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Data collected over time are common in applications and may contain censored or missing observations, making it difficult to use standard statistical procedures. This article proposes an algorithm to estimate the parameters of a censored linear regression model with errors serially correlated and innovations following a Student‐t distribution. This distribution is widely used in the statistical modelling of data containing outliers because its longer‐than‐normal tails provide a robust approach to handling such data. The maximum likelihood estimates of the proposed model are obtained through a stochastic approximation of the EM algorithm. The methods are applied to an environmental dataset regarding ammonia‐nitrogen concentration, which is subject to a limit of detection (left censoring) and contains missing observations. Additionally, two simulation studies are conducted to examine the asymptotic properties of the estimates and the robustness of the model. The proposed algorithm and methods are implemented in the R package ARCensReg. [ABSTRACT FROM AUTHOR]

Summary: Since the dawn of quantum computing (QC), theoretical developments like Shor's algorithm proved the conceptual superiority of QC over traditional computing. However, such quantum supremacy claims are difficult to achieve in practice because of the technical challenges of realizing noiseless qubits. In the near future, QC applications will need to rely on noisy quantum devices that offload part of their work to classical devices. One way to achieve this is by using parameterized quantum circuits in optimization or even in machine learning tasks. The energy requirements of quantum algorithms have not yet been studied extensively. In this article, we explore several optimization algorithms using both theoretical insights and numerical experiments to understand their impact on energy consumption. Specifically, we highlight why and how algorithms like quantum natural gradient descent, simultaneous perturbation stochastic approximations or circuit learning methods, are at least 2×$$ 2\times $$ to 4×$$ 4\times $$ more energy efficient than their classical counterparts; why feedback‐based quantum optimization is energy‐inefficient; and how techniques like Rosalin can improve the energy efficiency of other algorithms by a factor of ≥$$ \ge $$20×$$ \times $$. Finally, we use the NchooseK high‐level programming model to run optimization problems on both gate‐based quantum computers and quantum annealers. Empirical data indicate that these optimization problems run faster, have better success rates, and consume less energy on quantum annealers than on their gate‐based counterparts. [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]

Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis–Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi‐Random Parametric Expectation Maximization (QRPEM) for a realistic two‐compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log‐normal cases. [ABSTRACT FROM AUTHOR]

Recently, Kovács et al. considered a Mittag‐Leffler Euler integrator for a stochastic semilinear Volterra integral‐differential equation with additive noise and proved the strong convergence error estimates [see SIAM J. Numer. Anal. 58(1) 2020, pp. 66‐85]. In this article, we shall consider the Mittag‐Leffler integrators for more general models: stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise. The mild solutions of our models involve four different Mittag‐Leffler functions. We first consider the existence, uniqueness and the regularities of the solutions. We then introduce the full discretization schemes for solving the problems. The temporal discretization is based on the Mittag‐Leffler integrators and the spatial discretization is based on the spectral method. The optimal strong convergence error estimates are proved under the reasonable assumptions for the semilinear term and for the regularity of the noise. Numerical examples are given to show that the numerical results are consistent with the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we develop a mixed stochastic approximation expectation‐maximization (MSAEM) algorithm coupled with a Gibbs sampler to compute the marginalized maximum a posteriori estimate (MMAPE) of a confirmatory multidimensional four‐parameter normal ogive (M4PNO) model. The proposed MSAEM algorithm not only has the computational advantages of the stochastic approximation expectation‐maximization (SAEM) algorithm for multidimensional data, but it also alleviates the potential instability caused by label‐switching, and then improved the estimation accuracy. Simulation studies are conducted to illustrate the good performance of the proposed MSAEM method, where MSAEM consistently performs better than SAEM and some other existing methods in multidimensional item response theory. Moreover, the proposed method is applied to a real data set from the 2018 Programme for International Student Assessment (PISA) to demonstrate the usefulness of the 4PNO model as well as MSAEM in practice. [ABSTRACT FROM AUTHOR]

This article aims to address the stochastic scaled consensus issue in almost surely and mean square sense of stochastic multiagent systems (SMASs) with compound noises in a Markovian switching setting. At first, based on stochastic approximation technique and nearest‐neighbor interaction rules, the stochastic scaled consensus controller is built for SMASs in presence of multiplicative and additive noise by designing a time‐varying gain. Meanwhile, some consensus criterions of SMASs are addressed if the union of the graph and time‐varying gain fulfill some mild requirements. Furthermore, the scaled consensus means that the agents' state variables tend to a prescribed proportion rather than the common value, so this behavior can be seen as non‐convergent behavior. The difference with most of excellent literatures is that the coexistence of noncooperative behavior and multiplicative noise generates that it is not easy to transform the multiplicative noise term into the form of an error equation, which means that the Lyapunov methods cannot be directly utilized in our article. To cope with this, we first demonstrate the boundedness for each agent's state, and hence the convergence can be achieved. Finally, in order to reveal the efficiency of our proposed protocol, the corresponding example is given in the simulation part. [ABSTRACT FROM AUTHOR]

