Maximum likelihood estimation in the context of "Linear regression"

A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability of seeing that data under different parameter values of the model. It is constructed from the joint probability distribution of the random variable that (presumably) generated the observations. When evaluated on the actual data points, it becomes a function solely of the model parameters.

In maximum likelihood estimation, the model parameter(s) or argument that maximizes the likelihood function serves as a point estimate for the unknown parameter, while the Fisher information (often approximated by the likelihood's Hessian matrix at the maximum) gives an indication of the estimate's precision.

Computational phylogenetics, phylogeny inference, or phylogenetic inference focuses on computational and optimization algorithms, heuristics, and approaches involved in phylogenetic analyses. The goal is to find a phylogenetic tree representing optimal evolutionary ancestry between a set of genes, species, or taxa. Maximum likelihood, parsimony, Bayesian, and minimum evolution are typical optimality criteria used to assess how well a phylogenetic tree topology describes the sequence data. Nearest Neighbour Interchange (NNI), Subtree Prune and Regraft (SPR), and Tree Bisection and Reconnection (TBR), known as tree rearrangements, are deterministic algorithms to search for optimal or the best phylogenetic tree. The space and the landscape of searching for the optimal phylogenetic tree is known as phylogeny search space.

Maximum Likelihood (also likelihood) optimality criterion is the process of finding the tree topology along with its branch lengths that provides the highest probability observing the sequence data, while parsimony optimality criterion is the fewest number of state-evolutionary changes required for a phylogenetic tree to explain the sequence data.

Phylogenomics is the intersection of the fields of evolution and genomics. The term has been used in multiple ways to refer to analysis that involves genome data and evolutionary reconstructions. It is a group of techniques within the larger fields of phylogenetics and genomics. Phylogenomics draws information by comparing entire genomes, or at least large portions of genomes. Phylogenetics compares and analyzes the sequences of single genes, or a small number of genes, as well as many other types of data. Four major areas fall under phylogenomics:

• Prediction of gene function
• Establishment and clarification of evolutionary relationships
• Gene family evolution
• Prediction and retracing lateral gene transfer.

The ultimate goal of phylogenomics is to reconstruct the evolutionary history of species through their genomes. This history is usually inferred from a series of genomes by using a genome evolution model and standard statistical inference methods (e.g. Bayesian inference or maximum likelihood estimation).