculate several electronic states simultaneously at much less computational cost than the original MSQMC with the energy-dependent partitioning. The sampling of walkers in MSQMC is analyzed in the single reference limit using a stochastic algorithm for higher-order perturbation energies by the analogy of the deterministic case utilizing a full configuration interaction program. We further develop size-consistency corrections of the initiator adaptation (i-MSQMC) in three different ways, i.e., the coupled electron pair approximation, a posteriori, and second-order perturbative corrections. It is clearly demonstrated that most of the initiator error is originating from the deficiency of proper scaling of correlation energy due to its truncated CI nature of the initiator approximation and that the greater part of the error can be recovered by the size-consistency corrections developed in this work. [ABSTRACT FROM AUTHOR]

We present an unbiased online Monte Carlo method for rendering with many lights. Our method adapts both the hierarchical light clustering and the sampling distribution to our collected samples. Designing such a method requires us to make clustering decisions under noisy observation, and making sure that the sampling distribution adapts to our target. Our method is based on two key ideas: a coarse-to-fine clustering scheme that can find good clustering configurations even with noisy samples, and a discrete stochastic successive approximation method that starts from a prior distribution and provably converges to a target distribution. We compare to other state-of-the-art light sampling methods, and show better results both numerically and visually. [ABSTRACT FROM AUTHOR]

We introduce stochastic lightcuts by combining the lighting approximation of lightcuts with stochastic sampling for efficiently rendering scenes with a large number of light sources. Our stochastic lightcuts method entirely eliminates the sampling correlation of lightcuts and replaces it with noise. To minimize this noise, we present a robust hierarchical sampling strategy, combining the benefits of importance sampling, adaptive sampling, and stratified sampling. Our approach also provides temporally stable results and lifts any restrictions on the light types that can be approximated with lightcuts. We present examples of using stochastic lightcuts with path tracing and indirect illumination with virtual lights, achieving more than an order of magnitude faster render times than lightcuts by effectively approximating direct illumination using a small number of light samples, in addition to providing temporal stability. Our comparisons to other stochastic sampling techniques demonstrate that we provide superior sampling quality that matches and improves the excellent convergence rates of the lightcuts approach. [ABSTRACT FROM AUTHOR]

A single copolymer chain consisting of multiple flexible (F) and semiflexible (S) blocks has been studied using a continuum bead-spring model by Stochastic Approximation Monte Carlo simulations, which determine the density of states of the model. The only difference between F and S blocks is the intramolecular bending potential, all non-bonded interactions are equal. The state diagrams for this class of models display multiple nematic phases in the collapsed state, characterized through a demixing of the blocks of different stiffness and orientational ordering of the stiff blocks. We observe dumbbell-like morphologies, lamellar phases, and for the larger block lengths also Saturn-like structures with a core of flexible segments and the stiff segments forming a ring around the core. [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]

In this article, we introduce the notion "Lp-probabilistic convergence" (1 ≤ p ≤ ∞) of stochastic Bernstein polynomials built upon order statistics of identically, independently, and uniformly distributed random variables on [0,1]. We establish power and exponential convergence rates in terms of the modulus of continuity of a target function ƒ ∈ C[0,1]. For p in the range 1 ≤ p ≤ 2, we obtain Gaussian tail bounds for the corresponding probabilistic convergence. Our result for the case p = ∞ confirms a conjecture raised by the second and third authors. Monte Carlo simulations (presented at the end of the article) show that the stochastic Bernstein approximation scheme studied herein achieves comparable computational goals to the classical Bernstein approximation, and indicate strongly that the Gaussian tail bounds proved for 1 ≤ p ≤ 2 also hold true for the cases 2 < p ≤ ∞. [ABSTRACT FROM AUTHOR]

We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process that is strongly Hölder continuous in time, then this sequence converges in the strong sense even with respect to much stronger Hölder norms and the convergence rate is essentially reduced by the Hölder exponent. Our first application hereof establishes pathwise convergence rates for spectral Galerkin approximations of stochastic partial differential equations. Our second application derives strong convergence rates of multilevel Monte Carlo approximations of expectations of Banach-space-valued stochastic processes. [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]

