Elite Athletes Refine Their Internal Clocks: A Bayesian Analysis

Motor Control ◽  
2016 ◽  
Vol 20 (3) ◽  
pp. 255-265
Author(s):  
Yin-Hua Chen ◽  
Isabella Verdinelli ◽  
Paola Cesari
Keyword(s):  
Bayesian Analysis ◽  
Prior Distribution ◽  
Likelihood Function ◽  
Elite Athletes ◽  
Time Intervals ◽  
Design Data ◽  
Data Set ◽  
Short Intervals ◽  
Additional Support ◽  
The Bayesian Approach

This paper carries out a full Bayesian analysis for a data set examined in Chen & Cesari (2015). These data were collected for assessing people’s ability in evaluating short intervals of time. Chen & Cesari (2015) showed evidence of the existence of two independent internal clocks for evaluating time intervals below and above the second. We reexamine here, the same question by performing a complete statistical Bayesian analysis of the data. The Bayesian approach can be used to analyze these data thanks to the specific trial design. Data were obtained from evaluation of time ranges from two groups of individuals. More specifically, information gathered from a nontrained group (considered as baseline) allowed us to build a prior distribution for the parameter(s) of interest, and data from the trained group determined the likelihood function. This paper’s main goals are (i) showing how the Bayesian inferential method can be used in statistical analyses and (ii) showing that the Bayesian methodology gives additional support to the findings presented in Chen & Cesari (2015) regarding the existence of two internal clocks in assessing duration of time intervals.

scholarly journals An Accurate Asymptotic Approximation for Experience Rated Premiums

2004 ◽  
Vol 34 (01) ◽  
pp. 113-124
Author(s):  
Riccardo Gatto
Keyword(s):  
Numerical Methods ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Asymptotic Approximation ◽  
Good Accuracy ◽  
Likelihood Function ◽  
Analytical Calculation ◽  
Expected Loss ◽  
Exact Calculations ◽  
The Bayesian Approach

In the Bayesian approach, the experience rated premium is the value which minimizes an expected loss with respect to a posterior distribution. The posterior distribution is conditioned on the claim experience of the risk insured, represented by a n-tuple of observations. An exact analytical calculation for the experience rated premium is possible under restrictive circumstances only, regarding the prior distribution, the likelihood function, and the loss function. In this article we provide an analytical asymptotic approximation as n → ∞ for the experience rated premium. This approximation can be obtained under more general circumstances, it is simple to compute, and it inherits the good accuracy of the Laplace approximation on which it is based. In contrast with numerical methods, this approximation allows for analytical interpretations. When exact calculations are possible, some analytical comparisons confirm the good accuracy of this approximation, which can even lead to the exact experience rated premium.

scholarly journals An Accurate Asymptotic Approximation for Experience Rated Premiums

2004 ◽  
Vol 34 (1) ◽  
pp. 113-124
Author(s):  
Riccardo Gatto
Keyword(s):  
Numerical Methods ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Asymptotic Approximation ◽  
Good Accuracy ◽  
Likelihood Function ◽  
Analytical Calculation ◽  
Expected Loss ◽  
Exact Calculations ◽  
The Bayesian Approach

In the Bayesian approach, the experience rated premium is the value which minimizes an expected loss with respect to a posterior distribution. The posterior distribution is conditioned on the claim experience of the risk insured, represented by a n-tuple of observations. An exact analytical calculation for the experience rated premium is possible under restrictive circumstances only, regarding the prior distribution, the likelihood function, and the loss function. In this article we provide an analytical asymptotic approximation as n → ∞ for the experience rated premium. This approximation can be obtained under more general circumstances, it is simple to compute, and it inherits the good accuracy of the Laplace approximation on which it is based. In contrast with numerical methods, this approximation allows for analytical interpretations. When exact calculations are possible, some analytical comparisons confirm the good accuracy of this approximation, which can even lead to the exact experience rated premium.

USING FULL PROBABILITY MODELS TO COMPUTE PROBABILITIES OF ACTUAL INTEREST TO DECISION MAKERS

2001 ◽  
Vol 17 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Frank E. Harrell ◽  
Ya-Chen Tina Shih
Keyword(s):  
Bayesian Approach ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Likelihood Function ◽  
Scientific Evidence ◽  
A Priori ◽  
Relevant Information ◽  
Decision Makers ◽  
Probability Models ◽  
The Bayesian Approach

