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Multispecies Coalescent Process
Multispecies Coalescent Process is a stochastic process model that describes the genealogical relationships for a sample of DNA sequences taken from several species. It represents the application of coalescent theory to the case of multiple species. The multispecies coalescent results in cases where the relationships among species for an individual gene (the ''gene tree'') can differ from the broader history of the species (the ''species tree''). It has important implications for the theory and practice of phylogenetics and for understanding genome evolution. A ''gene tree'' is a binary graph that describes the evolutionary relationships between a sample of sequences for a non-recombining locus. A s''pecies tree'' describes the evolutionary relationships between a set of species, assuming tree-like evolution. However, several processes can lead to discordance between ''gene trees'' and ''species trees''. The Multispecies Coalescent model provides a framework for inferring species p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coalescent Theory
Coalescent theory is a model of how alleles sampled from a population may have originated from a common ancestor. In the simplest case, coalescent theory assumes no recombination, no natural selection, and no gene flow or population structure, meaning that each variant is equally likely to have been passed from one generation to the next. The model looks backward in time, merging alleles into a single ancestral copy according to a random process in coalescence events. Under this model, the expected time between successive coalescence events increases almost exponentially back in time (with wide variance). Variance in the model comes from both the random passing of alleles from one generation to the next, and the random occurrence of mutations in these alleles. The mathematical theory of the coalescent was developed independently by several groups in the early 1980s as a natural extension of classical population genetics theory and models, but can be primarily attributed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Inference
Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the Sequential analysis, dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". Introduction to Bayes' rule Formal explanation Bayesian inference derives the posterior probability as a consequence relation, consequence of two Antecedent (logic), antecedents: a prior probability and a "likelihood function" derived from a statistical model for the observed data. Bayesian inference computes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Inference
Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution, distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of a Statistical population, population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is Sampling (statistics), sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. In machine learning, the term ''inference'' is sometimes used instead to mean "make a prediction, by evaluating an already trained model"; in this context inferring properties of the model is referred to as ''training'' or ''learning'' (rather than ''inference''), and using a model for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Genetics
Statistical genetics is a scientific field concerned with the development and application of statistical methods for drawing inferences from genetic data. The term is most commonly used in the context of human genetics. Research in statistical genetics generally involves developing theory or methodology to support research in one of three related areas: *population genetics - Study of evolutionary processes affecting genetic variation between organisms * genetic epidemiology - Studying effects of genes on diseases *quantitative genetics - Studying the effects of genes on 'normal' phenotypes Statistical geneticists tend to collaborate closely with geneticists, molecular biologists, clinicians and bioinformaticians. Statistical genetics is a type of computational biology Computational biology refers to the use of data analysis, mathematical modeling and computational simulations to understand biological systems and relationships. An intersection of computer science, biology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudolikelihood
In statistical theory, a pseudolikelihood is an approximation to the joint probability distribution of a collection of random variables. The practical use of this is that it can provide an approximation to the likelihood function of a set of observed data which may either provide a computationally simpler problem for estimation, or may provide a way of obtaining explicit estimates of model parameters. The pseudolikelihood approach was introduced by Julian Besag in the context of analysing data having spatial dependence. Definition Given a set of random variables X = X_1, X_2, \ldots, X_n the pseudolikelihood of X = x = (x_1,x_2, \ldots, x_n) is :L(\theta) := \prod_i \mathrm_\theta(X_i = x_i\mid X_j = x_j \text j \neq i)=\prod_i \mathrm _\theta (X_i = x_i \mid X_=x_) in discrete case and :L(\theta) := \prod_i p_\theta(x_i \mid x_j \text j \neq i)=\prod_i p _\theta (x_i \mid x_)=\prod _i p_\theta (x_i \mid x_1,\ldots, \hat x_i, \ldots, x_n) in continuous one. Here X is a vector ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Mathematical Biology
