scholarly journals Bayesian statistics in human genetics

2020 ◽  
Vol 26 ◽  
pp. 316-319
Author(s):  
L. A. Atramentova
Keyword(s):  
Genetic Counseling ◽  
Posterior Probability ◽  
Bayesian Method ◽  
Human Genetics ◽  
Classical Method ◽  
A Priori ◽  
Genetic Data ◽  
Bayes Method ◽  
The Given ◽  
A Priori Probability

Using of the Bayes’ method in genetic counseling allows clarifying of the probability of a disease in the offspring, which in some cases can save probands from additional laboratory diagnostic tests due to the extremely low risk which can be calculated. The article is devoted to the usage of the Bayes’ method in human genetics. The concepts of a priori, conditional, total and posterior probabilities are introduced. As an example, a pedigree with a monogenic recessive X-linked trait is considered. An algorithm for calculating of the probability that a patient is a carrier of a pathological gene is presented. The prediction of results made with help of using the classical method of calculations and the Bayesian method are compared. An example for calculation of the gene mutation rate based on epidemiological and genetic data is given. The discussed topic can be taken into account for presenting of courses in human genetics and medical genetics at classical and medical universities, and the given problem can serve as an example for drawing up of tasks for students with pedigrees of various configurations and other attributes. Keywords: Bayesian method, a priori probability, posterior probability, teaching of genetics, genetic counseling.

BEING LOW ALONG A SEQUENCE AND ELSEWHERE

2019 ◽  
Vol 84 (02) ◽  
pp. 497-516
Author(s):  
WOLFGANG MERKLE ◽  
LIANG YU
Keyword(s):  
A Priori ◽  
Expected Value ◽  
Infinite Subset ◽  
Additive Constant ◽  
Almost All ◽  
The Given ◽  
Infinite Set ◽  
A Priori Probability

AbstractLet an oracle be called low for prefix-free complexity on a set in case access to the oracle improves the prefix-free complexities of the members of the set at most by an additive constant. Let an oracle be called weakly low for prefix-free complexity on a set in case the oracle is low for prefix-free complexity on an infinite subset of the given set. Furthermore, let an oracle be called low and weakly for prefix-free complexity along a sequence in case the oracle is low and weakly low, respectively, for prefix-free complexity on the set of initial segments of the sequence. Our two main results are the following characterizations. An oracle is low for prefix-free complexity if and only if it is low for prefix-free complexity along some sequences if and only if it is low for prefix-free complexity along all sequences. An oracle is weakly low for prefix-free complexity if and only if it is weakly low for prefix-free complexity along some sequence if and only if it is weakly low for prefix-free complexity along almost all sequences. As a tool for proving these results, we show that prefix-free complexity differs from its expected value with respect to an oracle chosen uniformly at random at most by an additive constant, and that similar results hold for related notions such as a priori probability. Furthermore, we demonstrate that on every infinite set almost all oracles are weakly low but are not low for prefix-free complexity, while by Shoenfield absoluteness there is an infinite set on which uncountably many oracles are low for prefix-free complexity. Finally, we obtain no-gap results, introduce weakly low reducibility, or WLK-reducibility for short, and show that all its degrees except the greatest one are countable.

Genetische Familienberatung: Ein Leitfaden Fur Den Arzt, by Walter Fuhrmann and Friedrich Vogel. Berlin/Heidelberg/ New York: Springer-Verlag, 1968, 98 pp., $2.20

PEDIATRICS ◽  
1969 ◽  
Vol 44 (3) ◽  
pp. 467-467
Author(s):  
Hans Zellweger
Keyword(s):  
New York ◽  
Genetic Counseling ◽  
Human Genetics ◽  
Medical Genetics ◽  
The Common

This small paperback appeared as Volume 42 in the series, Heidelberg Pocket Books (a translation of L. S. Penrose's Introduction to Human Genetics is Volume 4 of the same series). The authors, both directors of a German institute for human genetics, wrote this syllabus to familiarize the genetically uninformed physician with the common and practical aspects of medical genetics and genetic counseling. They advise the reader to consult a professional geneticist for more complicated genetic problems.

A General Analysis of Sequential Social Learning

2021 ◽  
Author(s):  
Itai Arieli ◽  
Manuel Mueller-Frank
Keyword(s):  
Social Learning ◽  
Utility Function ◽  
Posterior Probability ◽  
General Analysis ◽  
Sufficient Condition ◽  
Important Class ◽  
General Utility ◽  
Learning Game ◽  
Necessary And Sufficient ◽  
The Given

This paper analyzes a sequential social learning game with a general utility function, state, and action space. We show that asymptotic learning holds for every utility function if and only if signals are totally unbounded, that is, the support of the private posterior probability of every event contains both zero and one. For the case of finitely many actions, we provide a sufficient condition for asymptotic learning depending on the given utility function. Finally, we establish that for the important class of simple utility functions with finitely many actions and states, pairwise unbounded signals, which generally are a strictly weaker notion than unbounded signals, are necessary and sufficient for asymptotic learning.

scholarly journals Perceptions of Similarity Can Mislead Provenancing Strategies—An Example from Five Co-Distributed Acacia Species

Diversity ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 306
Author(s):  
Maurizio Rossetto ◽  
Peter D. Wilson ◽  
Jason Bragg ◽  
Joel Cohen ◽  
Monica Fahey ◽  
...  
Keyword(s):  
Genetic Diversity ◽  
A Priori ◽  
Genetic Data ◽  
Environmental Data ◽  
Specific Data ◽  
Acacia Species ◽  
Simple Observation ◽  
Source Plant ◽  
Species Specific

