Stochastic Estimation Research Articles

Flash proton radiation therapy via a stochastic three-operator splitting method

Abstract The inverse radiation therapy planning problem is crucial in achieving tumoricidal doses while minimizing radiation-induced normal-tissue toxicity. Compared to conventional radiation therapy (with conventional dose rates), flash proton radiation therapy (with ultra-high dose rates) can provide additional normal tissue sparing. However, this groundbreaking advancement in radiation oncology introduces a challenging nonconvex and nonsmooth optimization problem. In this paper, we propose a stochastic three-operator splitting (STOS) algorithm to address the flash proton radiation therapy problem. We establish the convergence and convergence rates of the STOS algorithm under the nonconvex framework for both unbiased gradient estimators and variance-reduced gradient estimators. These stochastic gradient estimators include the most popular ones, such as SGD, SAGA, SARAH, and SAG, among others. Experimental results demonstrate that the flash proton radiation therapy plans obtained by the STOS algorithm can effectively kill tumors while better protecting normal tissues.

Almost-Sure Convergence of Iterates and Multipliers in Stochastic Sequential Quadratic Optimization

Stochastic sequential quadratic optimization (SQP) methods for solving continuous optimization problems with nonlinear equality constraints have attracted attention recently, such as for solving large-scale data-fitting problems subject to nonconvex constraints. However, for a recently proposed subclass of such methods that is built on the popular stochastic-gradient methodology from the unconstrained setting, convergence guarantees have been limited to the asymptotic convergence of the expected value of a stationarity measure to zero. This is in contrast to the unconstrained setting in which almost-sure convergence guarantees (of the gradient of the objective to zero) can be proved for stochastic-gradient-based methods. In this paper, new almost-sure convergence guarantees for the primal iterates, Lagrange multipliers, and stationarity measures generated by a stochastic SQP algorithm in this subclass of methods are proved. It is shown that the error in the Lagrange multipliers can be bounded by the distance of the primal iterate to a primal stationary point plus the error in the latest stochastic gradient estimate. It is further shown that, subject to certain assumptions, this latter error can be made to vanish by employing a running average of the Lagrange multipliers that are computed during the run of the algorithm. The results of numerical experiments are provided to demonstrate the proved theoretical guarantees.

New Stochastic Restricted Biased Regression Estimators

In this paper, we propose three stochastic restricted biased estimators for the linear regression model. These new estimators generalize the least squares estimator, mixed estimator, and biased estimator. We derive the necessary and sufficient conditions for the superiority of the proposed estimators over existing ones, as well as their relative superiority among each other, using the mean squared error matrix as a criterion. A simulation study is conducted to validate the theoretical findings, and two real-world examples are provided to demonstrate the practical advantages of the proposed estimators.

Stochastic risk estimation due to non-stationary hazards using compound-NHPP

Stochastic risk estimation due to non-stationary hazards using compound-NHPP

Solving Inverse PDE Problems using Grid-Free Monte Carlo Estimators

Partial differential equations can model diverse physical phenomena including heat diffusion, incompressible flows, and electrostatic potentials. Given a description of an object's boundary and interior, traditional methods solve such PDEs by densely meshing the interior and then solving a large and sparse linear system derived from this mesh. Recent grid-free solvers take an alternative approach and avoid this complexity in exchange for randomness: they compute stochastic solution estimates and generally bear a striking resemblance to physically-based rendering algorithms. In this article, we develop algorithms targeting the inverse form of this problem: given an already existing solution of a PDE, we infer parameters characterizing the boundary and interior. In the grid-free setting, there are again significant connections to rendering, and we show how insights from both fields can be combined to compute unbiased derivative estimates that enable gradient-based optimization. In this process, we encounter new challenges that must be addressed to obtain practical solutions. We introduce acceleration and variance reduction strategies and show how to differentiate branching random walks in reverse mode. We finally demonstrate our approach on both simulated data and a real-world electrical impedance tomography experiment, where we reconstruct the position of a conducting object from voltage measurements taken in a saline-filled tank.

A CNN-accelerated workflow for stochastic seismic property estimation

As one of the major tools in resolving the non-uniqueness challenge in subsurface interpretation and reservoir characterization, stochastic inversion from post- and pre-stack seismic data remains challenging, which not only requires heavy computational resources but also relies on intensive manual supervision. Inspired by the recent advances in deep learning particularly convolutional neural networks (CNNs) for interdisciplinary data integration, this study proposes a deep learning workflow that enables stochastic property estimation by efficiently integrating seismic images with sparse wells. It starts with sampling a set of property prior models (PPMs) from densely-measured properties at well locations and corrupting local seismic patterns with Gaussian noise. The core idea is to train a structure-guided CNN by mapping the contaminated seismic with the sampled PPMs while enforcing structural consistency to avoid overfitting in the presence of sparse wells. Finally, the baseline and uncertainty of target properties are estimated by running multiple realizations of the trained CNN. As demonstrated by three examples, with minimum efforts of CNN architecture customization according to data availability, the proposed workflow can accommodate various use cases, including rock acoustic/elastic property estimation from 3D post-/angle-stack seismic and soil geotechnical properties from 2D ultra-high-resolution seismic. In all examples, the machine predictions match seismic patterns well and are of high lateral consistency.

