scholarly journals Modeling In-Match Sports Dynamics Using the Evolving Probability Method

2021 ◽  
Vol 11 (10) ◽  
pp. 4429
Author(s):  
Ana Šarčević ◽  
Damir Pintar ◽  
Mihaela Vranić ◽  
Ante Gojsalić
Keyword(s):  
Monte Carlo Simulation ◽  
Statistical Models ◽  
Empirical Bayes ◽  
Hybrid Approach ◽  
Real Life ◽  
Bayes Estimation ◽  
Probability Method ◽  
Specific Nature ◽  
Sport Event ◽  
Insight Into

The prediction of sport event results has always drawn attention from a vast variety of different groups of people, such as club managers, coaches, betting companies, and the general population. The specific nature of each sport has an important role in the adaption of various predictive techniques founded on different mathematical and statistical models. In this paper, a common approach of modeling sports with a strongly defined structure and a rigid scoring system that relies on an assumption of independent and identical point distributions is challenged. It is demonstrated that such models can be improved by introducing dynamics into the match models in the form of sport momentums. Formal mathematical models for implementing these momentums based on conditional probability and empirical Bayes estimation are proposed, which are ultimately combined through a unifying hybrid approach based on the Monte Carlo simulation. Finally, the method is applied to real-life volleyball data demonstrating noticeable improvements over the previous approaches when it comes to predicting match outcomes. The method can be implemented into an expert system to obtain insight into the performance of players at different stages of the match or to study field scenarios that may arise under different circumstances.

Parameter Estimations of Inverse Weibull Distribution

2011 ◽  
Vol 199-200 ◽  
pp. 564-568
Author(s):  
Wei An Yan ◽  
Bao Wei Song ◽  
Zhao Yong Mao ◽  
Huang Yong Le
Keyword(s):  
Monte Carlo Simulation ◽  
Weibull Distribution ◽  
Empirical Bayes ◽  
Bayes Estimation ◽  
Conjugate Prior ◽  
Monte Carlo Simulation Study ◽  
Empirical Bayes Estimation ◽  
Asymptotically Optimal ◽  
Parameter Estimations ◽  
Inverse Weibull Distribution

under entropy loss function, the E-Bayes estimation and empirical bayes estimation to the parameter of inverse Weibull distribution used conjugate prior are discussed. And we prove the empirical bayes estimation is asymptotically optimal. At last, the MSE of the estimations are compared based on Monte Carlo simulation study. According to these comparisons, it is suggested that the accuracy of E-Bayes estimation is close to the empirical bayes estimation.

scholarly journals An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics

Pharmaceutics ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 42
Author(s):  
Walter M. Yamada ◽  
Michael N. Neely ◽  
Jay Bartroff ◽  
David S. Bayard ◽  
James V. Burke ◽  
...  
Keyword(s):  
Drug Development ◽  
Population Pharmacokinetics ◽  
Empirical Bayes ◽  
Applied Mathematics ◽  
Grid Method ◽  
Bayes Estimation ◽  
Population Pharmacokinetic ◽  
Support Points ◽  
Primal Dual ◽  
Log Normal

Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing.

scholarly journals Modeling of a Real-Life Industrial Reactor for Hydrogenation of Benzene Process

Catalysts ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 412
Author(s):  
Mirosław K. Szukiewicz ◽  
Krzysztof Kaczmarski
Keyword(s):  
Catalyst Activity ◽  
Real Life ◽  
Operating Conditions ◽  
Reactor Operation ◽  
Reactor Model ◽  
High Scale ◽  
Industrial Reactor ◽  
Knowledge Based ◽  
Operation Conditions ◽  
Insight Into

A dynamic model of the hydrogenation of benzene to cyclohexane reaction in a real-life industrial reactor is elaborated. Transformations of the model leading to satisfactory results are presented and discussed. Operating conditions accepted in the simulations are identical to those observed in the chemical plant. Under those conditions, some components of the reaction mixture vanish, and the diffusion coefficients of the components vary along the reactor (they are strongly concentration-dependent). We came up with a final reactor model predicting with reasonable accuracy the reaction mixture’s outlet composition and temperature profile throughout the process. Additionally, the model enables the anticipation of catalyst activity and the remaining deactivated catalyst lifetime. Conclusions concerning reactor operation conditions resulting from the simulations are presented as well. Since the model provides deep insight into the process of simulating, it allows us to make knowledge-based decisions. It should be pointed out that improvements in the process run, related to operating conditions, or catalyst application, or both on account of the high scale of the process and its expected growth, will remarkably influence both the profits and environmental protection.

On empirical Bayes estimation in the location family

2002 ◽  
Vol 14 (4) ◽  
pp. 435-448 ◽  
Author(s):  
R. J. Karunamuni ◽  
R. S. Singh ◽  
S. Zhang
Keyword(s):  
Empirical Bayes ◽  
Bayes Estimation ◽  
Empirical Bayes Estimation ◽  
Location Family
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