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Introducing Grid WAR: Rethinking WAR for Starting Pitchers

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arXiv 2022年

作者： Brill, Ryan S. Wyner, Abraham J. Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Dept. of Statistics and Data Science The Wharton School University of Pennsylvania United States

The baseball statistic "Wins Above Replacement" (WAR) has emerged as one of the most popular evaluation metrics. But it is not readily observed and tabulated;WAR is an estimate of a parameter in a vaguely defined model with all its attendant assumptions. Industry-standard models of WAR for starting pitchers from FanGraphs and Baseball Reference all assume that season-long averages are sufficient statistics for a pitcher’s performance. This provides an invalid mathematical foundation for many reasons, especially because WAR should not be linear with respect to any counting statistic. To repair this defect, as well as many others, we devise a new measure, Grid WAR, which accurately estimates a starting pitcher’s WAR on a per-game basis. The convexity of Grid WAR diminishes the impact of "blow-up" games and up-weights exceptional games, raising the valuation of pitchers like Sandy Koufax, Whitey Ford, and Catfish Hunter who exhibit fundamental game-by-game variance. Although Grid WAR is designed to accurately measure historical performance, it has predictive value insofar as a pitcher’s Grid WAR is better than Fangraphs’ FIP WAR at predicting future performance. Finally, at https://*** we host a Shiny app which displays the Grid WAR results of each MLB game since 1952, including career, season, and game level results, which updates automatically every morning. Copyright © 2022, The Authors. All rights reserved.

关键词： Baseball

The Loser’s Curse and the Critical Role of the Utility Function

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arXiv 2024年

A longstanding question in the judgment and decision making literature is whether experts, even in high-stakes environments, exhibit the same cognitive biases observed in controlled experiments with inexperienced participants. In their seminal work, Massey and Thaler (2013) provide a notable example of bias and irrationality in expert decision making: general managers’ behavior in the National Football League draft pick trade market. They argue that general managers systematically overvalue top draft picks, which generate less surplus value on average than later first-round picks, a phenomenon known as the loser’s curse. Their conclusion hinges on the assumption that general managers should use expected surplus value as their utility function for evaluating draft picks. This assumption, however, is neither explicitly justified nor necessarily aligned with the strategic complexities of constructing a National Football League roster. In this paper, we challenge their framework by considering alternative utility functions, particularly those that emphasize the acquisition of transformational players––those capable of dramatically increasing a team’s chances of winning the Super Bowl. Under a decision rule that prioritizes the probability of acquiring elite players, which we construct from a novel Bayesian hierarchical Beta regression model, general managers’ draft trade behavior appears rational rather than systematically flawed. More broadly, our findings highlight the critical role of carefully specifying a utility function when evaluating the quality of decisions. © 2024, CC BY.

关键词： Hierarchical systems

Deep learning inter-atomic potential for thermal and phonon behaviour of silicon carbide with quantum accuracy

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arXiv 2021年

作者： Fu, Baoqin Sun, Yandong Zhang, Linfeng Wang, Han Xu, Ben Key Laboratory of Radiation Physics and Technology of the Ministry of Education Institute of Nuclear Science and Technology Sichuan University Chengdu610064 China Graduate School China Academy of Engineering Physics Beijing100193 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China

Silicon carbide (SiC) is an essential material for next generation semiconductors and components for nuclear plants. It’s applications are strongly dependent on its thermal conductivity, which is highly sensitive to microstructures. Molecular dynamics (MD) simulation is the most used methods to address thermal transportation mechanisms in devices or microstructures of nano-meters. However, the implementation of MD is limited in SiC because of lacking accurate inter-atomic potentials. In this work, using the Deep Potential (DP) methodology, we developed two inter-atomic potentials (DP-*Corresponding author. IAPs) for SiC based on two adaptively generated datasets within the density functional approximations at the local density and the generalized gradient levels. These two DP-IAPs manifest their speed with quantum accuracy in lattice dynamics simulations as well as scattering rate analysis of phonon transportation. Combining with molecular dynamics simulations, the thermal transport and mechanical properties were systematically investigated. The presented methodology and the inter-atomic potentials pave the way for a systematic approach to model heat transport in SiC related devices using multiscale modelling. Copyright © 2021, The Authors. All rights reserved.

关键词： Silicon carbide

AUTOAMG(θ): AN AUTO-TUNED AMG METHOD BASED ON DEEP LEARNING FOR STRONG THRESHOLD

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arXiv 2023年

作者： Zou, Haifeng Xu, Xiaowen Zhang, Chen-Song Mo, Zeyao Graduate School of China Academy of Engineering Physics China Academy of Engineering Physics China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics China Academy of Mathematics and Systems Science Chinese Academy of Sciences China

Algebraic Multigrid (AMG) is one of the most used iterative algorithms for solving large sparse linear equations Ax = b. In AMG, the coarse grid is a key component that affects the efficiency of the algorithm, the construction of which relies on the strong threshold parameter θ. This parameter is generally chosen empirically, with a default value in many current AMG solvers of 0.25 for 2D problems and 0.5 for 3D problems. However, for many practical problems, the quality of the coarse grid and the efficiency of the AMG algorithm are sensitive to θ;the default value is rarely optimal, and sometimes is far from it. Therefore, how to choose a better θ is an important question. In this paper, we propose a deep learning based auto-tuning method, AutoAMG(θ) for multiscale sparse linear equations, which are widely used in practical problems. The method uses Graph Neural Networks (GNNs) to extract matrix features, and a Multilayer Perceptron (MLP) to build the mapping between matrix features and the optimal θ, which can adaptively output θ values for different matrices. Numerical experiments show that AutoAMG(θ) can achieve significant speedup compared to the default θ value. Copyright © 2023, The Authors. All rights reserved.

