|
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 ''species 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 phy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coalescent Theory
Coalescent theory is a Scientific modelling, model of how alleles sampled from a population may have originated from a most recent common ancestor, common ancestor. In the simplest case, coalescent theory assumes no genetic recombination, recombination, no natural selection, and no gene flow or population structure (genetics), 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 exponential growth, 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 earl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Inference
Bayesian inference ( or ) is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available. Fundamentally, Bayesian inference uses a prior distribution to estimate posterior probabilities. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the 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 of two antecedents: a prior probability and a "likelihood function" derive ... [...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.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is 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 prediction is referred to as ''inference'' (instead of ''prediction''); se ... [...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 Population genetics is a subfield of genetics that deals with genetic differences within and among populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as Adaptation (biology), adaptation, s ... - 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. Statistic ... [...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 vect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Mathematical Biology
'' Journal of Mathematical Biology'' is a peer review, 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 (publisher), Gale *: Academic OneFile *: Expanded Academic *EBSCO ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum Evolution
Minimum evolution is a distance method employed in phylogenetics modeling. It shares with maximum parsimony the aspect of searching for the phylogeny that has the shortest total sum of branch lengths. The theoretical foundations of the minimum evolution (ME) criterion lay in the seminal works of both Kidd and Sgaramella-Zonta (1971) and Rzhetsky and Nei (1993). In these frameworks, the molecular sequences from taxa are replaced by a set of measures of their dissimilarity (i.e., the so-called "evolutionary distances") and a fundamental result states that if such distances were unbiased estimates of the ''true evolutionary distances'' from taxa (i.e., the distances that one would obtain if all the molecular data from taxa were available), then the ''true phylogeny'' of taxa would have an expected length shorter than any other possible phylogeny T compatible with those distances. Relationships with and comparison with other methods Maximum parsimony It is worth noting her ... [...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 Computational phylogenetics, 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, una ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Likelihood Estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimation theory, estimating the Statistical parameter, parameters of an assumed probability distribution, given some observed data. This is achieved by Mathematical optimization, maximizing a likelihood function so that, under the assumed statistical model, the Realization (probability), observed data is most probable. The point estimate, 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 function, 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 ... [...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
Conditional (if then) may refer to: * Causal conditional, if X then Y, where X is a cause of Y *Conditional probability, the probability of an event A given that another event B * Conditional proof, in logic: a proof that asserts a conditional, and proves that the antecedent leads to the consequent *Material conditional, in propositional calculus, or logical calculus in mathematics * Relevance conditional, in relevance logic * Conditional (computer programming), a statement or expression in computer programming languages *A conditional expression in computer programming languages such as ?: *Conditions in a contract A contract is an agreement that specifies certain legally enforceable rights and obligations pertaining to two or more parties. A contract typically involves consent to transfer of goods, services, money, or promise to transfer any of thos ... Grammar and linguistics * Conditional mood (or conditional tense), a verb form in many languages * Conditional se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
