Practical Nonparametric Sampling Strategies for Quantile-Based Ordinal Optimization

2021 ◽  
Author(s):  
Dongwook Shin ◽  
Mark Broadie ◽  
Assaf Zeevi
Keyword(s):  
Finite Time ◽  
Stochastic Systems ◽  
Probability Distributions ◽  
Sequential Estimation ◽  
Parametric Representation ◽  
Rate Function ◽  
Probability Of Error ◽  
Time Performance ◽  
Large Deviations Theory ◽  
The One

Given a finite number of stochastic systems, the goal of our problem is to dynamically allocate a finite sampling budget to maximize the probability of selecting the “best” system. Systems are encoded with the probability distributions that govern sample observations, which are unknown and only assumed to belong to a broad family of distributions that need not admit any parametric representation. The best system is defined as the one with the highest quantile value. The objective of maximizing the probability of selecting this best system is not analytically tractable. In lieu of that, we use the rate function for the probability of error relying on large deviations theory. Our point of departure is an algorithm that naively combines sequential estimation and myopic optimization. This algorithm is shown to be asymptotically optimal; however, it exhibits poor finite-time performance and does not lead itself to implementation in settings with a large number of systems. To address this, we propose practically implementable variants that retain the asymptotic performance of the former while dramatically improving its finite-time performance.

scholarly journals Finite-TimeH∞Control for Time-Delayed Stochastic Systems with Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenhua Gao ◽  
Feiqi Deng ◽  
Ruiqiu Zhang ◽  
Wenhui Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Time Stability ◽  
Finite Time Stability ◽  
Weighting Matrix ◽  
Simulation Results ◽  
Dependent State

This paper studies the problem of finite-timeH∞control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-timeH∞control is obtained. Simulation results illustrate the effectiveness of the proposed method.

Possibilistic Uncertainty Quantification in 1-D Consolidation Problems

2021 ◽  
Author(s):  
Djamalddine Boumezerane
Keyword(s):  
Uncertainty Quantification ◽  
Probability Distributions ◽  
Uncertainty Propagation ◽  
Possibility Distribution ◽  
Coefficient Of Consolidation ◽  
Consolidation Process ◽  
Possibility Distributions ◽  
Coverage Function ◽  
The One ◽  
Measure Of Uncertainty

Abstract In this study, we use possibility distribution as a basis for parameter uncertainty quantification in one-dimensional consolidation problems. A Possibility distribution is the one-point coverage function of a random set and viewed as containing both partial ignorance and uncertainty. Vagueness and scarcity of information needed for characterizing the coefficient of consolidation in clay can be handled using possibility distributions. Possibility distributions can be constructed from existing data, or based on transformation of probability distributions. An attempt is made to set a systematic approach for estimating uncertainty propagation during the consolidation process. The measure of uncertainty is based on Klir's definition (1995). We make comparisons with results obtained from other approaches (probabilistic…) and discuss the importance of using possibility distributions in this type of problems.

Pacific Salmon Environmental and Life History Models: Advancing Science for Sustainable Salmon in the Future

2009 ◽  
Keyword(s):  
Model Uncertainty ◽  
Pacific Salmon ◽  
Probability Distributions ◽  
Cultural Resources ◽  
Policy Makers ◽  
Recovery Planning ◽  
Habitat Recovery ◽  
Alternative Scenarios ◽  
The One

<em>Abstract.</em>—Natural resource management requires difficult decisions, broad societal costs, and sacrifices from private landowners and public agencies. With so many financial, ecological and cultural resources at stake, policy-makers, managers, and citizens need scientific predictions that can help resolve conflicts and balance the often competing needs of ecosystems and communities. Modeled information is essential for meeting this need. The words “model uncertainty” are often misinterpreted as describing a lack of knowledge about model output. In fact, they describe knowledge, not only of the one most likely modeled estimate, but also of all the other possible estimates that the model might have provided, and their likelihood. We present six case studies, from salmon habitat recovery planning, illustrating how scientists can provide more useful products by describing distributions of possible outcomes as formal probability distributions, as confidence intervals, or as descriptions of alternative scenarios. In terms of management effectiveness, the communication and use of model uncertainty can be at least as important as the quality of the original model.

scholarly journals Extinction for a Singular Diffusion Equation with Strong Gradient Absorption Revisited

2018 ◽  
Vol 18 (4) ◽  
pp. 785-797
Author(s):  
Razvan Gabriel Iagar ◽  
Philippe Laurençot
Keyword(s):  
Diffusion Equation ◽  
Finite Time ◽  
Extinction Time ◽  
Extinction Rates ◽  
Optimal Decay ◽  
Singular Diffusion ◽  
Finite Time Extinction ◽  
Strong Gradient ◽  
The One ◽  
Time Extinction

