scholarly journals Bayesian Analysis of Skills Importance in World Champions Men’s Volleyball across Ages

2019 ◽  
Vol 18 (1) ◽  
pp. 24-44 ◽  
Author(s):  
Sotirios Drikos ◽  
Ioannis Ntzoufras ◽  
Nikolaos Apostolidis
Keyword(s):  
Monte Carlo ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Bayesian Model ◽  
Transition Matrix ◽  
Transition Probabilities ◽  
Relative Importance ◽  
Marginal Probability ◽  
Sequential Structure ◽  
Probability Of Success

Abstract In volleyball, due to the sequential structure of the game, each outcome results from events that follow consistent consecutive patterns: pass–set–attack–outcome, serve–outcome and block–dig–set–counter attack–outcome. There are three possible outcomes: point won, point lost, and rally continuation. With the aim of quantifying the importance of volleyball skills, data of world champions of the male International Volleyball Federation tournaments for three age categories (Youth, Juniors and Men) were used to construct a transition matrix between subsequent moves and skills within the game. A Dirichlet-Multinomial Bayesian model was used to estimate the transition probabilities between the subsequent moves along with the marginal probability of success of each skill in the complex. The prior distribution of each transition probabilities between moves/skills was elicited to incorporate experts' opinion. For the final evaluation of the skills a simple Monte Carlo scheme was applied to obtain a random sample from the posterior distribution. The findings of the study indicate that the relative importance of volleyball skills is robust across world champions of different age categories. Slight variations are observed on specific skills. A new index (Quantile Mid-range Ratio) is proposed for highlighting skills that are valuable for team’s gameplay.

scholarly journals A Bayesian model for binary Markov chains

2004 ◽  
Vol 2004 (8) ◽  
pp. 421-429 ◽  
Author(s):  
Souad Assoudou ◽  
Belkheir Essebbar
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chains ◽  
Bayesian Estimation ◽  
Bayesian Model ◽  
Transition Probabilities ◽  
Simulated Data ◽  
Bayesian Estimator ◽  
Jeffreys Prior ◽  
Data Set

This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC) techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.

Bayesian petroelastic inversion with multiple prior models

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. M57-M71 ◽  
Author(s):  
Dario Grana
Keyword(s):  
Posterior Distribution ◽  
Prior Distribution ◽  
Transition Probabilities ◽  
Mathematical Formulation ◽  
Seismic Inversion ◽  
Seismic Facies ◽  
Bayesian Inversion ◽  
Prior Model ◽  
Facies Classification ◽  
Prior Models

Bayesian methods are commonly used for geophysical inverse problems, such as seismic and rock-physics inversion, for the prediction of petroelastic properties. Bayesian inversion is based on Bayes’ theorem and combines the information from a prior distribution and a likelihood function; in geophysical applications, the prior model generally includes the available geologic information about the model variables, whereas the likelihood includes the geophysical models that link the model to the data. The goal of Bayesian inversion is to estimate the posterior distribution of the model variables conditioned by the measured data. The focus is on the prior model and its parameters. Typically, the parameters of the prior distributions are assumed to be fixed, for example, the mean and standard deviation of the prior distribution of petroelastic properties in seismic inversion or the facies proportions and transition probabilities in facies classification. I have studied the posterior distribution of the model given the data in a Bayesian setting using multiple prior models. The posterior distribution is assessed by summing the contributions of all of the likelihood functions of the model given the data, using different sets of parameters, weighted by the probabilities of the parameters. I apply the mathematical formulation in different problems, including log-facies classification, seismic-facies classification, and petrophysical property prediction and using different methods for the prior model generation such as transition matrices, training images, and Gaussian mixture models with multiple modes. The results show that multiple prior models can match the data and that the uncertainty in the prior parameters should be accounted for in the posterior distribution of the reservoir properties.

scholarly journals A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 228
Author(s):  
Ángel Berihuete ◽  
Marta Sánchez-Sánchez ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Monte Carlo ◽  
Prior Distribution ◽  
Bayesian Model ◽  
Real Data ◽  
Intensity Function ◽  
Specific Region ◽  
Mcmc Methods ◽  
Homogeneous Poisson Process ◽  
Gompertz Curve ◽  
Non Homogeneous Poisson Process

The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an intensity function based on the Gompertz curve. We discuss the prior distribution of the parameter and we generate samples from the posterior distribution by using Markov Chain Monte Carlo (MCMC) methods. Finally, we illustrate our method analyzing real data associated with COVID-19 in a specific region located at the south of Spain.