Tafolecimab, a novel fully human monoclonal antibody targeting PCSK9, has been assessed in Chinese healthy volunteers and patients with hypercholesterolemia. This analysis is to develop and qualify a population pharmacokinetics (PopPKs)/LDL‐C model to characterize tafolecimab PK and LDL‐C profiles, evaluate the impact of potential covariates on tafolecimab, estimate individual predicted exposure, and LDL‐C decreasing, furthermore, explore exposure–response relationship to support clinical use. Data from six clinical trials in China were used to develop the PopPK/LDL‐C model. A Michaelis–Menten approximation of the target‐mediated drug disposition (TMDD) model was used to describe PK data and indirect response (IDR) model was developed to estimate the LDL‐C profile. A stochastic approximation expectation maximization algorithm was applied to estimate PopPK/LDL‐C parameters. The PK/LDL‐C time course data for tafolecimab were well described by TMDD/IDR model. Baseline covariates resulting in statistically significant changes in PK/LDL‐C parameters included: body weight and sex on absorption rate constant; body weight, sex, and unbound PCSK9 on central volume; body weight and sex on clearance; baseline LDL‐C on first‐order rate constants for the removal of an effect); and disease and sex on maximum effect. However, the magnitudes of changes associated with these covariates do not necessitate dose adjustment. Exposure–efficacy relationship indicated that the nadir of LDL‐C reduction achieved with the steady‐state trough plasma concentration (Ctrough) of tafolecimab at 5 μg/mL, and no further LDL‐C decreasing with the increasing Ctrough. There was no exposure dependency observed in exposure‐safety exploration. The PopPK/LDL‐C model was successfully developed, validated, and predicted tafolecimab/LDL‐C concentrations and individual exposures. [ABSTRACT FROM AUTHOR]

In this work, we propose an extension of a semiparametric nonlinear mixed‐effects model for longitudinal data that incorporates more flexibility with penalized splines (P‐splines) as smooth terms. The novelty of the proposed approach consists of the formulation of the model within the stochastic approximation version of the EM algorithm for maximum likelihood, the so‐called SAEM algorithm. The proposed approach takes advantage of the formulation of a P‐spline as a mixed‐effects model and the use of the computational advantages of the existing software for the SAEM algorithm for the estimation of the random effects and the variance components. Additionally, we developed a supervised classification method for these non‐linear mixed models using an adaptive importance sampling scheme. To illustrate our proposal, we consider two studies on pregnant women where two biomarkers are used as indicators of changes during pregnancy. In both studies, information about the women's pregnancy outcomes is known. Our proposal provides a unified framework for the classification of longitudinal profiles that may have important implications for the early detection and monitoring of pregnancy‐related changes and contribute to improved maternal and fetal health outcomes. We show that the proposed models improve the analysis of this type of data compared to previous studies. These improvements are reflected both in the fit of the models and in the classification of the groups. [ABSTRACT FROM AUTHOR]

Quantification of evolving uncertainties is required for both probabilistic forecasting and data assimilation in weather prediction. In current practice, the ensemble of model simulations is often used as a primary tool to describe the required uncertainties. In this work, we explore an alternative approach, the so‐called stochastic Galerkin (SG) method, which integrates uncertainties forward in time using a spectral approximation in stochastic space. In an idealized two‐dimensional model that couples nonhydrostatic weakly compressible Navier–Stokes equations to cloud variables, we first investigate the propagation of initial uncertainty. Propagation of initial perturbations is followed through time for all model variables during two types of forecast: the ensemble forecast and the SG forecast. Series of experiments indicate that differences in performance of the two methods depend on the system state and truncations used. For example, in more stable conditions, the SG method outperforms the ensemble of simulations for every truncation and every variable. However, in unstable conditions, the ensemble of simulations would need more than 100 members (depending on the model variable) and the SG method more than a truncation at five to produce comparable but not identical results. As estimates of the uncertainty are crucial for data assimilation, secondly we instigate the use of these two methods with the stochastic ensemble Kalman filter. The use of the SG method avoids evolution of a large ensemble, which is usually the most expensive component of the data assimilation system, and provides results comparable with the ensemble Kalman filter in the cases investigated. [ABSTRACT FROM AUTHOR]

This article investigates the Carathéodory approximation scheme for stochastic differential equations (SDEs) in the G‐Lévy process framework. In the context of the G‐Lévy process, the possibility of SDE solutions has been developed. The solution's boundedness and uniqueness have been discussed. The convergence of approximate Carathéodory solutions xi(t),i≥1$$ {x}^i(t),\kern0.3em i\ge 1 $$ to the unique solution x(t)$$ x(t) $$ of the given SDEs has been determined. The G‐Lévy framework is used to obtain exponential estimates for solutions to SDEs. An example has been provided to validate the results. [ABSTRACT FROM AUTHOR]

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]

This article presents a data‐driven control algorithm for a variable‐speed wind turbine in the partial load region. The controller is designed and optimized online to capture maximum energy from the wind. The online optimization is based on the simultaneous perturbation stochastic approximation method (SPSA) that is data‐driven, has a low computational load, and converges rapidly. In the control structure, the generator torque control is activated, and the aerodynamical models and the wind speed value are not required. A suitable cost function is defined, and a time window optimization problem is solved via the SPSA algorithm. The efficiency of the proposed method is evaluated on a 4.8 MW wind turbine benchmark. [ABSTRACT FROM AUTHOR]

