Bayes estimation of autocorrelation coefficient

Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science, and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website. The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.

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Modeling In-Match Sports Dynamics Using the Evolving Probability Method

Applied Sciences ◽

10.3390/app11104429 ◽

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.

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Bayes Estimation of Species Divergence Times and Ancestral Population Sizes Using DNA Sequences From Multiple Loci

Genetics ◽

10.1093/genetics/164.4.1645 ◽

2003 ◽

Vol 164 (4) ◽

pp. 1645-1656 ◽

Cited By ~ 3

Author(s):

Bruce Rannala ◽

Ziheng Yang

Keyword(s):

Dna Sequences ◽

Gene Tree ◽

Species Tree ◽

Bayes Estimation ◽

Ancestral Population ◽

Divergence Times ◽

Gene Trees ◽

Species Divergence ◽

Multiple Loci ◽

Population Sizes

Abstract The effective population sizes of ancestral as well as modern species are important parameters in models of population genetics and human evolution. The commonly used method for estimating ancestral population sizes, based on counting mismatches between the species tree and the inferred gene trees, is highly biased as it ignores uncertainties in gene tree reconstruction. In this article, we develop a Bayes method for simultaneous estimation of the species divergence times and current and ancestral population sizes. The method uses DNA sequence data from multiple loci and extracts information about conflicts among gene tree topologies and coalescent times to estimate ancestral population sizes. The topology of the species tree is assumed known. A Markov chain Monte Carlo algorithm is implemented to integrate over uncertain gene trees and branch lengths (or coalescence times) at each locus as well as species divergence times. The method can handle any species tree and allows different numbers of sequences at different loci. We apply the method to published noncoding DNA sequences from the human and the great apes. There are strong correlations between posterior estimates of speciation times and ancestral population sizes. With the use of an informative prior for the human-chimpanzee divergence date, the population size of the common ancestor of the two species is estimated to be ∼20,000, with a 95% credibility interval (8000, 40,000). Our estimates, however, are affected by model assumptions as well as data quality. We suggest that reliable estimates have yet to await more data and more realistic models.

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

Pharmaceutics ◽

10.3390/pharmaceutics13010042 ◽

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.

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