This paper studies the convergence of the stochastic algorithm of the modified Robbins–Monro form for a Markov random field (MRF), in which some of the nodes are clamped to be observed variables while the others are hidden ones. Based on the theory of stochastic approximation, we propose proper assumptions to guarantee the Hölder regularity of both the update function and the solution of the Poisson equation. Under these assumptions, it is proved that the control parameter sequence is almost surely bounded and accordingly the algorithm converges to the stable point of the log-likelihood function with probability  1. [ABSTRACT FROM AUTHOR]

Expectation maximization (EM) is a technique for estimating maximum-likelihood parameters of a latent variable model given observed data by alternating between taking expectations of sufficient statistics, and maximizing the expected log likelihood. For situations where sufficient statistics are intractable, stochastic approximation EM (SAEM) is often used, which uses Monte Carlo techniques to approximate the expected log likelihood. Two common implementations of SAEM, Batch EM (BEM) and online EM (OEM), are parameterized by a "learning rate", and their efficiency depend strongly on this parameter. We propose an extension to the OEM algorithm, termed Introspective Online Expectation Maximization (IOEM), which removes the need for specifying this parameter by adapting the learning rate to trends in the parameter updates. We show that our algorithm matches the efficiency of the optimal BEM and OEM algorithms in multiple models, and that the efficiency of IOEM can exceed that of BEM/OEM methods with optimal learning rates when the model has many parameters. Finally we use IOEM to fit two models to a financial time series. A Python implementation is available at https://github.com/luntergroup/IOEM.git. [ABSTRACT FROM AUTHOR]

This study examines whether speech-in-noise tests that use adaptive procedures to assess a speech reception threshold in noise (SRT50n) can be optimized using stochastic approximation (SA) methods, especially in cochlear-implant (CI) users. A simulation model was developed that simulates intelligibility scores for words from sentences in noise for both CI users and normal-hearing (NH) listeners. The model was used in Monte Carlo simulations. Four different SA algorithms were optimized for use in both groups and compared with clinically used adaptive procedures. The simulation model proved to be valid, as its results agreed very well with existing experimental data. The four optimized SA algorithms all provided an efficient estimation of the SRT50n. They were equally accurate and produced smaller standard deviations (SDs) than the clinical procedures. In CI users, SRT50n estimates had a small bias and larger SDs than in NH listeners. At least 20 sentences per condition and an initial signal-to-noise ratio below the real SRT50n were required to ensure sufficient reliability. In CI users, bias and SD became unacceptably large for a maximum speech intelligibility score in quiet below 70%. In conclusion, SA algorithms with word scoring in adaptive speech-in-noise tests are applicable to various listeners, from CI users to NH listeners. In CI users, they lead to efficient estimation of the SRT50n as long as speech intelligibility in quiet is greater than 70%. SA procedures can be considered as a valid, more efficient, and alternative to clinical adaptive procedures currently used in CI users. [ABSTRACT FROM AUTHOR]

In this paper we study the asymptotic behavior of the normalized weighted empirical occupation measures of a diffusion process on a compact manifold which is killed at a smooth rate and then regenerated at a random location, distributed according to the weighted empirical occupation measure. We show that the weighted occupation measures almost surely comprise an asymptotic pseudo-trajectory for a certain deterministic measure-valued semiflow, after suitably rescaling the time, and that with probability one they converge to the quasi-stationary distribution of the killed diffusion. These results provide theoretical justification for a scalable quasi-stationary Monte Carlo method for sampling from Bayesian posterior distributions. [ABSTRACT FROM AUTHOR]

We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo approaches, the proposed method is derived from an approximation of the Langevin diffusion. However, instead of the conventional Euler--Maruyama approximation that underpins existing proximal Monte Carlo methods, here we use a state-of-the-art orthogonal Runge--Kutta--Chebyshev stochastic approximation [A. Abdulle, I. Aimuslimani, and G. Vilmart, SIAM/ASA J. Uncertain. Quantif., 6 (2018), pp. 937-964] that combines several gradient evaluations to significantly accelerate its convergence speed, similarly to accelerated gradient optimization methods. The proposed methodology is demonstrated via a range of numerical experiments, including non-blind image deconvolution, hyperspectral unmixing, and tomographic reconstruction, with total-variation and ℓ1-type priors. Comparisons with Eulertype proximal Monte Carlo methods confirm that the Markov chains generated with our method exhibit significantly faster convergence speeds, achieve larger effective sample sizes, and produce lower mean-square estimation errors at equal computational budget. [ABSTRACT FROM AUTHOR]