The objective of this paper is to illustrate the advantages of the Bayesian approach in quantifying, presenting, and reporting scientific evidence and in assisting decision making. Three basic components in the Bayesian framework are the prior distribution, likelihood function, and posterior distribution. The prior distribution describes analysts' belief a priori; the likelihood function captures how data modify the prior knowledge; and the posterior distribution synthesizes both prior and likelihood information. The Bayesian approach treats the parameters of interest as random variables, uses the entire posterior distribution to quantify the evidence, and reports evidence in a “probabilistic” manner. Two clinical examples are used to demonstrate the value of the Bayesian approach to decision makers. Using either an uninformative or a skeptical prior distribution, these examples show that the Bayesian methods allow calculations of probabilities that are usually of more interest to decision makers, e.g., the probability that treatment A is similar to treatment B, the probability that treatment A is at least 5% better than treatment B, and the probability that treatment A is not within the “similarity region” of treatment B, etc. In addition, the Bayesian approach can deal with multiple endpoints more easily than the classic approach. For example, if decision makers wish to examine mortality and cost jointly, the Bayesian method can report the probability that a treatment achieves at least 2% mortality reduction and less than $20,000 increase in costs. In conclusion, probabilities computed from the Bayesian approach provide more relevant information to decision makers and are easier to interpret.

scholarly journals Critically evaluating the theory and performance of Bayesian analysis of macroevolutionary mixtures

2016 ◽  
Vol 113 (34) ◽  
pp. 9569-9574 ◽  
Author(s):  
Brian R. Moore ◽  
Sebastian Höhna ◽  
Michael R. May ◽  
Bruce Rannala ◽  
John P. Huelsenbeck
Keyword(s):  
Bayesian Analysis ◽  
Prior Distribution ◽  
Likelihood Function ◽  
Compound Poisson Process ◽  
Diversification Rate ◽  
Model Parameters ◽  
Bayesian Approaches ◽  
And Performance ◽  
Theoretical Issues ◽  
Lineage Diversification

Bayesian analysis of macroevolutionary mixtures (BAMM) has recently taken the study of lineage diversification by storm. BAMM estimates the diversification-rate parameters (speciation and extinction) for every branch of a study phylogeny and infers the number and location of diversification-rate shifts across branches of a tree. Our evaluation of BAMM reveals two major theoretical errors: (i) the likelihood function (which estimates the model parameters from the data) is incorrect, and (ii) the compound Poisson process prior model (which describes the prior distribution of diversification-rate shifts across branches) is incoherent. Using simulation, we demonstrate that these theoretical issues cause statistical pathologies; posterior estimates of the number of diversification-rate shifts are strongly influenced by the assumed prior, and estimates of diversification-rate parameters are unreliable. Moreover, the inability to correctly compute the likelihood or to correctly specify the prior for rate-variable trees precludes the use of Bayesian approaches for testing hypotheses regarding the number and location of diversification-rate shifts using BAMM.

Rotational Characteristics of the Green Solar Corona: 1947-1991

1994 ◽  
Vol 144 ◽  
pp. 139-141 ◽  
Author(s):  
J. Rybák ◽  
V. Rušin ◽  
M. Rybanský
Keyword(s):  
Solar Corona ◽  
World Wide ◽  
Rotation Period ◽  
Original Data ◽  
Coronal Emission ◽  
Time Intervals ◽  
Data Set ◽  
The World ◽  
Coronal Emission Line ◽  
Homogeneous Data

AbstractFe XIV 530.3 nm coronal emission line observations have been used for the estimation of the green solar corona rotation. A homogeneous data set, created from measurements of the world-wide coronagraphic network, has been examined with a help of correlation analysis to reveal the averaged synodic rotation period as a function of latitude and time over the epoch from 1947 to 1991.The values of the synodic rotation period obtained for this epoch for the whole range of latitudes and a latitude band ±30° are 27.52±0.12 days and 26.95±0.21 days, resp. A differential rotation of green solar corona, with local period maxima around ±60° and minimum of the rotation period at the equator, was confirmed. No clear cyclic variation of the rotation has been found for examinated epoch but some monotonic trends for some time intervals are presented.A detailed investigation of the original data and their correlation functions has shown that an existence of sufficiently reliable tracers is not evident for the whole set of examinated data. This should be taken into account in future more precise estimations of the green corona rotation period.