关键词： Linear equations

CONVERGENCE SPEED AND APPROXIMATION ACCURACY OF NUMERICAL MCMC

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arXiv 2022年

作者： Cui, Tiangang Dong, Jing Jasra, Ajay Tong, Xin T. School of Mathematics Monash University Australia Graduate School of Business Columbia University United States Applied Mathematics and Computational Science Program Computer Electrical Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Mathematics National University of Singapore Singapore

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has similar convergence speed and high approximation accuracy as well. We discuss two different analysis frameworks: ergodicity and spectral gap, both are widely used in the literature. Our results can be easily extended to obtain non-asymptotic error bounds for MCMC estimators. We also demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis and Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally we present some simple numerical examples to verify our theoretical claims. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior

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Gaussian Process Port-Hamiltonian Systems: Bayesian Learning...

IEEE Conference on Decision and Control

作者： Thomas Beckers Jacob Seidman Paris Perdikaris George J. Pappas Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia PA USA graduate program in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA USA Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia PA USA

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct. We propose Gaussian Process Port-Hamiltonian systems (GPPHS) as a physics-informed Bayesian learning approach with uncertainty quantification. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Hamiltonians instead of a single point estimate. Due to the underlying physics model, a GP-PHS generates passive systems with respect to designated inputs and outputs. Further, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.

关键词： Uncertainty Gaussian processes Probabilistic logic Data models Bayes methods Behavioral sciences Kernel

To Sharpen or not to Sharpen? On the Effect of Sharpening Filters applied to Magnified Images 14

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To Sharpen or not to Sharpen? On the Effect of Sharpening Fi...

14th International Conference on Digital Image Processing, ICDIP 2022

作者： Emmendorfer, Leonardo R. de Olviveira, Vinicius Menezes Schein, Tatiana T. de Jesus, Junior C. Rodriguez, Bárbara D.A. Electrical Energy Processing Department Federal University of Santa Maria 97105-340 Brazil Center for Computational Science Federal University of Rio Grande 96201-900 Brazil Computational Modeling PhD Program Federal University of Rio Grande 96201-900 Brazil Computer Engineering Graduate Program Federal University of Rio Grande 96201-900 Brazil Institute of Mathematics Statistics and Physics Federal University of Rio Grande 96201-900 Brazil

ISBN: (纸本)9781510657564

Super-resolution algorithms aim to produce magnified high-resolution versions from low-resolution images. Some methods, however, are prone to generate blur during the process. Simple sharpening filters are adopted to alleviate this type of artifact. However, the actual effectiveness of this approach is not clear-cut in the literature. This work evaluates the effect of three simple sharpening filters on the quality of images obtained from super-resolution methods. Two metrics were considered in the evaluation: the Peak signal-to-noise ratio (PSNR) metric, and the Learned Perceptual Image Patch Similarity (LPIPS). One of the filters could consistently improve the LPIPS metric of magnified images from diverse benchmark sets on top of seven super-resolution methods. The increments obtained for the perceptual metric seem to occur due to the sharpening effect. Improvements on PSNR values were not as consistent. © 2022 SPIE.

关键词： Quality control

IMPROVED EFFICIENCY OF MULTILEVEL MONTE CARLO FOR STOCHASTIC PDE THROUGH STRONG PAIRWISE COUPLING

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arXiv 2021年

作者： Chada, Neil K. Hoel, Håkon Jasra, Ajay Zouraris, Georgios E. Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Mathematics for Uncertainty Quantification RWTH Aachen University Aachen Germany Department of Mathematics and Applied Mathematics Voutes Campus Crete HeraklionGR-700 13 Greece

Multilevel Monte Carlo (MLMC) has become an important methodology in applied mathematics for reducing the computational cost of weak approximations. For many problems, it is well-known that strong pairwise coupling of numerical solutions in the multilevel hierarchy is needed to obtain efficiency gains. In this work, we show that strong pairwise coupling indeed is also important when MLMC is applied to stochastic partial differential equations (SPDE) of reaction-diffusion type, as it can improve the rate of convergence and thus improve tractability. For the MLMC method with strong pairwise coupling that was developed and studied numerically on filtering problems in [Chernov et al., Numer. Math., 147 (2021), 71-125], we prove that the rate of computational efficiency is higher than for existing methods. We also provide numerical comparisons with alternative coupling ideas on linear and nonlinear SPDE to illustrate the importance of this *** Codes 65C05, 65N35, 60H35, 65C30 © 2021, CC BY.

关键词： Monte Carlo methods

PRIKRY-TYPE FORCINGS AFTER COLLAPSING A HUGE CARDINAL

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arXiv 2022年

作者： Tsukuura, Kenta Doctoral Program in Mathematics Pure and Applied Sciences Graduate School of Science and Technology University of Tsukuba Tsukuba305-8571 Japan

Some models of combinatorial principles have been obtained by collapsing a huge cardinal in the case of the successors of regular cardinals. For example, saturated ideals, Chang's conjecture, polarized partition relations, and transfer principles for chromatic numbers of graphs. In this paper, we study these in the case of the successors of singular cardinals. In particular, we show that Prikry forcing preserves the centeredness of ideals but kills the layeredness. We also study (Equation presented) in the extension by Prikry forcing at µ.MSC Codes 03E35, 03E40, 03E55 Copyright © 2022, The Authors. All rights reserved.

关键词： Combinatorial mathematics