Bayesian Inference of Recent Migration Rates Using Multilocus Genotypes

Genetics ◽  
2003 ◽  
Vol 163 (3) ◽  
pp. 1177-1191 ◽  
Author(s):  
Gregory A Wilson ◽  
Bruce Rannala
Keyword(s):  
Probability Distributions ◽  
Gray Wolf ◽  
Data Sets ◽  
Genotype Data ◽  
Migration Rates ◽  
Multilocus Genotypes ◽  
Monte Carlo Techniques ◽  
Inbreeding Coefficients ◽  
Genotype Frequencies ◽  
Marker Loci

Abstract A new Bayesian method that uses individual multilocus genotypes to estimate rates of recent immigration (over the last several generations) among populations is presented. The method also estimates the posterior probability distributions of individual immigrant ancestries, population allele frequencies, population inbreeding coefficients, and other parameters of potential interest. The method is implemented in a computer program that relies on Markov chain Monte Carlo techniques to carry out the estimation of posterior probabilities. The program can be used with allozyme, microsatellite, RFLP, SNP, and other kinds of genotype data. We relax several assumptions of early methods for detecting recent immigrants, using genotype data; most significantly, we allow genotype frequencies to deviate from Hardy-Weinberg equilibrium proportions within populations. The program is demonstrated by applying it to two recently published microsatellite data sets for populations of the plant species Centaurea corymbosa and the gray wolf species Canis lupus. A computer simulation study suggests that the program can provide highly accurate estimates of migration rates and individual migrant ancestries, given sufficient genetic differentiation among populations and sufficient numbers of marker loci.

scholarly journals Stochastic Order and Generalized Weighted Mean Invariance

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 662
Author(s):  
Mateu Sbert ◽  
Jordi Poch ◽  
Shuning Chen ◽  
Víctor Elvira
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Arithmetic Mean ◽  
Stochastic Orders ◽  
Arithmetic Means ◽  
Increasing Convex Order ◽  
Monte Carlo Techniques ◽  
Multiple Importance Sampling ◽  
Invariance Properties

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

scholarly journals An FDA-Based Approach for Clustering Elicited Expert Knowledge

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 184-204
Author(s):  
Carlos Barrera-Causil ◽  
Juan Carlos Correa ◽  
Andrew Zamecnik ◽  
Francisco Torres-Avilés ◽  
Fernando Marmolejo-Ramos
Keyword(s):  
Functional Data ◽  
Expert Knowledge ◽  
Probability Distributions ◽  
Knowledge Elicitation ◽  
Parallel Analysis ◽  
Data Sets ◽  
Dimensional Problem ◽  
Prior Distributions ◽  
Infinite Dimensional ◽  
Finite Dimensional

Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian inference is then to find ways to reconcile discrepant elicited prior distributions. This paper proposes the parallel analysis of clusters of prior distributions through a hierarchical method for clustering distributions and that can be readily extended to functional data. The proposed method consists of (i) transforming the infinite-dimensional problem into a finite-dimensional one, (ii) using the Hellinger distance to compute the distances between curves and thus (iii) obtaining a hierarchical clustering structure. In a simulation study the proposed method was compared to k-means and agglomerative nesting algorithms and the results showed that the proposed method outperformed those algorithms. Finally, the proposed method is illustrated through an EKE experiment and other functional data sets.

scholarly journals The extended odd family of probability distributions with practice to a submodel

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3855-3867 ◽  
Author(s):  
Hassan Bakouch ◽  
Christophe Chesneau ◽  
Muhammad Khan
Keyword(s):  
Heavy Tails ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Tuning Parameter ◽  
Data Sets ◽  
New Family ◽  
Rate Functions ◽  
Special Case ◽  
Family Of Distributions

In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.

Benfordʼs Law Geometry

Benford's Law ◽  
2015 ◽  
Author(s):  
Lawrence Leemis
Keyword(s):  
Empirical Data ◽  
Probability Distributions ◽  
Benford’S Law ◽  
Data Sets ◽  
Normal Distributions ◽  
Benford's Law ◽  
Using Data

This chapter switches from the traditional analysis of Benford's law using data sets to a search for probability distributions that obey Benford's law. It begins by briefly discussing the origins of Benford's law through the independent efforts of Simon Newcomb (1835–1909) and Frank Benford, Jr. (1883–1948), both of whom made their discoveries through empirical data. Although Benford's law applies to a wide variety of data sets, none of the popular parametric distributions, such as the exponential and normal distributions, agree exactly with Benford's law. The chapter thus highlights the failures of several of these well-known probability distributions in conforming to Benford's law, considers what types of probability distributions might produce data that obey Benford's law, and looks at some of the geometry associated with these probability distributions.