Benefits of Compiling and Analyzing Hydraulic-Design Data for Bridges

2021 ◽  
pp. 036119812110237
Author(s):  
Stephen T. Benedict ◽  
Thomas P. Knight
Keyword(s):  
South Carolina ◽  
Bridge Scour ◽  
Hydraulic Characteristics ◽  
Bridge Design ◽  
Design Data ◽  
Data Set ◽  
Engineering Knowledge ◽  
Hydraulic Design ◽  
Strong Measure ◽  
Design Characteristics

The hydraulic design of bridges is a discipline that requires a strong measure of engineering judgment. Developing good engineering judgment can take years of experience, and generally increases one project at a time. A supplemental tool that can promote the development of engineering knowledge and judgment is to compile, analyze, and graphically present hydraulic data associated with stream and bridge-design characteristics from previously analyzed bridges. If the data set is sufficiently large, graphs developed from such an effort can provide the engineer with an enhanced picture of stream and bridge-design characteristics, helping them further develop their engineering knowledge and judgment. Furthermore, such graphs can function as project scoping tools and hydraulic-design review tools. Using selected data from approximately 300 bridge-scour studies in South Carolina, previously conducted by the U.S. Geological Survey, and limited hydraulic bridge-design data for approximately 200 bridges in South Carolina, trends in stream and bridge-hydraulic characteristics were evaluated including channel width, floodplain width, flood flow depths, stream slopes, bridge backwater, bridge flow velocity, and bridge lengths. Selected relationships are presented in this paper and should serve as a valuable tool for better understanding stream and bridge-hydraulic characteristics in South Carolina.

scholarly journals A System for Phenotype Harmonization in the NHLBI Trans-Omics for Precision Medicine (TOPMed) Program

2021 ◽  
Author(s):  
Adrienne M Stilp ◽  
Leslie S Emery ◽  
Jai G Broome ◽  
Erin J Buth ◽  
Alyna T Khan ◽  
...  
Keyword(s):  
Precision Medicine ◽  
Association Studies ◽  
Controlled Vocabulary ◽  
National Institutes Of Health ◽  
Design Data ◽  
Data Set ◽  
Data Repositories ◽  
Phenotype Data ◽  
National Heart Lung ◽  
Centralized System

Abstract Genotype-phenotype association studies often combine phenotype data from multiple studies to increase power. Harmonization of the data usually requires substantial effort due to heterogeneity in phenotype definitions, study design, data collection procedures, and data set organization. Here we describe a centralized system for phenotype harmonization that includes input from phenotype domain and study experts, quality control, documentation, reproducible results, and data sharing mechanisms. This system was developed for the National Heart, Lung and Blood Institute’s Trans-Omics for Precision Medicine program, which is generating genomic and other omics data for >80 studies with extensive phenotype data. To date, 63 phenotypes have been harmonized across thousands of participants from up to 17 studies per phenotype (participants recruited 1948-2012). We discuss challenges in this undertaking and how they were addressed. The harmonized phenotype data and associated documentation have been submitted to National Institutes of Health data repositories for controlled-access by the scientific community. We also provide materials to facilitate future harmonization efforts by the community, which include (1) the code used to generate the 63 harmonized phenotypes, enabling others to reproduce, modify or extend these harmonizations to additional studies; and (2) results of labeling thousands of phenotype variables with controlled vocabulary terms.

Metropolis-Hastings Algorithms for DSGE Models

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Random Walk ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Large Scale ◽  
Likelihood Function ◽  
Dsge Models ◽  
Posterior Distributions ◽  
Dsge Model ◽  
Alternative Proposal ◽  
Posterior Moments

This chapter talks about the most widely used method to generate draws from posterior distributions of a DSGE model: the random walk MH (RWMH) algorithm. The DSGE model likelihood function in combination with the prior distribution leads to a posterior distribution that has a fairly regular elliptical shape. In turn, the draws from a simple RWMH algorithm can be used to obtain an accurate numerical approximation of posterior moments. However, in many other applications, particularly those involving medium- and large-scale DSGE models, the posterior distributions could be very non-elliptical. Irregularly shaped posterior distributions are often caused by identification problems or misspecification. In lieu of the difficulties caused by irregularly shaped posterior surfaces, the chapter reviews various alternative MH samplers, which use alternative proposal distributions.

A Survey of Bayesian Data Mining

Data Mining ◽  
2011 ◽  
pp. 1-26 ◽  
Author(s):  
Stefan Arnborg
Keyword(s):  
Data Mining ◽  
Bayesian Analysis ◽  
Graphical Models ◽  
Bayesian Approach ◽  
Data Sets ◽  
Media Distribution ◽  
Dirichlet Prior ◽  
Approach Problem ◽  
The Bayesian Approach ◽  
Selection Of

This chapter reviews the fundamentals of inference, and gives a motivation for Bayesian analysis. The method is illustrated with dependency tests in data sets with categorical data variables, and the Dirichlet prior distributions. Principles and problems for deriving causality conclusions are reviewed, and illustrated with Simpson’s paradox. The selection of decomposable and directed graphical models illustrates the Bayesian approach. Bayesian and EM classification is shortly described. The material is illustrated on two cases, one in personalization of media distribution, one in schizophrenia research. These cases are illustrations of how to approach problem types that exist in many other application areas.

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