Ecological restoration requires balancing levels of genetic diversity to achieve present-day establishment as well as long-term sustainability. Assumptions based on distributional, taxonomic or functional generalizations are often made when deciding how to source plant material for restoration. We investigate this assumption and ask whether species-specific data is required to optimize provenancing strategies. We use population genetic and environmental data from five congeneric and largely co-distributed species of Acacia to specifically ask how different species-specific genetic provenancing strategies are based on empirical data and how well a simple, standardized collection strategy would work when applied to the same species. We find substantial variability in terms of patterns of genetic diversity and differentiation across the landscape among these five co-distributed Acacia species. This variation translates into substantial differences in genetic provenancing recommendations among species (ranging from 100% to less than 1% of observed genetic variation across species) that could not have been accurately predicted a priori based on simple observation or overall distributional patterns. Furthermore, when a common provenancing strategy was applied to each species, the recommended collection areas and the evolutionary representativeness of such artificially standardized areas were substantially different (smaller) from those identified based on environmental and genetic data. We recommend the implementation of the increasingly accessible array of evolutionary-based methodologies and information to optimize restoration efforts.

scholarly journals X. On Hamilton's numbers

1887 ◽  
Vol 178 ◽  
pp. 285-312
Keyword(s):  
General Equation ◽  
Minimum Degree ◽  
A Priori ◽  
Senior Author ◽  
System Of Equations ◽  
Absolute Minimum ◽  
Doctor Of Philosophy ◽  
The University ◽  
The Given ◽  
Trinomial Equation

In the year 1786 Erland Samuel Bring, Professor at the University of Lund in Sweden, showed how by an extension of the method of Tschirnhausen it was possible to deprive the general algebraical equation of the 5th degree of three of its terms without solving an equation higher than the 3rd degree. By a well-understood, however singular, academical fiction, this discovery was ascribed by him to one of his own pupils, a certain Sven Gustaf Sommelius, and embodied in a thesis humbly submitted to himself for approval by that pupil, as a preliminary to his obtaining his degree of Doctor of Philosophy in the University. The process for effecting this reduction seems to have been overlooked or forgotten, and was subsequently re-discovered many years later by Mr. Jerrard. In a report contained in the ‘Proceedings of the British Association’ for 1836, Sir William Hamilton showed that Mr. Jerrard was mistaken in supposing that the method was adequate to taking away more than three terms of the equation of the 5th degree, but supplemented this somewhat unnecessary refutation of a result, known à priori to be impossible, by an extremely valuable discussion of a question raised by Mr. Jerrard as to the number of variables required in order that any system of equations of given degrees in those variables shall admit of being satisfied without solving any equation of a degree higher than the highest of the given degrees. In the year 1886 the senior author of this memoir showed in a paper in Kronecker'e (better known as Crelle’s ) ‘Journal that the trinomial equation of the 5th degree, upon which by Bring’s method the general equation of that degree can be made to depend, has necessarily imagmaiy coefficients except in the case where four of the roots of the original equation are imaginary, and also pointed out method of obtaining the absolute minimum degree M of an equation from which an given number of specified terms can be taken away subject to the condition of no having to solve any equation of a degree higher than M. The numbers furnished be Hamilton’s method, it is to be observed, are not minima unless a more stringer condition than this is substituted, viz., that the system of equations which have to be resolved in order to take away the proposed terms shall be the simplest possible i. e ., of the lowest possible weight and not merely of the lowest order; in the memo: in ‘Crelle,’ above referred to, he has explained in what sense the words weight an order are here employed. He has given the name of Hamilton’s Numbers to these relative minima (minima, i. e ., in regard to weight) for the case where the terms to be taken away from the equation occupy consecutive places in it, beginning with the second.

scholarly journals Bayesian Interpolation

1992 ◽  
Vol 4 (3) ◽  
pp. 415-447 ◽  
Author(s):  
David J. C. MacKay
Keyword(s):  
Posterior Probability ◽  
Bayesian Method ◽  
Model Comparison ◽  
Basis Sets ◽  
Effective Number ◽  
Noise Levels ◽  
Data Set ◽  
Inference Problem ◽  
Posterior Probability Distribution ◽  
Bayesian Interpolation

Although Bayesian analysis has been in use since Laplace, the Bayesian method of model-comparison has only recently been developed in depth. In this paper, the Bayesian approach to regularization and model-comparison is demonstrated by studying the inference problem of interpolating noisy data. The concepts and methods described are quite general and can be applied to many other data modeling problems. Regularizing constants are set by examining their posterior probability distribution. Alternative regularizers (priors) and alternative basis sets are objectively compared by evaluating the evidence for them. “Occam's razor” is automatically embodied by this process. The way in which Bayes infers the values of regularizing constants and noise levels has an elegant interpretation in terms of the effective number of parameters determined by the data set. This framework is due to Gull and Skilling.

Virtual Material Model with the Given Crystallographic Orientation of the Structure

2016 ◽  
Vol 684 ◽  
pp. 134-142 ◽  
Author(s):  
Fedor V. Grechnikov ◽  
Yaroslav A. Erisov
Keyword(s):  
Aluminum Alloy ◽  
Crystallographic Orientation ◽  
Metal Forming ◽  
Theoretical Basis ◽  
A Priori ◽  
Material Model ◽  
Product Performance ◽  
Material Models ◽  
Cubic Crystal ◽  
The Given

The article represents the theoretical basis for the generation of virtual material models with the given crystallographic orientation (CGO) of the structure in metals and alloys with the cubic crystal lattice. The obtained functional interrelations allow to take into consideration a metal sheet CGO in technological calculations of metal forming processes and, most significantly, a priori by means of calculations to determine the structure CGO meeting the requirements of increasing the materials formability and the product performance. It is given an example of the implementation of the calculated CGO of the structure while rolling can sheet from aluminum alloy 3104.

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