scholarly journals Breeding value evaluation in Polish fur animals: Statistical description of fur coat and reproduction traits – relationship and inbreeding

2011 ◽  
Vol 49 (No. 1) ◽  
pp. 16-27 ◽  
Author(s):  
H. Wierzbicki ◽  
A. Filistowicz ◽  
W. Jagusiak
Keyword(s):  
Fixed Effects ◽  
Breeding Value ◽  
The Arctic ◽  
Arctic Fox ◽  
Data Sets ◽  
Value Evaluation ◽  
Inbreeding Coefficients ◽  
Silver Fox ◽  
Reproduction Traits ◽  
As Relationship

Three data sets were available: records on conformation and coat traits for the arctic fox from one farm (5 540 observations, collected between 1983 and 1997), and the same traits for the silver fox from three farms (8 199 observations, collected between 1984 and 1999). The third set comprised 5 829 observations on reproductive performance of the arctic fox from one farm, collected between 1984 and 1999. The GLM procedure was used to test the significance of fixed effects on the analysed reproduction traits as well as differences between groups. Phenotypic trends as well as relationship and inbreeding across the studied years were computed. Most of the phenotypic trends were positive. Low relationship and inbreeding coefficients in the arctic and silver fox populations under study were estimated. The average relationship coefficients for the silver and arctic fox populations were 0.015 and 0.010, respectively, whereas the average inbreeding coefficients for the same species were 0.0039 and 0.0016, respectively. No inbreeding was found in the arctic fox breeding females.  

scholarly journals A Robust Dynamic Classifier Selection Approach for Hyperspectral Images with Imprecise Label Information

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5262
Author(s):  
Meizhu Li ◽  
Shaoguang Huang ◽  
Jasper De Bock ◽  
Gert de Cooman ◽  
Aleksandra Pižurica
Keyword(s):  
Hyperspectral Image ◽  
Probability Distributions ◽  
Imprecise Probabilities ◽  
Data Sets ◽  
Classifier Selection ◽  
Training Samples ◽  
Proposed Model ◽  
Label Information ◽  
Dynamic Classifier Selection ◽  
The Individual

Supervised hyperspectral image (HSI) classification relies on accurate label information. However, it is not always possible to collect perfectly accurate labels for training samples. This motivates the development of classifiers that are sufficiently robust to some reasonable amounts of errors in data labels. Despite the growing importance of this aspect, it has not been sufficiently studied in the literature yet. In this paper, we analyze the effect of erroneous sample labels on probability distributions of the principal components of HSIs, and provide in this way a statistical analysis of the resulting uncertainty in classifiers. Building on the theory of imprecise probabilities, we develop a novel robust dynamic classifier selection (R-DCS) model for data classification with erroneous labels. Particularly, spectral and spatial features are extracted from HSIs to construct two individual classifiers for the dynamic selection, respectively. The proposed R-DCS model is based on the robustness of the classifiers’ predictions: the extent to which a classifier can be altered without changing its prediction. We provide three possible selection strategies for the proposed model with different computational complexities and apply them on three benchmark data sets. Experimental results demonstrate that the proposed model outperforms the individual classifiers it selects from and is more robust to errors in labels compared to widely adopted approaches.

Maintenance management of load haul dumper using reliability analysis

2019 ◽  
Vol 26 (2) ◽  
pp. 290-310 ◽  
Author(s):  
Balaraju Jakkula ◽  
Govinda Raj M. ◽  
Murthy Ch.S.N.
Keyword(s):  
Reliability Analysis ◽  
Probability Distributions ◽  
Parametric Estimation ◽  
Maintenance Management ◽  
Data Sets ◽  
Content Type ◽  
Theoretical Probability ◽  
Reliability Level ◽  
Kolmogorov Smirnov ◽  
Best Fit

