6,052 articles
Population protocol
A population protocol is a model of distributed computation, introduced in 2004, in which anonymous identical finite-state agents collectively compute a function through random pairwise interactions.
Pore-scale simulation
Pore-scale simulation models fluid flow, solute transport, and chemical reaction directly inside the pore geometry of a porous medium, computing permeability and capillary pressure from 3D images.
Porous medium equation
The porous medium equation is a nonlinear degenerate parabolic equation, a modification of the heat equation that models gas flow in porous media with finite propagation speed.
Posit arithmetic
Posit arithmetic is a format for representing and computing with real numbers, designed by John Gustafson and Isaac Yonemoto in 2017 as a drop-in replacement for IEEE 754 floating point.
Position vector
A position vector, also called a location vector or radius vector, points from a coordinate system's origin to a given point, representing its location as a directed displacement.
Positive and negative predictive values
Positive and negative predictive values (PPV and NPV), also called precision rate, are the probabilities that a test result correctly reflects whether a person has the condition tested for.
Positive definite matrix
A positive definite matrix is a Hermitian or real symmetric matrix for which the quadratic form is positive for every nonzero vector, equivalently all its eigenvalues are positive.
Positive matrix factorization
Positive matrix factorization (PMF) is a non-negative matrix factorization method, introduced by Paatero and Tapper in 1994, that decomposes environmental measurements into source profiles and contributions, weighting each data point by its uncertainty.
Positive-definite kernel
A positive-definite kernel is a symmetric function whose Gram matrix on any finite set of points is positive semidefinite, used in Gaussian processes and machine learning.
Possible world
A possible world, also called a possible universe, is a complete way things could have been, used in modal logic to define possibility and necessity.
Post-hoc analysis
A post-hoc analysis is a comparison of treatment means chosen after the data are collected, usually to locate which group differences drive a significant ANOVA result.
Post-selection inference
Post-selection inference, also called selective inference, is a collection of statistical methods giving valid confidence intervals and tests for parameters chosen after a data-driven selection step.
Post-stratification
Post-stratification is a survey-estimation technique in which a sample is classified into strata after data collection and combined using population stratum weights taken from a census or other external source.
Posterior consistency in Bayesian nonparametrics
Posterior consistency in Bayesian nonparametrics is the property that, as observations grow, the posterior concentrates on the true infinite-dimensional parameter rather than staying spread over the prior.
Posterior contraction rates and Bernstein–von Mises phenomena in nonparametric Bayes
Posterior contraction rates and Bernstein–von Mises phenomena in nonparametric Bayes measure how fast posteriors concentrate around the truth and whether they become Gaussian, which depends on the norm used.
Posterior predictive distribution
The posterior predictive distribution is the probability distribution of new observations given observed data, formed in Bayesian inference by averaging the sampling distribution over the posterior parameter distribution.
Posterior probability
A posterior probability, also called the posterior distribution, is the probability assigned to a hypothesis after data are observed, produced by combining a prior with the likelihood through Bayes' theorem.
Posterior sampling
Posterior sampling is the task of drawing representative samples from a Bayesian posterior distribution, usually by Markov chain Monte Carlo, to estimate moments and intervals.
Potato paradox
The potato paradox is a veridical mathematical puzzle: potatoes at 99% water dried to 98% weigh 50 kg, half the original 100 kg, not the intuitive 99.
Potential theory
Potential theory is the branch of mathematics that studies harmonic functions and potentials, named for the scalar potential of gravity and electrostatics, with links to Brownian motion and probability.
Power analysis
Power analysis is the statistical calculation of how sample size, significance level, power, and effect size determine one another, letting researchers design studies to detect a given effect.
Power iteration
Power iteration, also called the power method or Von Mises iteration, is a numerical linear algebra algorithm that finds a square matrix's dominant eigenvalue and a corresponding eigenvector.
Power law
A power law is a mathematical relationship in which one quantity is proportional to a fixed power of another, describing city sizes, earthquake magnitudes, wealth, and word frequencies.
Power of 10
A power of 10 is a number like 100 or 1000, written 10 to the nth power, that underlies decimal notation and the SI metric prefixes.
Power of a test
The power of a test, also called statistical power, is the probability that a test rejects a false null hypothesis for a given effect size.
Power of two
A power of two is a number written as 2 to a whole-number exponent, beginning 1, 2, 4, 8, 16, 32, and important in computing.
Power series
A power series is an infinite series of the form Σcₙ(x−a)ⁿ, an infinite polynomial that represents functions, converging within a radius of convergence R around its center.
Power set
The power set of a set A, written P(A) or 2^A, is the set of all subsets of A, always including the empty set and A itself.
Power transform
A power transform is a family of parametric data transformations built from powers of a variable that reshapes a distribution toward normality, constant variance, or linearity, including the Box–Cox transformation.
Power-associative algebra
A power-associative algebra is a not-necessarily-associative algebra in which powers of any single element are well defined, a concept introduced by A. A. Albert in his 1948 paper Power-Associative Rings.