The use of sequential Monte Carlo within simulation for path-dependent option pricing is proposed and evaluated. Recently, it was shown that explicit solutions and importance sampling are valuable for efficient simulation of spot price and volatility, especially for purposes of path-dependent option pricing. The resulting simulation algorithm is an analog to the weighted particle filtering algorithm that might be improved by resampling or branching. Indeed, some branching algorithms are shown herein to improve pricing performance substantially while some resampling algorithms are shown to be less suitable in certain cases. A historical property is given and explained as the distinguishing feature between the sequential Monte Carlo algorithms that work on path-dependent option pricing and those that do not. In particular, it is recommended to use the so-called effective particle branching algorithm within importance-sampling Monte Carlo methods for path-dependent option pricing. All recommendations are based upon numeric comparison of option pricing problems in the Heston model. [ABSTRACT FROM AUTHOR]

We propose smoothing spline mixed-effects density models for nonparametric estimations of density and conditional density functions with clustered data. The random effects in a density model introduce within-cluster correlation, enabling us to borrow strength across clusters by shrinking cluster-specific density functions to the population average, where the amount of shrinkage is decided by the data. Estimations are carried out using the penalized likelihood and are computed using a Markov chain Monte Carlo stochastic approximation algorithm. We derive an approximate cross-validation estimate of the aggregated Kullback--Leibler loss for the selection of the smoothing parameters. Our simulation study indicates that the proposed estimation method performs well. We apply our methods to investigate the evolution of hemoglobin density functions over time in response to guideline changes on anemia management for dialysis patients. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly overdamped) Langevin diffusion and establish guarantees on its error measured in the Wasserstein-2 distance. Our guarantees improve or extend the state-of-the-art results in three directions. First, we provide an upper bound on the error of the first-order Langevin Monte Carlo (LMC) algorithm with optimized varying step-size. This result has the advantage of being horizon free (we do not need to know in advance the target precision) and to improve by a logarithmic factor the corresponding result for the constant step-size. Second, we study the case where accurate evaluations of the gradient of the log-density are unavailable, but one can have access to approximations of the aforementioned gradient. In such a situation, we consider both deterministic and stochastic approximations of the gradient and provide an upper bound on the sampling error of the first-order LMC that quantifies the impact of the gradient evaluation inaccuracies. Third, we establish upper bounds for two versions of the second-order LMC, which leverage the Hessian of the log-density. We provide non asymptotic guarantees on the sampling error of these second-order LMCs. These guarantees reveal that the second-order LMC algorithms improve on the first-order LMC in ill-conditioned settings. [ABSTRACT FROM AUTHOR]

We present the partial-propensity stochastic simulation algorithm with composition-rejection sampling (PSSA-CR). It is an exact formulation of the stochastic simulation algorithm (SSA) for well-stirred systems of coupled chemical reactions. The new formulation is a partial-propensity variant [R. Ramaswamy, N. González-Segredo, and I. F. Sbalzarini, J. Chem. Phys. 130, 244104 (2009)] of the composition- rejection SSA [A. Slepoy, A. P. Thompson, and S. J. Plimpton, J. Chem. Phys. 128, 205101 (2008)]. The computational cost of this new formulation is bounded by a constant for weakly coupled reaction networks, and it increases at most linearly with the number of chemical species for strongly coupled reaction networks. PSSA-CR thus combines the advantages of partial-propensity methods and the composition-rejection SSA, providing favorable scaling of the computational cost for all classes of reaction networks. [ABSTRACT FROM AUTHOR]

Gillespie’s exact stochastic simulation algorithm (SSA) [J. Phys. Chem. 81, 2350 (1977)] has been widely used to simulate the stochastic dynamics of chemically reacting systems. In this algorithm, it is assumed that all reactions occur instantly. While this is true in many cases, it is also possible that some chemical reactions, such as gene transcription and translation in living cells, take certain time to finish after they are initiated. Thus, the product of such reactions will emerge after certain delays. Apparently, Gillespie’s SSA is not an exact algorithm for chemical reaction systems with delays. In this paper, the author develops an exact SSA for chemical reaction systems with delays, based upon the same fundamental premise of stochastic kinetics used by Gillespie in the development of his SSA. He then shows that an algorithm modified from Gillespie’s SSA by Barrio et al. [PLOS Comput. Biol. 2, 1017 (2006)] is also an exact SSA for chemical reaction systems with delays, but it needs to generate more random variables than the author’s algorithm. [ABSTRACT FROM AUTHOR]