Hybrid Stealthy Attacks on Stochastic Event-Based Remote Estimation Under Packet Dropouts

Hybrid Stealthy Attacks on Stochastic Event-Based Remote Estimation Under Packet Dropouts

Model-free distributed state estimation with local measurements.

In this paper, the state estimation problem of physical plants with unknown system dynamic is revisited from the perspective of limited output information measurement, which corresponds to those with characteristics of high-dimensional, wide-area coverage and scatter. Given this fact, a network of sensors are used to carry out the measurement with each one accessing only partial outputs of the targeted systems and a novel model-free state estimation approach, named distributed stochastic variational inference state estimation, is proposed. The key idea of this method is to compensate for the impacts of local output measurements by adding nearest-neighbor rule-based information interaction among estimators to complete the state estimation. It finds from the numerical experiments that the proposed method has clear advantages in both estimation accuracy and speed, and it also provides guidance on how to improve the efficiency of state estimation under local measurements.

Physics-informed data-driven reconstruction of turbulent wall-bounded flows from planar measurements

Obtaining accurate and dense three-dimensional estimates of turbulent wall-bounded flows is notoriously challenging, and this limitation negatively impacts geophysical and engineering applications, such as weather forecasting, climate predictions, air quality monitoring, and flow control. This study introduces a physics-informed variational autoencoder model that reconstructs realizable three-dimensional turbulent velocity fields from two-dimensional planar measurements thereof. Physics knowledge is introduced as soft and hard constraints in the loss term and network architecture, respectively, to enhance model robustness and leverage inductive biases alongside observational ones. The performance of the proposed framework is examined in a turbulent open-channel flow application at friction Reynolds number Reτ=250. The model excels in precisely reconstructing the dynamic flow patterns at any given time and location, including turbulent coherent structures, while also providing accurate time- and spatially-averaged flow statistics. The model outperforms state-of-the-art classical approaches for flow reconstruction such as the linear stochastic estimation method. Physical constraints provide a modest but discernible improvement in the prediction of small-scale flow structures and maintain better consistency with the fundamental equations governing the system when compared to a purely data-driven approach.

A Study of Mixed Non-Motorized Traffic Flow Characteristics and Capacity Based on Multi-Source Video Data.

Mixed non-motorized traffic is largely unaffected by motor vehicle congestion, offering high accessibility and convenience, and thus serving as a primary mode of "last-mile" transportation in urban areas. To advance stochastic capacity estimation methods and provide reliable assessments of non-motorized roadway capacity, this study proposes a stochastic capacity estimation model based on power spectral analysis. The model treats discrete traffic flow data as a time-series signal and employs a stochastic signal parameter model to fit stochastic traffic flow patterns. Initially, UAVs and video cameras are used to capture videos of mixed non-motorized traffic flow. The video data were processed with an image detection algorithm based on the YOLO convolutional neural network and a video tracking algorithm using the DeepSORT multi-target tracking model, extracting data on traffic flow, density, speed, and rider characteristics. Then, the autocorrelation and partial autocorrelation functions of the signal are employed to distinguish among four classical stochastic signal parameter models. The model parameters are optimized by minimizing the AIC information criterion to identify the model with optimal fit. The fitted parametric models are analyzed by transforming them from the time domain to the frequency domain, and the power spectrum estimation model is then calculated. The experimental results show that the stochastic capacity model yields a pure EV capacity of 2060-3297 bikes/(h·m) and a pure bicycle capacity of 1538-2460 bikes/(h·m). The density-flow model calculates a pure EV capacity of 2349-2897 bikes/(h·m) and a pure bicycle capacity of 1753-2173 bikes/(h·m). The minimal difference between these estimates validates the effectiveness of the proposed model. These findings hold practical significance in addressing urban road congestion.

Towards a Field-Based Bayesian Evidence Inference from Nested Sampling Data.