Aim: nlmixr offers first‐order conditional estimation (FOCE), FOCE with interaction (FOCEi) and stochastic approximation estimation‐maximisation (SAEM) to fit nonlinear mixed‐effect models (NLMEM). We modelled metformin's pharmacokinetic data using nlmixr and investigated SAEM and FOCEi's performance with respect to bias and precision of parameter estimates, and robustness to initial estimates. Method: Compartmental models were fitted. The final model was determined based on the objective function value and inspection of goodness‐of‐fit plots. The bias and precision of parameter estimates were compared between SAEM and FOCEi using stochastic simulations and estimations. For robustness, parameters were re‐estimated as the initial estimates were perturbed 100 times and resultant changes evaluated. Results: The absorption kinetics of metformin depend significantly on food status. Under the fasted state, the first‐order absorption into the central compartment was preceded by zero‐order infusion into the depot compartment, whereas for the fed state, the absorption into the depot was instantaneous followed by first‐order absorption from depot into the central compartment. The means of relative mean estimation error (rMEE) (MEESAEMMEEFOCEi) and rRMSE (RMSESAEMRMSEFOCEi) were 0.48 and 0.35, respectively. All parameter estimates given by SAEM appeared to be narrowly distributed and were close to the true value used for simulation. In contrast, the distribution of estimates from FOCEi were skewed and more biased. When initial estimates were perturbed, FOCEi estimates were more biased and imprecise. Discussion: nlmixr is reliable for NLMEM. SAEM was superior to FOCEi in terms of bias and precision, and more robust against initial estimate perturbations. [ABSTRACT FROM AUTHOR]

Antenna arrays have gained significant interest in millimetre‐wave communication systems as an enabling technology to achieve higher capacity and mitigate the high propagation loss. Such arrays with a large bandwidth need to be efficiently calibrated to maximise their performance. An antenna array calibration method based on a stochastic approximation algorithm and simultaneous perturbation has been developed and the procedures to implement it in both frequency and time domains have been presented. The approaches to define objective functions and establish gradient approximations to fulfill a successful convergence for acquiring calibration coefficients in both domains have been explored. In the time domain implementation, only a fraction of the measurement time was required to calibrate an antenna array of ultrawide bandwidth compared with other methods using a perturbation technique. The effectiveness of the proposed method has been validated via numerical experiments in both domains. [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]

Joint models of longitudinal process and time‐to‐event data have recently gained attention, notably to provide individualized dynamic predictions. In the presence of competing risks, models published mostly involve cause‐specific hazard functions jointly estimated with a linear or generalized linear model. Here we propose to extend the modeling to full parametric joint estimation of a nonlinear mixed‐effects model and a subdistribution hazard model. We apply this approach on 6046 patients admitted in intensive care unit (ICU) for sepsis with daily Sequential Organ Failure Assessment (SOFA) score measurements. The joint model is built on a randomly selected training set of two thirds of patients and links the current predicted SOFA measurement to the instantaneous risks of ICU death and discharge from ICU, both adjusted on the patient age. Stochastic Approximation Expectation Maximization algorithm in Monolix is used for estimation. SOFA evolution is significantly associated with both risks: 0.37, 95% confidence interval (CI) = [0.35, 0.39] for the risk of death and −0.38, 95% CI = [−0.39, −0.36] for the risk of discharge. A simulation study, inspired from the real data, shows the good estimation properties of the parameters. We assess on the validation set the added value of modeling the longitudinal SOFA follow‐up for the prediction of death compared with a model that includes only SOFA at baseline. Time‐dependent receiver operating characteristic area under the curve and Brier scores show that when enough longitudinal individual information is available, joint modeling provides better predictions. The methodology can easily be applied to other clinical applications because of the general form of the model. [ABSTRACT FROM AUTHOR]

This article investigates resilient distributed online estimation (DOE) in unreliable directed networks with differential privacy requirements. In the network considered, some agents are subject to Byzantine attacks and thus could send arbitrary incorrect messages to their neighbors. The remaining agents aim to collaboratively estimate the value of an unknown vector parameter while protecting their private data. In this article, by adding private noises to mask the estimate, a stochastic approximation‐type resilient differentially private DOE algorithm is proposed to protect the privacy of sensitive information. A time‐varying step size is introduced to attenuate the divergence caused by the private noise, and furthermore, guarantees the convergence of the algorithm. When the directed graph is (2F$$ \Big(2F $$+1)‐robust, the algorithm is shown to be both mean square and almost sure convergence in the sense of ϵ$$ \epsilon $$‐differential privacy. A simulation example is given to verify the effectiveness and superiority of the algorithm. [ABSTRACT FROM AUTHOR]

We observe that embeddings into random metrics can be fruitfully used to study the L1$L_1$‐embeddability of lamplighter graphs or groups, and more generally lamplighter metric spaces. Once this connection has been established, several new upper bound estimates on the L1$L_1$‐distortion of lamplighter metrics follow from known related estimates about stochastic embeddings into dominating tree‐metrics. For instance, every lamplighter metric on an n$n$‐point metric space embeds bi‐Lipschitzly into L1$L_1$ with distortion O(logn)$O(\log n)$. In particular, for every finite group G$G$ the lamplighter group H=Z2≀G$H=\mathbb {Z}_2\wr G$ bi‐Lipschitzly embeds into L1$L_1$ with distortion O(loglog|H|)$O(\log \log |H|)$. In the case where the ground space in the lamplighter construction is a graph with some topological restrictions, better distortion estimates can be achieved. Finally, we discuss how a coarse embedding into L1$L_1$ of the lamplighter group over the d$d$‐dimensional infinite lattice Zd$\mathbb {Z}^d$ can be constructed from bi‐Lipschitz embeddings of the lamplighter graphs over finite d$d$‐dimensional grids, and we include a remark on Lipschitz free spaces over finite metric spaces. [ABSTRACT FROM AUTHOR]