AbstractWhen {2N/(N+1)<p<2} and {0<q<p/2}, non-negative solutions to the singular diffusion equation with gradient absorption\partial_{t}u-\Delta_{p}u+|\nabla u|^{q}=0\quad\text{in }(0,\infty)\times% \mathbb{R}^{N}vanish after a finite time. This phenomenon is usually referred to as finite-time extinction and takes place provided the initial condition {u_{0}} decays sufficiently rapidly as {|x|\to\infty}. On the one hand, the optimal decay of {u_{0}} at infinity guaranteeing the occurrence of finite-time extinction is identified. On the other hand, assuming further that {p-1<q<p/2}, optimal extinction rates near the extinction time are derived.

scholarly journals An Improved Algorithm for Low-Level Turbulence Forecasting

2018 ◽  
Vol 57 (6) ◽  
pp. 1249-1263 ◽  
Author(s):  
Domingo Muñoz-Esparza ◽  
Robert Sharman
Keyword(s):  
Probability Distributions ◽  
Atmospheric Stability ◽  
Energy Dissipation Rate ◽  
Probability Of Detection ◽  
Percentage Error ◽  
Unmanned Aerial Systems ◽  
Low Level ◽  
Forecasting System ◽  
The One ◽  
Aerial Systems

AbstractA low-level turbulence (LLT) forecasting algorithm is proposed and implemented within the Graphical Turbulence Guidance (GTG) turbulence forecasting system. The LLT algorithm provides predictions of energy dissipation rate (EDR; turbulence dissipation to the one-third power), which is the standard turbulence metric used by the aviation community. The algorithm is based upon the use of distinct log-Weibull and lognormal probability distributions in a statistical remapping technique to represent accurately the behavior of turbulence in the atmospheric boundary layer for daytime and nighttime conditions, respectively, thus accounting for atmospheric stability. A 1-yr-long GTG LLT calibration was performed using the High-Resolution Rapid Refresh operational model, and optimum GTG ensembles of turbulence indices for clear-air and mountain-wave turbulence that minimize the mean absolute percentage error (MAPE) were determined. Evaluation of the proposed algorithm with in situ EDR data from the Boulder Atmospheric Observatory tower covering a range of altitudes up to 300 m above the surface demonstrates a reduction in the error by a factor of approximately 2.0 (MAPE = 55%) relative to the current operational GTG system (version 3). In addition, the probability of detection of typical small and large EDR values at low levels is increased by approximately 15%–20%. The improved LLT algorithm is expected to benefit several nonconventional turbulence-prediction sectors such as unmanned aerial systems and wind energy.

Empirically comparing the finite-time performance of simulation-optimization algorithms

2017 ◽  
Author(s):  
Naijia Anna Dong ◽  
David J. Eckman ◽  
Xueqi Zhao ◽  
Shane G. Henderson ◽  
Matthias Poloczek
Keyword(s):  
Finite Time ◽  
Simulation Optimization ◽  
Optimization Algorithms ◽  
Time Performance

scholarly journals Interacting vacuum at infinity

2019 ◽  
Vol 16 (04) ◽  
pp. 1950052
Author(s):  
G. Kittou
Keyword(s):  
Finite Time ◽  
Central Extension ◽  
Vacuum Model ◽  
Time Singularity ◽  
Attractor Solution ◽  
The One ◽  
Finite Time Singularity

We apply the central extension technique of Poincaré to dynamics involving an interacting mixture of pressureless matter and vacuum near a finite-time singularity. We show that the only attractor solution on the circle of infinity is the one describing a vanishing matter-vacuum model at early times.

scholarly journals Application of Asymmetrical Statistical Distributions for 1D Simulation of Solute Transport in Streams

Water ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 2145
Author(s):  
Sokáč ◽  
Velísková ◽  
Gualtieri
Keyword(s):  
Probability Distributions ◽  
New Approach ◽  
Dead Zones ◽  
Advection Dispersion ◽  
Small Streams ◽  
Computational Speed ◽  
Transient Storage Zones ◽  
The One ◽  
Published Research ◽  
Substance Transport

Analytical solutions of the one-dimensional (1D) advection–dispersion equations, describing the substance transport in streams, are often used because of their simplicity and computational speed. Practical computations, however, clearly show the limits and the inaccuracies of this approach. These are especially visible in cases where the streams deform concentration distribution of the transported substance due to hydraulic and morphological conditions, e.g., by transient storage zones (dead zones), vegetation, and irregularities in the stream hydromorphology. In this paper, a new approach to the simulation of 1D substance transport is presented, adapted, and tested on tracer experiments available in the published research, and carried out in three small streams in Slovakia with dead zones. Evaluation of the proposed methods, based on different probability distributions, confirmed that they approximate the measured concentrations significantly better than those based upon the commonly used Gaussian distribution. Finally, an example of the application of the proposed methods to an iterative (inverse) task is presented.

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