Nested sampling (NS) is a stochastic method for computing the log-evidence of a Bayesian problem. It relies on stochastic estimates of prior volumes enclosed by likelihood contours, which limits the accuracy of the log-evidence calculation. We propose to transform the prior volume estimation into a Bayesian inference problem, which allows us to incorporate a smoothness assumption for likelihood-prior-volume relations. As a result, we aim to increase the accuracy of the volume estimates and thus improve the overall log-evidence calculation using NS. The method presented works as a post-processing step for NS and provides posterior samples of the likelihood-prior-volume relation, from which the log-evidence can be calculated. We demonstrate an implementation of the algorithm and compare its results with plain NS on two synthetic datasets for which the underlying evidence is known. We find a significant improvement in accuracy for runs with less than one hundred active samples in NS but a proneness for numerical problems beyond this point.

Comparisons between the first- and second-order spectral stochastic estimations in investigating the multiphysics couplings for a supersonic turbulent channel flow

Comparisons between the first- and second-order spectral stochastic estimations in investigating the multiphysics couplings for a supersonic turbulent channel flow

Option pricing under stochastic volatility on a quantum computer

We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under typical market conditions. These algorithms are based on combining well-established numerical methods for stochastic differential equations and quantum amplitude estimation technique. In particular, we empirically show that, despite its simplicity, weak Euler method achieves the same level of accuracy as the better-known strong Euler method in this task. Furthermore, by eliminating the expensive procedure of preparing Gaussian states, the quantum algorithm based on weak Euler scheme achieves drastically better efficiency than the one based on strong Euler scheme. Our resource analysis suggests that option pricing under stochastic volatility is a promising application of quantum computers, and that our algorithms render the hardware requirement for reaching practical quantum advantage in financial applications less stringent than prior art.

Life cycle assessment of metal powder production: a Bayesian stochastic Kriging model-based autonomous estimation

Metal powder contributes to the environmental burdens of additive manufacturing (AM) substantially. Current life cycle assessments (LCAs) of metal powders present considerable variations of lifecycle environmental inventory due to process divergence, spatial heterogeneity, or temporal fluctuation. Most importantly, the amounts of LCA studies on metal powder are limited and primarily confined to partial material types. To this end, based on the data surveyed from a metal powder supplier, this study conducted an LCA of titanium and nickel alloy produced by electrode-inducted and vacuum-inducted melting gas atomization, respectively. Given that energy consumption dominates the environmental burden of powder production and is influenced by metal materials’ physical properties, we proposed a Bayesian stochastic Kriging model to estimate the energy consumption during the gas atomization process. This model considered the inherent uncertainties of training data and adaptively updated the parameters of interest when new environmental data on gas atomization were available. With the predicted energy use information of specific powder, the corresponding lifecycle environmental impacts can be further autonomously estimated in conjunction with the other surveyed powder production stages. Results indicated the environmental impact of titanium alloy powder is slightly higher than that of nickel alloy powder and their lifecycle carbon emissions are around 20 kg CO2 equivalency. The proposed Bayesian stochastic Kriging model showed more accurate predictions of energy consumption compared with conventional Kriging and stochastic Kriging models. This study enables data imputation of energy consumption during gas atomization given the physical properties and producing technique of powder materials.

Generalized likelihood ratio method for stochastic models with uniform random numbers as inputs

We propose a new unbiased stochastic gradient estimator for a family of stochastic models driven by uniform random numbers as inputs. Dropping the requirement that the tails of the density of the input random variables decay smoothly, the estimator extends the applicability of the generalized likelihood ratio (GLR) method. We demonstrate the new estimator for several general classes of input random variates, including independent inverse transform random variates and dependent input random variables governed by an Archimedean copula. We show how the new estimator works in settings such as density estimation, and we illustrate applications to credit risk derivatives. Numerical experiments substantiate broad applicability and flexibility in dealing with discontinuities in the sample performance.

Interim analysis, a tool to enhance efficiency of pharmacokinetic studies: Pharmacokinetics of rifampicin in lactating mother-infant pairs.

Pharmacokinetic studies are important for understanding drug disposition in the human body. However, pregnant and lactating women are often excluded from primary pharmacokinetic studies and as such there is often limited dosing information regarding drug use in pregnant and/or lactating women. The objectives of this interim analysis were to define the transfer of rifampicin to a breastfed infant and to determine the area under the concentration-time curve of rifampicin in maternal plasma, breastmilk and infant plasma. Performing this interim analysis enabled us to substantiate whether prior assumptions we made on several study design issues including patient sample size and pharmacokinetic sampling times held and whether we needed to amend our protocol or not. We enrolled lactating mothers on treatment for tuberculosis with their breastfeeding infants (below 12 months of age), performed intensive pharmacokinetic sampling (0-24 h post-dose) on plasma samples from both the mother, infant(s) and breastmilk samples from the mother on two separate occasions (once during the initiation phase and another during the continuation phase of tuberculosis treatment). The initial study design, including sampling times, was informed by a stochastic simulation and estimation exercise, with very limited prior breastmilk data. An interim analysis after recruiting 6 mother-infant pairs ascertained that our initial assumptions were ideal for achieving our study objectives and no amendments to the sampling times were necessary. Initial data from 6 mother-infant pairs show that rifampicin penetrates breastmilk with an approximate milk-to-plasma ratio of 0.169 and 0.189 on two separate visits. However, it was undetectable in most infants.