This work presents a new computational optimization framework for the robust control of parks of Wave Energy Converters (WEC) in irregular waves. The power of WEC parks is maximized with respect to the individual control damping and stiffness coefficients of each device. The results are robust with respect to the incident wave direction, which is treated as a random variable. Hydrodynamic properties are computed using the linear potential model, and the dynamics of the system is computed in the frequency domain. A slamming constraint is enforced to ensure that the results are physically realistic. We show that the stochastic optimization problem is well posed. Two optimization approaches for dealing with stochasticity are then considered: stochastic approximation and sample average approximation. The outcomes of the above mentioned methods in terms of accuracy and computational time are presented. The results of the optimization for complex and realistic array configurations of possible engineering interest are then discussed. Results of extensive numerical experiments demonstrate the efficiency of the proposed computational framework. • The control optimization of wave energy converters arrays is treated as a stochastic optimization problem. • Stochastic approximation (SA) and sample average approximation (SAA) methods are compared. • Indications for the preliminary control design are obtained. [ABSTRACT FROM AUTHOR]

Stochastic chemical kinetics more accurately describes the dynamics of “small” chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques. [ABSTRACT FROM AUTHOR]

The paper shows a new weak approximation method for stochastic differential equations as a generalization and an extension of Heath–Platen's scheme for multidimensional diffusion processes. We reformulate the Heath–Platen estimator from the viewpoint of asymptotic expansion. The proposed scheme is implemented by a Monte Carlo method and its variance is much reduced by the asymptotic expansion which works as a kind of control variate. Numerical examples for the local stochastic volatility model are shown to confirm the efficiency of the method. [ABSTRACT FROM AUTHOR]

Calibration of credible regions derived from under- or misspecified models is an important and challenging problem. In this paper, we introduce a scalar tuning parameter that controls the posterior distribution spread, and develop a Monte Carlo algorithm that sets this parameter so that the corresponding credible region achieves the nominal frequentist coverage probability. [ABSTRACT FROM AUTHOR]

This study examines whether speech-in-noise tests that use adaptive procedures to assess a speech reception threshold in noise (SRT50n) can be optimized using stochastic approximation (SA) methods, especially in cochlear-implant (CI) users. A simulation model was developed that simulates intelligibility scores for words from sentences in noise for both CI users and normal-hearing (NH) listeners. The model was used in Monte Carlo simulations. Four different SA algorithms were optimized for use in both groups and compared with clinically used adaptive procedures. The simulation model proved to be valid, as its results agreed very well with existing experimental data. The four optimized SA algorithms all provided an efficient estimation of the SRT50n. They were equally accurate and produced smaller standard deviations (SDs) than the clinical procedures. In CI users, SRT50n estimates had a small bias and larger SDs than in NH listeners. At least 20 sentences per condition and an initial signal-to-noise ratio below the real SRT50n were required to ensure sufficient reliability. In CI users, bias and SD became unacceptably large for a maximum speech intelligibility score in quiet below 70%. In conclusion, SA algorithms with word scoring in adaptive speech-in-noise tests are applicable to various listeners, from CI users to NH listeners. In CI users, they lead to efficient estimation of the SRT50n as long as speech intelligibility in quiet is greater than 70%. SA procedures can be considered as a valid, more efficient, and alternative to clinical adaptive procedures currently used in CI users. [ABSTRACT FROM AUTHOR]

The autoregressive (AR) model is a widely used model to understand time series data. Traditionally, the innovation noise of the AR is modeled as Gaussian. However, many time series applications, for example, financial time series data, are non-Gaussian, therefore, the AR model with more general heavy-tailed innovations is preferred. Another issue that frequently occurs in time series is missing values due to system data record failure or unexpected data loss. Although there are numerous works about Gaussian AR time series with missing values, as far as we know, there does not exist any work addressing the issue of missing data for the heavy-tailed AR model. In this paper, we consider this issue for the first time, and propose an efficient framework for parameter estimation from incomplete heavy-tailed time series based on a stochastic approximation expectation maximization coupled with a Markov Chain Monte Carlo procedure. The proposed algorithm is computationally cheap and easy to implement. The convergence of the proposed algorithm to a stationary point of the observed data likelihood is rigorously proved. Extensive simulations and real datasets analyses demonstrate the efficacy of the proposed framework. [ABSTRACT FROM AUTHOR]