'' Journal of Mathematical Biology'' is a peer-reviewed, mathematics journal, published by Springer Verlag. Founded in 1974, the journal publishes articles on mathematical biology. In particular, papers published in this journal 'should either provide biological insight as a result of mathematical analysis or identify and open up challenging new types of mathematical problems that derive from biological knowledge'. It is the official journal of the European Society for Mathematical and Theoretical Biology. The editors-in-chief are Thomas Hillen, Anna Marciniak-Czochra, and Mark Lewis. Its 2020 impact factor is 2.259. Abstracting and indexing This journal is indexed in the following databases: *Thomson Reuters *: BIOSIS *: Biological Abstracts *: Current Contents / Life Sciences *: Journal Citation Reports *: Science Citation Index Expanded *: Zoological Record *: PubMed/Medline ( Web of Knowledge) *Gale *: Academic OneFile *: Expanded Academic *EBSCO host *: Academic Search *: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neighbor Joining
In bioinformatics, neighbor joining is a bottom-up (agglomerative) clustering method for the creation of phylogenetic trees, created by Naruya Saitou and Masatoshi Nei in 1987. Usually based on DNA or protein sequence data, the algorithm requires knowledge of the distance between each pair of taxa (e.g., species or sequences) to create the phylogenetic tree. The algorithm Neighbor joining takes a distance matrix, which specifies the distance between each pair of taxa, as input. The algorithm starts with a completely unresolved tree, whose topology corresponds to that of a star network, and iterates over the following steps, until the tree is completely resolved, and all branch lengths are known: # Based on the current distance matrix, calculate a matrix Q (defined below). # Find the pair of distinct taxa i and j (i.e. with i \neq j) for which Q(i,j) is smallest. Make a new node that joins the taxa i and j, and connect the new node to the central node. For example, in part (B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Inference In Phylogeny
Bayesian inference of phylogeny combines the information in the prior and in the data likelihood to create the so-called posterior probability of trees, which is the probability that the tree is correct given the data, the prior and the likelihood model. Bayesian inference was introduced into molecular phylogenetics in the 1990s by three independent groups: Bruce Rannala and Ziheng Yang in Berkeley, Bob Mau in Madison, and Shuying Li in University of Iowa, the last two being PhD students at the time. The approach has become very popular since the release of the MrBayes software in 2001, and is now one of the most popular methods in molecular phylogenetics. Bayesian inference of phylogeny background and bases Bayesian inference refers to a probabilistic method developed by Reverend Thomas Bayes based on Bayes' theorem. Published posthumously in 1763 it was the first expression of inverse probability and the basis of Bayesian inference. Independently, unaware of Bayes' work, Pierre- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Likelihood Estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when all observed outcomes are assumed to have Normal distributions with the same variance. From the perspective of Bayesian infere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consistent Estimator
In statistics, a consistent estimator or asymptotically consistent estimator is an estimator—a rule for computing estimates of a parameter ''θ''0—having the property that as the number of data points used increases indefinitely, the resulting sequence of estimates converges in probability to ''θ''0. This means that the distributions of the estimates become more and more concentrated near the true value of the parameter being estimated, so that the probability of the estimator being arbitrarily close to ''θ''0 converges to one. In practice one constructs an estimator as a function of an available sample of size ''n'', and then imagines being able to keep collecting data and expanding the sample ''ad infinitum''. In this way one would obtain a sequence of estimates indexed by ''n'', and consistency is a property of what occurs as the sample size “grows to infinity”. If the sequence of estimates can be mathematically shown to converge in probability to the true value ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Distribution
In probability theory and statistics, given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X is the probability distribution of Y when X is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value x of X as a parameter. When both X and Y are categorical variables, a conditional probability table is typically used to represent the conditional probability. The conditional distribution contrasts with the marginal distribution of a random variable, which is its distribution without reference to the value of the other variable. If the conditional distribution of Y given X is a continuous distribution, then its probability density function is known as the conditional density function. The properties of a conditional distribution, such as the moments, are often referred to by corresponding names such as the conditional mean and conditional variance. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