A GIS-coupled thermal response model for predicting the population growth potential of the red cotton bug, Dysdercus koenigii (Fabricius) (Hemiptera: Pyrrhocoridae) in India under climate change conditions

Recently, the red cotton bug has become a significant menace to cotton in India. With the potential for increased habitat suitability due to predicted temperature rise of 2.5 °C under future climate change in India, this pest could become even more severe in certain regions. Addressing the knowledge gap on the temperature-driven population growth of this pest is crucial for developing a climate-resilient pest management strategy. In this study, life history data gathered at various constant temperatures (15 °C–35 °C) were used to estimate temperature thresholds and thermal requirements for the red cotton bug development. Stochastic estimation of life table parameters and validation with real-time weather data were performed. The phenology model, integrated into a geographic information system, projected the future pest status based on SSP126 temperature change scenarios for the year 2050. The temperatures between 8.35 and 10.83 °C were estimated as lower developmental thresholds for various immature life stages. The optimum and upper threshold temperatures estimated for different life stages ranged between 22.14 – 28.32 °C and 35.80–39.08 °C, respectively. Thermal requirements of 447.97° days for life cycle completion were estimated. The optimum immature survival rates (>70%) were observed at temperatures between 25 and 30 °C. The temperature-dependent decrease in generation times from 90.45 days (15 °C) to 25.44 days (35 °C) was observed, whereas maximum fecundity was recorded at 32 °C. Simulation at fluctuating temperatures across different cotton growing locations provided reasonably similar results on potential population increase (finite rate of increase: 0.99–1.04 females/female/day and a generation time of 44.25–83.97 days). Risk mapping highlighted moderate to high suitability (ERI >0.4, GI > 6, and AI >4) of various cotton growing areas under current climate, and projected shifts in suitability under future climate change. The study has generated information valuable for implementing effective and timely pest management strategies for red cotton bug. Integrating the field observations with model outputs can enhance a practical understanding of red cotton bug dynamics.

Enhanced methods for multicollinearity mitigation in stochastic frontier analysis estimation

Enhanced methods for multicollinearity mitigation in stochastic frontier analysis estimation

On the Consistency of Stochastic Noise Properties and Velocity Estimations from Different Analysis Strategies and Centers with Environmental Loading and CME Corrections

The analysis of the Global NFavigation Satellite System (GNSS) time series provides valuable information for geodesy and geodynamics researcFh. Precise data analysis strategies are crucial for accurately obtaining the linear velocity of GNSS stations, enabling high-precision applications of GNSS time series. This study investigates the impact of different stochastic noise models on velocity estimations derived from GNSS time series, specifically under conditions of environmental loading correction and common mode error (CME) removal. By comparing data from various data centers, we find that post-correction, different analysis strategies exhibit high consistency in their noise characteristics and velocity estimation results. Across various analysis strategies, the optimal noise models were predominantly Power Law with White Noise (PLWN) and Fractional Noise with White Noise (FNWN), with the optimal noise models including COMB/JPL, COMB/SOPAC, and COMB/NGL for approximately 50% of the datasets. Most of the stations (approximately 80%) showed velocity differences below 0.3 mm/year and velocity estimation uncertainties below 0.1 mm/year. Nonetheless, variations in amplitudes and periodic signals persisted due to differences in the processing of raw GNSS observations. For instance, the NGL and JPL datasets, which were processed using GipsyX 2.1 software, showed higher amplitudes of the 5.5-day periodic signal. These findings provide a solid empirical foundation for advancing data analysis methods and enhancing the reliability of GNSS time series results in future research.

Online Estimation and Optimization of Utility-Based Shortfall Risk

Utility-based shortfall risk (UBSR) is a risk metric that is increasingly popular in financial applications, owing to certain desirable properties that it enjoys. We consider the problem of estimating UBSR in a recursive setting, in which samples from the underlying loss distribution are available one at a time. We cast the UBSR estimation problem as a root-finding problem and propose stochastic approximation-based estimation schemes. We derive nonasymptotic bounds on the estimation error in the number of samples. We also consider the problem of UBSR optimization within a parameterized class of random variables. We propose a stochastic gradient descent–based algorithm for UBSR optimization and derive nonasymptotic bounds on its convergence.