Uncertainty quantification in seismic facies inversion

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. M43-M56
Author(s):  
Erick Costa e Silva Talarico ◽  
Dario Grana ◽  
Leandro Passos de Figueiredo ◽  
Sinesio Pesco
Keyword(s):  
Inverse Problem ◽  
Vertical Distribution ◽  
Uncertainty Quantification ◽  
Posterior Distribution ◽  
Seismic Data ◽  
Transition Matrix ◽  
Transition Probabilities ◽  
Vertical Direction ◽  
Seismic Facies ◽  
Transition Matrices

In seismic reservoir characterization, facies prediction from seismic data often is formulated as an inverse problem. However, the uncertainty in the parameters that control their spatial distributions usually is not investigated. In a probabilistic setting, the vertical distribution of facies often is described by statistical models, such as Markov chains. Assuming that the transition probabilities in the vertical direction are known, the most likely facies sequence and its uncertainty can be obtained by computing the posterior distribution of a Bayesian inverse problem conditioned by seismic data. Generally, the model hyperparameters such as the transition matrix are inferred from seismic data and nearby wells using a Bayesian inference framework. It is assumed that there is a unique set of hyperparameters that optimally fit the measurements. The novelty of the proposed work is to investigate the nonuniqueness of the transition matrix and show the multimodality of their distribution. We then generalize the Bayesian inversion approach based on Markov chain models by assuming that the hyperparameters, the facies prior proportions and transition matrix, are unknown and derive the full posterior distribution. Including all of the possible transition matrices in the inversion improves the uncertainty quantification of the predicted facies conditioned by seismic data. Our method is demonstrated on synthetic and real seismic data sets, and it has high relevance in exploration studies due to the limited number of well data and in geologic environments with rapid lateral variations of the facies vertical distribution.

scholarly journals TRANSITION MATRIX MONTE CARLO

1999 ◽  
Vol 10 (08) ◽  
pp. 1563-1569 ◽  
Author(s):  
ROBERT H. SWENDSEN ◽  
BRIAN DIGGS ◽  
JIAN-SHENG WANG ◽  
SHING-TE LI ◽  
CHRISTOPHER GENOVESE ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Transition Matrix ◽  
Transition Probabilities ◽  
Simulation Technique ◽  
Efficient Approach ◽  
Complementary Approach ◽  
Combining Data ◽  
The Matrix

Although histogram methods have been extremely effective for analyzing data from Monte Carlo simulations, they do have certain limitations, including the range over which they are valid and the difficulties of combining data from independent simulations. In this paper, we describe a complementary approach to extracting information from Monte Carlo simulations that uses the matrix of transition probabilities. Combining the Transition Matrix with an N-fold way simulation technique produces an extremely flexible and efficient approach to rather general Monte Carlo simulations.

scholarly journals The Markov model as a pattern for earthquakes recurrence in South America

2001 ◽  
Vol 34 (4) ◽  
pp. 1611 ◽  
Author(s):  
T. M. TSAPANOS
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Markov Process ◽  
South America ◽  
Markov Chains ◽  
Stochastic Model ◽  
Markov Model ◽  
Transition Matrix ◽  
Transition Probabilities ◽  
Large Earthquakes

The well known stochastic model of the Markov chains is applied in south America, in order to search for pattern of great earthquakes recurrence. The model defines a process in which successive state occupancies are governed by the transition probabilities pij, of the Markov process and are presented as a transition matrix say P, which has NxN dimensions. We considered as states in the present study the predefined seismic zones of south America. Thus the visits from zone to zone, which is from state to state, carry with them the number of the zone in which they occurred. If these visits are considered to be earthquake occurrences we can inspect their migration between the zones (states) and estimate their genesis in a statistical way, through the transition probabilities. Attention is given in zones where very large earthquakes with Ms>7.8 have occurred. A pattern is revealed which is suggested migration of these large shocks from south towards north. The use of Monte Carlo simulation verify the defined pattern.

Bayesian Applications in Auditory Research

2019 ◽  
Vol 62 (3) ◽  
pp. 577-586 ◽  
Author(s):  
Garnett P. McMillan ◽  
John B. Cannon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Interim Analysis ◽  
Iterative Process ◽  
Bayes Theorem ◽  
Sound Therapy ◽  
The Many ◽  
Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

scholarly journals A look-ahead Monte Carlo simulation method for improving parental selection in trait introgression

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Saba Moeinizade ◽  
Ye Han ◽  
Hieu Pham ◽  
Guiping Hu ◽  
Lizhi Wang
Keyword(s):  
Monte Carlo ◽  
State Of The Art ◽  
Simulation Method ◽  
Multiple Trait ◽  
Look Ahead ◽  
Probability Of Success ◽  
Genetic Distribution ◽  
Selection Of ◽  
Trait Introgression

AbstractMultiple trait introgression is the process by which multiple desirable traits are converted from a donor to a recipient cultivar through backcrossing and selfing. The goal of this procedure is to recover all the attributes of the recipient cultivar, with the addition of the specified desirable traits. A crucial step in this process is the selection of parents to form new crosses. In this study, we propose a new selection approach that estimates the genetic distribution of the progeny of backcrosses after multiple generations using information of recombination events. Our objective is to select the most promising individuals for further backcrossing or selfing. To demonstrate the effectiveness of the proposed method, a case study has been conducted using maize data where our method is compared with state-of-the-art approaches. Simulation results suggest that the proposed method, look-ahead Monte Carlo, achieves higher probability of success than existing approaches. Our proposed selection method can assist breeders to efficiently design trait introgression projects.

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