We consider dynamic assortment optimization with incomplete information under the uncapacitated multinomial logit choice model. We propose an anytime stochastic approximation policy and prove that the regret—the cumulative expected revenue loss caused by offering suboptimal assortments—after T$$ T $$ time periods is bounded by T$$ \sqrt{T} $$ times a constant that is independent of the number of products. In addition, we prove a matching lower bound on the regret for any policy that is valid for arbitrary model parameters—slightly generalizing a recent regret lower bound derived for specific revenue parameters. Numerical illustrations suggest that our policy outperforms alternatives by a significant margin when T$$ T $$ and the number of products N$$ N $$ are not too small. [ABSTRACT FROM AUTHOR]

This paper presents a simultaneous perturbation stochastic approximation (SPSA) approach for unknown but bounded disturbances in a typical closed loop system. These random disturbances are represented by a sequence of uncertainties along with the measured system output. Further, the proposed approach constructs a sequence of estimates and formulates an optimization problem which is minimized to achieve the adaptive control. In addition, the convergence conditions and additional generalizations are proposed to enhance the operation of SPSA algorithms for trail perturbation properties. To address the major challenges with unknown disturbances on the closed loop system, a balancing control problem with two degree of freedom (2DoF) ball balancer system and proportional integral derivative (PID) controller is considered. The proposed SPSA method minimizes the optimization problem to obtain the gain values of the PID controller. Simulation and experimental analysis are carried out, and the results substantiate that the PID gains optimized using SPSA provide better control when compared to conventional control approach in terms of tracking response under random uncertainties. [ABSTRACT FROM AUTHOR]

In this article, we propose a class of discrete‐time approximation schemes for stochastic optimal control problems under the G‐expectation framework. The proposed schemes are constructed recursively based on piecewise constant policy. We prove the convergence of the discrete schemes and determine the convergence rates. Several numerical examples are presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

The success of correctly identifying all the components of a nonlinear mixed‐effects model is far from straightforward: it is a question of finding the best structural model, determining the type of relationship between covariates and individual parameters, detecting possible correlations between random effects, or also modeling residual errors. We present the Stochastic Approximation for Model Building Algorithm (SAMBA) procedure and show how this algorithm can be used to speed up this process of model building by identifying at each step how best to improve some of the model components. The principle of this algorithm basically consists in "learning something" about the "best model," even when a "poor model" is used to fit the data. A comparison study of the SAMBA procedure with Stepwise Covariate Modeling (SCM) and COnditional Sampling use for Stepwise Approach (COSSAC) show similar performances on several real data examples but with a much reduced computing time. This algorithm is now implemented in Monolix and in the R package Rsmlx. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fully discrete finite element based discretization for the numerical approximation of the stochastic Allen‐Cahn‐Navier‐Stokes system on a bounded polygonal domain of Rd$\mathbb {R}^{d}$, d=2,3$ d=2,3$. We prove that the proposed numerical scheme is unconditionally solvable, has finite energies and constructs weak martingale solutions of the stochastic Allen‐Cahn‐Navier‐Stokes system when the discretisation step (both in time and in space) tends to zero. [ABSTRACT FROM AUTHOR]

The maximum mean discrepancy (MMD) has found numerous applications in statistics and machine learning, among which is its use as a penalty in the Wasserstein auto‐encoder (WAE). In this paper, we compute closed‐form expressions for estimating the Gaussian kernel‐based MMD between a given distribution and the standard multivariate normal distribution. This formula reveals a connection to the Baringhaus–Henze–Epps–Pulley (BHEP) statistic of the Henze–Zirkler test and provides further insights about the MMD. We introduce the standardized version of MMD as a penalty for the WAE training objective, allowing for a better interpretability of MMD values and more compatibility across different hyperparameter settings. Next, we propose code normalization–using batch normalization at the code layer–which has the benefits of making the kernel width selection easier, reducing the training effort, and preventing outliers in the aggregate code distribution. Our experiments on synthetic and real data show that the analytic formulation improves over the commonly used stochastic approximation of the MMD and demonstrate that code normalization provides significant benefits when training WAEs. [ABSTRACT FROM AUTHOR]

This article presents a proper generalized decomposition (PGD) based Padé approximant for efficient analysis of the stochastic frequency response. Due to the high nonlinearity of the stochastic response with respect to the input uncertainties, the classical stochastic Galerkin (SG) method utilizing polynomial chaos exhibits slow convergence near the resonance. Furthermore, the dimension of the SG method is the product of deterministic and stochastic approximation spaces, and hence resolution over a banded frequency range is computationally expensive or even prohibitive. In this study, to tackle these problems, the PGD first generates the solution of stochastic frequency equations as a separated representation of deterministic and stochastic components. For the banded frequency range computations, the deterministic vectors are exploited as a reduced basis in conjunction with singular value decomposition. Subsequently, the Padé approximant is applied based on the PGD solution, and the stochastic frequency response is represented by a rational function. Through various numerical studies, it is demonstrated that the proposed framework improves not only the accuracy in the vicinity of resonance but also the computational efficiency, compared with the SG method. [ABSTRACT FROM AUTHOR]

