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Parallel postulate
The parallel postulate, also known as Euclid's fifth postulate, is the plane geometry axiom stating that through a point not on a line passes exactly one parallel line.
Parallel process model
The parallel process model is a structural equation modeling approach for longitudinal data that estimates latent growth curves of two or more repeated measures at the same time.
Parallel tempering
Parallel tempering, also called replica exchange, is an MCMC method where chains at different temperatures swap states, helping sampling escape local modes of multimodal distributions.
Parallelepiped
A parallelepiped is a three-dimensional solid whose six faces are all parallelograms, the 3D analog of a parallelogram, with cubes and rectangular blocks as special cases.
Parallelogram
A parallelogram is a quadrilateral whose opposite sides are parallel, so opposite sides and angles are equal and diagonals bisect each other; squares, rectangles, and rhombuses are special cases.
Parameter
In statistics, a parameter is a fixed number describing a population or model, such as a population mean, whose unknown value must be estimated from samples.
Parameter space
A parameter space is the set of all values that the parameters of a statistical model may take; each point selects one probability distribution of the model.
Parameterization and prior choice in MCMC
Parameterization and prior choice in MCMC are modeling decisions that leave the posterior unchanged but reshape the geometry a sampler must traverse, determining efficiency or convergence failure.
Parametric bootstrap
The parametric bootstrap is a resampling method, introduced by Bradley Efron in 1979, that approximates a statistic's sampling distribution by simulating datasets from a fitted parametric model.
Parametric equation
A parametric equation, also called a parametric representation, expresses a coordinate as an explicit function of parameters, describing curves like the circle x = r cos t, y = r sin t.
Parametric polymorphism
Parametric polymorphism is a form of polymorphism in which one piece of code written with type variables works uniformly at many types, as in Java or Haskell generics.
Parametric programming
Parametric programming is the study of optimization problems whose objective or constraints depend on deterministic parameters, producing a solution map computed offline for fast online evaluation.
Parametric statistics
Parametric statistics is the branch of statistics in which data are analyzed through a mathematical model depending on a finite number of unknown parameters, contrasted with non-parametric methods.
Paramodulation
Paramodulation is an inference rule in automated theorem proving, introduced by George Robinson and Larry Wos in 1969 to build equality reasoning into resolution while eliminating explicit equality axioms.
Parareal algorithm
The parareal algorithm is a parallel-in-time integration method for time-dependent differential equations, introduced by Lions, Maday, and Turinici in 2001, which iteratively corrects a cheap coarse solution using fine computations run in parallel.
Pareto chart
A Pareto chart, or Pareto diagram, is a bar graph ranking causes by frequency or cost, used in quality management as one of the seven basic quality tools.
Pareto distribution
The Pareto distribution, also known as the Bradford distribution, is a heavy-tailed power-law probability distribution derived by Vilfredo Pareto from 1890s income data, underlying the 80/20 rule.
Paris–Harrington theorem
The Paris–Harrington theorem, proved by Jeff Paris and Leo Harrington in 1977, strengthens the finite Ramsey theorem and is true but unprovable in Peano Arithmetic.
Parity (mathematics)
Parity (mathematics), also called even and odd numbers, is the property of an integer of being even or odd, depending on whether it is divisible by 2.
Parity bit
A parity bit, also called a check bit, is an extra binary digit appended to data so the count of 1s is even or odd, detecting single-bit errors.
Parity of a permutation
The parity of a permutation, also called its sign or signature, classifies a permutation as even or odd according to the number of transpositions in any decomposition.
Parity of zero
The parity of zero is the mathematical fact that zero is an even number: it is divisible by 2, and it sits between the odd numbers −1 and 1.
Parity problem in sieve theory
The parity problem in sieve theory is the limitation that classical sieve methods cannot distinguish integers with an odd number of prime factors from integers with an even number.
Parking function
A parking function is a sequence of positive integers where cars with those preferences can all park in a line of spots, named by Konheim and Weiss in 1966.
Parse tree
A parse tree, also called a derivation tree, is an ordered, rooted tree recording how a context-free grammar generates a string, with leaves spelling it out.
Parseval's identity
Parseval's identity, also known as Rayleigh's energy theorem, is a Fourier analysis result equating a signal's energy in the time domain with the energy of its frequency components.
Parsing expression grammar
A parsing expression grammar (PEG) is a formalism for describing syntax in which rules are recognition procedures with ordered choice, formalized by Bryan Ford in 2004.
Part III of the Mathematical Tripos
Part III of the Mathematical Tripos, also called the Certificate of Advanced Studies in Mathematics, is a nine-month taught master's course in mathematics at the University of Cambridge.
Partial correlation
Partial correlation, written r12.3, is the correlation between two variables after control variables' linear influence is removed from both, as if the controls were held constant.
Partial derivative
A partial derivative, or partial differentiation, is the derivative of a multivariable function with respect to one variable, the others held constant, computed with ordinary differentiation rules.