Background: Tandem repeat sequences are common in the genomes of many organisms and are known to cause important phenomena such as gene silencing and rapid morphological changes. Due to the presence of multiple copies of the same pattern in tandem repeats and their high variability, they contain a wealth of information about the mutations that have led to their formation. The ability to extract this information can enhance our understanding of evolutionary mechanisms. Results: We present a stochastic model for the formation of tandem repeats via tandem duplication and substitution mutations. Based on the analysis of this model, we develop a method for estimating the relative mutation rates of duplications and substitutions, as well as the total number of mutations, in the history of a tandem repeat sequence. We validate our estimation method via Monte Carlo simulation and show that it outperforms the state-of-the-art algorithm for discovering the duplication history. We also apply our method to tandem repeat sequences in the human genome, where it demonstrates the different behaviors of micro- and mini-satellites and can be used to compare mutation rates across chromosomes. It is observed that chromosomes that exhibit the highest mutation activity in tandem repeat regions are the same as those thought to have the highest overall mutation rates. However, unlike previous works that rely on comparing human and chimpanzee genomes to measure mutation rates, the proposed method allows us to find chromosomes with the highest mutation activity based on a single genome, in essence by comparing (approximate) copies of the pattern in tandem repeats. Conclusion: The prevalence of tandem repeats in most organisms and the efficiency of the proposed method enable studying various aspects of the formation of tandem repeats and the surrounding sequences in a wide range of settings. Availability: The implementation of the estimation method is available at http://ips.lab.virginia.edu/smtr. [ABSTRACT FROM AUTHOR]

Highlights • Wind load analysis of slender monopole towers is studied. • Uncertainties related to wind loads and structural properties are considered. • A Layered Stochastic-Approximation-Monte-Carlo is used to estimate fragility curves. • Monte Carlo simulations are employed to verify the LSAMC results. • The proposed algorithm is a viable alternative to standard Monte Carlo sampling. Abstract This paper describes a novel numerical algorithm for the simulation of the along-wind dynamic response of a prototype of slender towers under turbulent winds, using a Layered Stochastic Approximation Monte Carlo algorithm (LSAMC). The proposed algorithm is applied to derive the statistics of the dynamic response in the presence of uncertainties in the structural properties and in the wind loading. Standard "brute force" Monte-Carlo methods are also used for validating the LSAMC results. The proposed methodology efficiently estimates structural fragility curves under extreme wind loads. The methodology enables a significant speedup in the computing time compared to standard Monte Carlo sampling. Furthermore, it is demonstrated that accuracy in the estimation of structural fragility curves is superior to ordinary reliability methods (e.g. "First-order reliability methods" or FORM). [ABSTRACT FROM AUTHOR]

The Basel Committee of Banking Supervision has recently set out the revised standards for minimum capital requirements for market risk. The Committee has focused, among other things, on the two key areas of moving from Value-at-Risk (VaR) to Expected Shortfall (ES) and considering a comprehensive incorporation of the risk of market illiquidity by extending the risk measurement horizon. The estimation of the ES for several trading desks and taking into account different liquidity horizons is computationally very involved. We present a novel numerical method to compute the VaR and ES of a given portfolio within the stochastic holding period framework. Two approaches are considered, the delta–gamma approximation, for modelling the change in value of the portfolio as a quadratic approximation of the change in value of the risk factors, and some of the state-of-the-art stochastic processes for driving the dynamics of the log-value change of the portfolio like the Merton jump–diffusion model and the Kou model. Central to this procedure is the application of the SWIFT method developed for option pricing, that appears to be a very efficient and robust Fourier inversion method for risk management purposes. [ABSTRACT FROM AUTHOR]

The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the covariance matrix, such as the marginal variances, which may be nontrivial to obtain when the dimension is large. This article introduces a fast Rao-Blackwellized Monte Carlo sampling-based method for efficiently approximating selected elements of the covariance matrix. The variance and confidence bounds of the approximations can be precisely estimated without additional computational costs. Furthermore, a method that iterates over subdomains is introduced, and is shown to additionally reduce the approximation errors to practically negligible levels in an application on functional magnetic resonance imaging data. Both methods have low memory requirements, which is typically the bottleneck for competing direct methods. [ABSTRACT FROM AUTHOR]