Robust topology optimization (RTO) improves the robustness of designs with respect to random sources in real‐world structures, yet an accurate sensitivity analysis requires the solution of many systems of equations at each optimization step, leading to a high computational cost. To open up the full potential of RTO under a variety of random sources, this article presents a momentum‐based accelerated mirror descent stochastic approximation (AC‐MDSA) approach to efficiently solve RTO problems involving various types of load uncertainties. The proposed framework performs high‐quality design updates with highly noisy and biased stochastic gradients. The sample size is reduced to two (minimum for unbiased variance estimation) and is shown to be sufficient for evaluating stochastic gradients to obtain robust designs, thus drastically reducing the computational cost. The AC‐MDSA update formula based on entropic ℓ1‐norm is derived, which mimics the feasible space geometry. A momentum‐based acceleration scheme is integrated to accelerate the convergence, stabilize the design evolution, and alleviate step size sensitivity. Several 2D and 3D examples are presented to demonstrate the effectiveness and efficiency of the proposed AC‐MDSA to handle RTO involving various loading uncertainties. Comparison with other methods shows that the proposed AC‐MDSA is superior in computational cost, stability, and convergence speed. [ABSTRACT FROM AUTHOR]

Geophysical models make predictions relying on parameter values to be estimated from data. However, existing methods are costly because they require either many runs of the complex geophysical model or to implement an adjoint model. Here, we propose an alternative approach based on optimal control theory which is the simultaneous perturbations stochastic approximation (SPSA). This gradient‐descent method is generic and easy to implement, and its computational cost does not increase with the number of parameters to optimize. This study aims at highlighting the potential of SPSA for parameter identification in geophysical models. Through the example of vertical turbulent mixing in the upper ocean, we show with twin experiments that the method could successfully identify parameter values that minimize model‐data discrepancy. The efficient and easy‐to‐get results provided by SPSA in this study should pave the way for a broader use of parameter identification in the complex and embedded models commonly used in geophysical sciences. Plain Language Summary: Predictions on the past and future state of geophysical systems are made through mathematical models, which rely on numerous constant values (parameters) to be calibrated from prior knowledge and available data. Fine‐tuning those parameter values is one of the major means of improving the accuracy of model predictions. To achieve that goal for complex geophysical models in which multiple scales and processes are nested, existing methods are limited by either (a) an important computational cost or (b) an important cost in terms of development and implementation of an adjoint model. Here, we highlight a method from optimal control theory, called simultaneous perturbations stochastic approximation (SPSA). This generic method is easy to implement, and its computational cost is comparatively low. To show the potential of SPSA for parameter identification in geophysical science, we apply it to the example of wind‐induced turbulent mixing near the ocean surface. Using the approach of twin experiments, we show that the method can successfully tune the parameter values to minimize the discrepancy between model predictions and empirical data. The efficient and easy‐to‐get results provided by SPSA in this study pave the way for a broader use of parameter identification in the complex models commonly used in geophysical sciences. Key Points: Parameters identification is a key to reduce model uncertainty in geophysical modelsWe present a method from optimal control called simultaneous perturbations stochastic approximation (SPSA) that is easy to implement and fast to runWe illustrate the potential of SPSA with a simplified example of turbulent mixing in the ocean [ABSTRACT FROM AUTHOR]

Multiple imputation and maximum likelihood estimation (via the expectation‐maximization algorithm) are two well‐known methods readily used for analyzing data with missing values. While these two methods are often considered as being distinct from one another, multiple imputation (when using improper imputation) is actually equivalent to a stochastic expectation‐maximization approximation to the likelihood. In this article, we exploit this key result to show that familiar likelihood‐based approaches to model selection, such as Akaike's information criterion (AIC) and the Bayesian information criterion (BIC), can be used to choose the imputation model that best fits the observed data. Poor choice of imputation model is known to bias inference, and while sensitivity analysis has often been used to explore the implications of different imputation models, we show that the data can be used to choose an appropriate imputation model via conventional model selection tools. We show that BIC can be consistent for selecting the correct imputation model in the presence of missing data. We verify these results empirically through simulation studies, and demonstrate their practicality on two classical missing data examples. An interesting result we saw in simulations was that not only can parameter estimates be biased by misspecifying the imputation model, but also by overfitting the imputation model. This emphasizes the importance of using model selection not just to choose the appropriate type of imputation model, but also to decide on the appropriate level of imputation model complexity. [ABSTRACT FROM AUTHOR]

A new class of stochastic Runge–Kutta (SRK) methods for the strong approximation of Stratonovich stochastic ordinary differential equations (SODEs) is presented. The proposed method is an alternative to the method of Xiao and Tang (Numer. Algor. 72: 259–296, 2016) and converges with order 2 in the strong sense. To validate the efficiency and to compare with some known methods, numerical simulations which involve generating Stratonovich stochastic integrals of level 3, are finally given. [ABSTRACT FROM AUTHOR]