Purpose Load haul dumper (LHD) is one of the main ore transporting machineries used in underground mining industry. Reliability of LHD is very significant to achieve the expected targets of production. The performance of the equipment should be maintained at its highest level to fulfill the targets. This can be accomplished only by reducing the sudden breakdowns of component/subsystems in a complex system. The identification of defective component/subsystems can be possible by performing the downtime analysis. Hence, it is very important to develop the proper maintenance strategies for replacement or repair actions of the defective ones. Suitable maintenance management actions improve the performance of the equipment. This paper aims to discuss this issue. Design/methodology/approach Reliability analysis (renewal approach) has been used to analyze the performance of LHD machine. Allocations of best-fit distribution of data sets were made by the utilization of Kolmogorov–Smirnov (K–S) test. Parametric estimation of theoretical probability distributions was made by utilizing the maximum likelihood estimate (MLE) method. Findings Independent and identical distribution (IID) assumption of data sets was validated through trend and serial correlation tests. On the basis of test results, the data sets are in accordance with IID assumption. Therefore, renewal process approach has been utilized for further investigation. Allocations of best-fit distribution of data sets were made by the utilization of Kolmogorov–Smirnov (K–S) test. Parametric estimation of theoretical probability distributions was made by utilizing the MLE method. Reliability of each individual subsystem has been computed according to the best-fit distribution. In respect of obtained reliability results, the reliability-based preventive maintenance (PM) time schedules were calculated for the expected 90 percent reliability level. Research limitations/implications As the reliability analysis is one of the complex techniques, it requires strategic decision making knowledge for the selection of methodology to be used. As the present case study was from a public sector company, operating under financial constraints the conclusions/findings may not be universally applicable. Originality/value The present study throws light on this equipment that need a tailored maintenance schedule, partly due to the peculiar mining conditions, under which they operate. This study mainly focuses on estimating the performance of four numbers of well-mechanized LHD systems with reliability, availability and maintainability (RAM) modeling. Based on the drawn results, reasons for performance drop of each machine were identified. Suitable recommendations were suggested for the enhancement of performance of capital intensive production equipment. As the maintenance management is only the means for performance improvement of the machinery, PM time intervals were estimated with respect to the expected rate of reliability level.

scholarly journals Sequential Monte Carlo Methods to Train Neural Network Models

2000 ◽  
Vol 12 (4) ◽  
pp. 955-993 ◽  
Author(s):  
J. F. G. de Freitas ◽  
M. Niranjan ◽  
A. H. Gee ◽  
A. Doucet
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Probability Distributions ◽  
Network Models ◽  
Computational Time ◽  
Optimization Strategy ◽  
Neural Network Models ◽  
Monte Carlo Techniques ◽  
Monte Carlo Algorithms ◽  
Importance Resampling

We discuss a novel strategy for training neural networks using sequential Monte Carlo algorithms and propose a new hybrid gradient descent/sampling importance resampling algorithm (HySIR). In terms of computational time and accuracy, the hybrid SIR is a clear improvement over conventional sequential Monte Carlo techniques. The new algorithm may be viewed as a global optimization strategy that allows us to learn the probability distributions of the network weights and outputs in a sequential framework. It is well suited to applications involving on-line, nonlinear, and nongaussian signal processing. We show how the new algorithm outperforms extended Kalman filter training on several problems. In particular, we address the problem of pricing option contracts, traded in financial markets. In this context, we are able to estimate the one-step-ahead probability density functions of the options prices.

Allozyme Genotype and Differential Resistance to Mercury Pollution in the Caddisfly, Nectopsyche albida. II. Multilocus Genotypes

1992 ◽  
Vol 49 (1) ◽  
pp. 147-149 ◽  
Author(s):  
Michael J. Benton ◽  
Sheldon I. Guttman
Keyword(s):  
Survival Time ◽  
Inorganic Mercury ◽  
Differential Resistance ◽  
Single Locus ◽  
Multilocus Genotype ◽  
Starch Gel Electrophoresis ◽  
Time To Death ◽  
Multilocus Genotypes ◽  
Genotype Frequencies ◽  
Starch Gel

While a number of papers document that sensitivity to pollution is correlated with single-locus genotype, only one has addressed associations with multilocus complexes. We exposed larval caddisflies, Nectopsyche albida, to inorganic mercury and recorded individual times to death, genetically characterized each individual at six polymorphic loci by starch gel electrophoresis, and tested the effects of multilocus genotype on time to death. Two two-locus complexes and two three-locus complexes were significantly correlated with survival time. This supports earlier studies that monitoring multilocus and single-locus genotype frequencies may be useful in detecting and measuring environmental impacts; however, we disagree that variation in survival time among genotypes per se supports selectionist theory, because no heritability of resistance has been demonstrated. We also disagree that enzyme systems not exhibiting such variation are nonadaptive and discuss how the elimination of sensitive multilocus genotypes may hinder population persistence.

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