In this paper, we provide two new stable online algorithms for the problem of prediction in reinforcement learning, i.e., estimating the value function of a model-free Markov reward process using the linear function approximation architecture and with memory and computation costs scaling quadratically in the size of the feature set. The algorithms employ the multi-timescale stochastic approximation variant of the very popular cross entropy optimization method which is a model based search method to find the global optimum of a real-valued function. A proof of convergence of the algorithms using the ODE method is provided. We supplement our theoretical results with experimental comparisons. The algorithms achieve good performance fairly consistently on many RL benchmark problems with regards to computational efficiency, accuracy and stability. [ABSTRACT FROM AUTHOR]

Ordinary differential equations (ODEs) are popularly used to model complex dynamic systems by scientists; however, the parameters in ODE models are often unknown and have to be inferred from noisy measurements of the dynamic system. One conventional method is to maximize the likelihood function, but the likelihood function often has many local modes due to the complexity of ODEs, which makes the optimizing algorithm be vulnerable to trap in local modes. In this paper, we solve the global optimization issue of ODE parameters with the help of the Stochastic Approximation Monte Carlo (SAMC) algorithm which is shown to be self-adjusted and escape efficiently from the “local-trapping” problem. Our simulation studies indicate that the SAMC method is a powerful tool to estimate ODE parameters globally. The efficiency of SAMC method is demonstrated by estimating a predator-prey ODEs model from real experimental data. [ABSTRACT FROM AUTHOR]

The analysis of misspecification was extended to the recently introduced stochastic restricted biased estimators when multicollinearity exists among the explanatory variables. The Stochastic Restricted Ridge Estimator (SRRE), Stochastic Restricted Almost Unbiased Ridge Estimator (SRAURE), Stochastic Restricted Liu Estimator (SRLE), Stochastic Restricted Almost Unbiased Liu Estimator (SRAULE), Stochastic Restricted Principal Component Regression Estimator (SRPCRE), Stochastic Restricted r-k (SRrk) class estimator, and Stochastic Restricted r-d (SRrd) class estimator were examined in the misspecified regression model due to missing relevant explanatory variables when incomplete prior information of the regression coefficients is available. Further, the superiority conditions between estimators and their respective predictors were obtained in the mean square error matrix (MSEM) sense. Finally, a numerical example and a Monte Carlo simulation study were used to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

We present different ways of an approximate extrapolation of an optimal policy of a small model to that of a large equivalent of the model, which itself is too large to find its exact policy directly using probabilistic model checking (PMC). In particular, we obtain a global optimal resolution of non–determinism in several small Markov Decision Processes (MDP) or its extensions like Stochastic Multi-player Games (SMG) using PMC. We then use that resolution to form a hypothesis about an analytic decision boundary representing a respective policy in an equivalent large MDP/SMG. The resulting hypothetical decision boundary is then statistically approximately verified, if it is locally optimal and if it indeed represents a ”good enough” policy. The verification either weakens or strengthens the hypothesis. The criterion of the optimality of the policy can be expressed in any modal logic that includes a version of the probabilistic operator P~p[·], and for which a PMC method exists. [ABSTRACT FROM AUTHOR]

This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the corresponding statistical properties of this model, discuss the spectral likelihood estimation and investigate the finite sample properties via Monte Carlo experiments. We provide empirical evidence by applying the GLMSV model to three exchange rate return series and conjecture that the results of out-of-sample forecasts adequately confirm the use of GLMSV model in certain financial applications. [ABSTRACT FROM AUTHOR]

We introduce a broad family of generalised self-exciting point processes with CIR-type intensities, and we develop associated algorithms for their exact simulation. The underlying models are extensions of the classical Hawkes process, which already has numerous applications in modelling the arrival of events with clustering or contagion effect in finance, economics, and many other fields. Interestingly, we find that the CIR-type intensity, together with its point process, can be sequentially decomposed into simple random variables, which immediately leads to a very efficient simulation scheme. Our algorithms are also pretty accurate and flexible. They can be easily extended to further incorporate externally excited jumps, or, to a multidimensional framework. Some typical numerical examples and comparisons with other well-known schemes are reported in detail. In addition, a simple application for modelling a portfolio loss process is presented. The online appendix is available at [ABSTRACT FROM AUTHOR]