This paper proposes an alternative method to deal with spatiotemporal data with censored and missing responses using the SAEM algorithm. This algorithm is a stochastic approximation of the widely used EM algorithm and is an important tool for models in which the E‐step does not have an analytic form. Besides the algorithm developed to estimate the model parameters from a likelihood‐based perspective, we present analytical expressions to compute the observed information matrix. Global influence measures are also developed and presented. Several simulation studies are conducted to examine the asymptotic properties of the SAEM estimates. The proposed method is illustrated by environmental data analysis. The computing codes are implemented in the new R package StempCens. [ABSTRACT FROM AUTHOR]

The conditional scenario (CS) approach was introduced as an effective approximation to the two‐stage stochastic mixed‐integer linear programming problem. Although the original definition of CS is general, in practice it is basically suitable for the multivariate normal distribution. In this paper, we propose a new definition of CS that is suitable for approximating any multivariate distribution (continuous or discrete). This definition allows the approximation of a potentially large set of scenarios using a small set of CSs, unlike the previous definition. In the computational study, dedicated to solving the portfolio optimization problem with hard real‐world constraints, the CS approach has clearly outperformed the sample average approximation approach in terms of solution time. [ABSTRACT FROM AUTHOR]

The maximum mean discrepancy (MMD) has found numerous applications in statistics and machine learning, among which is its use as a penalty in the Wasserstein auto-encoder (WAE). In this paper, we compute closed-form expressions for estimating the Gaussian kernel-based MMD between a given distribution and the standard multivariate normal distribution. This formula reveals a connection to the Baringhaus-Henze-Epps-Pulley (BHEP) statistic of the Henze-Zirklertest and provides further insights about the MMD. We introduce the standardized version of MMD as a penalty for the WAE training objective, allowing for a better interpretability of MMD values and more compatibility across different hyperparameter settings. Next, we propose code normalization-using batch normalization at the code layer-which has the benefits of making the kernel width selection easier, reducing the training effort, and preventing outliers in the aggregate code distribution. Our experiments on synthetic and real data show that the analytic formulation improves over the commonly used stochastic approximation of the MMD and demonstrate that code normalization provides significant benefits when training WAEs. [ABSTRACT FROM AUTHOR]

Understanding the biological principles that govern blood vessel growth in the retina has important clinical implications, for the prevention of possible retinopathies, which may eventually lead to blindness. The availability of a realistic mathematical model of the relevant phenomenon may support the medical community in both issues, diagnosis being related to inverse problems, and therapy to optimal control strategies. The mathematical modeling of retinal angiogenesis leads to an highly complex problem, because of dimension, nonlinearity, and intrinsic randomness. In this paper, we propose a reduced model which leads to numerical simulations that somehow reproduce normal vascularization and predict possible pathologies. We call our model hybrid because it includes the coupling of a fully stochastic model for the construction of a vessel network in the retina, with continuum underlying fields describing relevant factors, such as growth factors and oxygen. We perform numerical simulations of a stochastic particle system coupled with partial differential equations (PDEs)' so to obtain images of vessel structure resembling real retina vasculatures. We then derive a possible mean field approximation of the stochastic vessel network, so to obtain a fully deterministic PDE system for the evolution of the underlying fields. Actually, in order to reproduce the geometric structure of the retina vessel network, we have to keep a stochastic model (though simplified) for its construction. Future investigations may concern the use of such a mean field approximation in the numerical simulations of the retina vasculature. Inverse and optimal control problems being the final goal of our research plan. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic age‐structured population model with Markovian switching is investigated in a polluted environment. Both the stochastic disturbance of environment and the Markovian switching are incorporated into the model. By Itô formula and several assumptions, the boundedness in the qth moment of exact solutions of model are proved. Furthermore, making use of truncated Euler–Maruyama (EM) method, the strong convergence criterion of numerical approximation in the qth moment is established, and the rate of convergence is estimated. Numerical simulations are carried out to illustrate the theoretical results. Our results indicate that the truncated EM method can be used for stochastic age‐structured population system in a polluted environment. [ABSTRACT FROM AUTHOR]

While payoff‐based learning models are almost exclusively devised for finite action games, where players can test every action, it is harder to design such learning processes for continuous games. We construct a stochastic learning rule, designed for games with continuous action sets, which requires no sophistication from the players and is simple to implement: players update their actions according to variations in own payoff between current and previous action. We then analyze its behavior in several classes of continuous games and show that convergence to a stable Nash equilibrium is guaranteed in all games with strategic complements as well as in concave games, while convergence to Nash equilibrium occurs in all locally ordinal potential games as soon as Nash equilibria are isolated. [ABSTRACT FROM AUTHOR]

Summary: Our problem of interest is to minimize a sequence of scalar‐valued loss functions fk(·) or to locate the root(s) of a sequence of vector‐valued functions gk(·) corresponding to time τk with respect to a parameter θ∈ℝp. The available information for the minimization/root‐finding is the noise‐corrupted observation(s) of either fk(·) or gk(·) evaluated at a few of certain design points only. Taking both the dynamics and randomness into consideration, we use stochastic approximation (SA) algorithms to solve the time‐varying problem, but with a nondecaying gain (stepsize). The tracking performance of the nondecaying gain SA algorithm is guaranteed by a computable bound for the root‐mean‐squared error and mean‐absolute‐deviation. The only assumption imposed on the drifts is that the average distance between two consecutive underlying true parameters is bounded from above—this assumption allows the varying target to change abruptly. The error term arising from using the noisy evaluation of fk(·) or gk(·) in constructing the search direction is assumed to have bounded second‐moment—this allows for biased estimator to be used in the SA algorithms. Given the lenient assumptions on the drift and error term, the error bounds apply to a broad class of time‐varying scenarios and are useful for finite‐sample analysis. Since the tracking capability characterizes the average performance across all possible sample paths, it may not provide much guidance on the gain‐tuning strategies useful for one single run. Hence, we propose a data‐dependent gain‐tuning strategy based on estimating the Hessian information and the noise level. The adaptive rule is advantageous as it enables the step size to vary with information gathered during the progress of the estimation procedure. [ABSTRACT FROM AUTHOR]

We consider the problem of nonparametric multi‐product dynamic pricing with unknown demand and show that the problem may be formulated as an online model‐free stochastic program, which can be solved by the classical Kiefer‐Wolfowitz stochastic approximation (KWSA) algorithm. We prove that the expected cumulative regret of the KWSA algorithm is bounded above by κ1T+κ2 where κ1, κ2 are positive constants and T is the number of periods for any T = 1, 2, .... Therefore, the regret of the KWSA algorithm grows in the order of T, which achieves the lower bounds known for parametric dynamic pricing problems and shows that the nonparametric problems are not necessarily more difficult to solve than the parametric ones. Numerical experiments further demonstrate the effectiveness and efficiency of our proposed KW pricing policy by comparing with some pricing policies in the literature. [ABSTRACT FROM AUTHOR]

Summary: This article is concerned with the parameter identification problem of nonlinear dynamic responses for the linear time‐invariant system by means of an impulse excitation signal and discrete observation data. Using the impulse signal as the input, the impulse response experiment is carried out and the dynamical moving sampling is designed to generate the measured data for deriving new identification algorithms. By applying the moving window data that contain the dynamical information of the system to be identified, an objective function with respect to the parameters of the systems is constructed according to the impulse response. In accordance with different functional relations between the system parameters and the system output response, the unknown parameter vector of the system is separated into a linear parameter vector and a nonlinear parameter vector. Based on the separated parameter vectors, two subidentification models are constructed and a separable identification algorithm is presented through the gradient search to improve the accuracy. Moreover, for the purpose of enhancing the estimation accuracy and capturing the dynamical feature of the systems, the moving window data are employed to develop the separable identification algorithm. The performance of the proposed separable identification method is illustrated via a numerical example. [ABSTRACT FROM AUTHOR]

By Gyöngy's theorem, a local and stochastic volatility model is calibrated to the market prices of all European call options with positive maturities and strikes if its local volatility (LV) function is equal to the ratio of the Dupire LV function over the root conditional mean square of the stochastic volatility factor given the spot value. This leads to a stochastic differential equation (SDE) nonlinear in the sense of McKean. Particle methods based on a kernel approximation of the conditional expectation, as presented in Guyon and Henry‐Labordère [Risk Magazine, 25, 92–97], provide an efficient calibration procedure even if some calibration errors may appear when the range of the stochastic volatility factor is very large. But so far, no global existence result is available for the SDE nonlinear in the sense of McKean. When the stochastic volatility factor is a jump process taking finitely many values and with jump intensities depending on the spot level, we prove existence of a solution to the associated Fokker–Planck equation under the condition that the range of the squared stochastic volatility factor is not too large. We then deduce existence to the calibrated model by extending the results in Figalli [Journal of Functional Analysis, 254(1), 109–153]. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the stochastic containment control problem for distributed network with multiplicative and additive noises, in which the stochastic approximation technique is utilized. A major challenge, compared with the existing results with multiplicative and additive noises, is that the involving leaders are dynamically changing. It is shown that finite boundedness for dynamical leaders is of great importance for addressing the stochastic containment control issue. A suitable approach is proposed to handle multiplicative and additive noises based on the stochastic approximation, and some necessary/sufficient conditions are derived for mean square convergence with mild requirements. Furthermore, the convergence rates are studied for both dynamical leaders and static leaders scenarios. We conclude this paper by using two illustrative examples to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Summary: Kalman filtering for linear systems is known to provide the minimum variance estimation error, under the assumption that the model dynamics is known. While many system identification tools are available for computing the system matrices from experimental data, estimating the statistics of the output and process noises is still an open problem. Correlation‐based approaches are very fast and sufficiently accurate, but there are typically restrictions on the number of noise covariance elements that can be estimated. On the other hand, maximum likelihood methods estimate all elements with high accuracy, but they are computationally expensive, and they require the use of external optimization solvers. In this paper, we propose an alternative solution, tailored for process noise covariance estimation and based on stochastic approximation and gradient‐free optimization, that provides a good trade‐off in terms of performance and computational load, and is also easy to implement. The effectiveness of the method as compared to the state of the art is shown on a number of recently proposed benchmark examples. [ABSTRACT FROM AUTHOR]

The free and open‐source package nlmixr implements pharmacometric nonlinear mixed effects model parameter estimation in R. It provides a uniform language to define pharmacometric models using ordinary differential equations. Performances of the stochastic approximation expectation‐maximization (SAEM) and first order‐conditional estimation with interaction (FOCEI) algorithms in nlmixr were compared with those found in the industry standards, Monolix and NONMEM, using the following two scenarios: a simple model fit to 500 sparsely sampled data sets and a range of more complex compartmental models with linear and nonlinear clearance fit to data sets with rich sampling. Estimation results obtained from nlmixr for FOCEI and SAEM matched the corresponding output from NONMEM/FOCEI and Monolix/SAEM closely both in terms of parameter estimates and associated standard errors. These results indicate that nlmixr may provide a viable alternative to existing tools for pharmacometric parameter estimation. [ABSTRACT FROM AUTHOR]

A stochastic approximation EM algorithm (SAEM) is described for exploratory factor analysis of dichotomous or ordinal variables. The factor structure is obtained from sufficient statistics that are updated during iterations with the Robbins-Monro procedure. Two large-scale simulations are reported that compare accuracy and CPU time of the proposed SAEM algorithm to the Metropolis-Hasting Robbins-Monro procedure and to a generalized least squares analysis of the polychoric correlation matrix. A smaller-scale application to real data is also reported, including a method for obtaining standard errors of rotated factor loadings. A simulation study based on the real data analysis is conducted to study bias and error estimates. The SAEM factor algorithm requires minimal lines of code, no derivatives, and no large-matrix inversion. It is programmed entirely in R. [ABSTRACT FROM AUTHOR]

The objective of this study was to develop a nonlinear mixed‐effects model of vitacoxib disposition kinetics in dogs after intravenous (I.V.), oral (P.O.), and subcutaneous (S.C.) dosing. Data were pooled from four consecutive pharmacokinetic studies in which vitacoxib was administered in various dosing regimens to 14 healthy beagle dogs. Plasma concentration versus time data were fitted simultaneously using the stochastic approximation expectation maximization (SAEM) algorithm for nonlinear mixed‐effects as implemented in Monolix version 2018R2. Correlations between random effects and significance of covariates on population parameter estimates were evaluated using multiple samples from the posterior distribution of the random effects. A two‐compartment mamillary model with first‐order elimination and first‐order absorption after P.O. and S.C. administration, best described the available pharmacokinetic data. Final parameter estimates indicate that vitacoxib has a low‐to‐moderate systemic clearance (0.35 L hr−1 kg−1) associated with a low global extraction ratio, but a large volume of distribution (6.43 L/kg). The absolute bioavailability after P.O. and S.C. administration was estimated at 10.5% (fasted) and 54.6%, respectively. Food intake was found to increase vitacoxib oral bioavailability by a fivefold, while bodyweight (BW) had a significant impact on systemic clearance, thereby confirming the need for BW adjustment with vitacoxib dosing in dogs. [ABSTRACT FROM AUTHOR]

In this paper, we establish a small‐time large deviation principle for the strong solution of three‐dimensional stochastic primitive equations driven by multiplicative noise, which involves not only the study of small noise but also the challenging nonlinear drift terms. [ABSTRACT FROM AUTHOR]

The vast potential of demand-side resources (DSR)—including flexible loads and distributed energy resources—in the optimal operation of a power system is being increasingly recognized. Such potential can be fully realized through the access of a DSR aggregator to the power market. In this paper, a DSR aggregator is introduced for the collective management of DSRs in the power system. A bi-level optimization model consisting of power market clearing and DSR aggregator internal scheduling is formulated and solved through stochastic programing. A thorough evaluation of the DSR aggregator's performance under three different operation modes, namely energy consumer mode, energy prosumer mode, and eco-friendliness mode, is carried out to study its influence on system operation concerning social welfare, system purchase cost, carbon emission, and so on. Simulation results show that even though DSR acquires a segment of the market social welfare, it brings in benefits in economic and environmental operation of the system and contributes to DSR uncertainty alleviation. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

Summary: In this paper, local iterative methods for solving the stochastic Hamilton‐Jacobi‐Bellman equation arising in the stochastic optimal control of affine nonlinear systems are discussed. Superquadratic and quadratic convergence of the methods is established under fairly mild assumptions, and an example is solved to demonstrate the effectiveness of the methods. Finally, as a by‐product, an existence result for the solution to the stochastic Hamilton‐Jacobi‐Bellman equation is also established under the same assumptions. [ABSTRACT FROM AUTHOR]

Summary: This paper deals with disturbance‐observer–based control for Markov jump systems with time‐varying delay. A disturbance observer is constructed to estimate the disturbance generated by an exogenous dynamic system. Meantime, a control scheme is proposed to guarantee the corresponding system to be stochastically stable and achieve the purpose of suppressing the corresponding disturbance. By constructing the stochastic Lyapunov‐Krasovskii functional, the desired observer and the controller are designed to ensure stochastic stability of the closed‐loop system. Finally, the simulation results illustrate the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we study zero‐sum two‐player stochastic differential games in which the state equations are competing Brownian particles and the cost functional is defined by generalized backward stochastic differential equations with more than one increasing process. After we study the regularity of competing Brownian particles, we establish the dynamic programming principle for the upper and lower value functions and show that these are the unique viscosity solution of the associated upper and lower Isaacs' equations, which are fully nonlinear parabolic partial differential equations with nonlinear Neumann boundary conditions. [ABSTRACT FROM AUTHOR]