All articles starting with P
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Probabilistic error cancellation
Probabilistic error cancellation (PEC), introduced by Kristan Temme and colleagues in 2017, is a quantum error mitigation technique that cancels device noise statistically through quasiprobability sampling.
Probabilistic forecasting
Probabilistic forecasting issues a full probability distribution over future quantities or events instead of a single value, so uncertainty can be quantified and used in decisions.
Probabilistic logic
Probabilistic logic is a family of formal frameworks combining logical representation with probability theory, so inference returns the probability of a query instead of a plain true-or-false verdict.
Probabilistic logic programming
Probabilistic logic programming (PLP) is a family of methods combining logic programs with probability distributions to represent uncertain relational knowledge, underlying languages including PRISM, ProbLog, and LPADs.
Probabilistic method
The probabilistic method is a nonconstructive technique for proving a mathematical object exists by showing a randomly chosen object has the property with positive probability, founded by Paul Erdős.
Probabilistic model checking
Probabilistic model checking is an automated verification technique that builds a Markov-chain model of a system and computes probabilities or expectations for properties in probabilistic temporal logic.
Probabilistic Movement Primitives
Probabilistic Movement Primitives (ProMPs) are a robot learning framework that represents a movement skill as a probability distribution over whole trajectories, introduced by Paraschos, Daniel, Peters, and Neumann at TU Darmstadt in 2013.
Probabilistic neural network
A probabilistic neural network (PNN) is a feedforward network introduced by Donald Specht in 1990 that classifies inputs through kernel density estimation and Bayes' rule.
Probabilistic number theory
Probabilistic number theory is a branch of number theory treating arithmetic objects as random variables, born with the 1940 Erdős–Kac theorem on prime factors of random integers.
Probabilistic programming languages and systems
A probabilistic programming language (PPL) is a language or embedded library where users write probability models as programs and the system performs inference automatically, pioneered by BUGS in 1994.
Probabilistic reversal learning task
The probabilistic reversal learning task is a behavioral paradigm in which participants choose between options with partially reliable reward probabilities that periodically swap, probing reward learning under uncertainty.
Probabilistic risk assessment
Probabilistic risk assessment (PRA) is a structured method that quantifies the likelihood and consequences of failures in complex engineered systems, used widely in nuclear regulation.
Probabilistic roadmap
A probabilistic roadmap (PRM), also called the probabilistic path planner, is a sampling-based motion planning algorithm that builds a graph of collision-free robot configurations and searches it for paths.
Probabilistic seismic hazard analysis
Probabilistic seismic hazard analysis (PSHA) is a method that estimates the annual frequency of earthquake ground shaking exceeding specified levels at a site, formalized by C. Allin Cornell in 1968.
Probabilistic solar forecasting
Probabilistic solar forecasting predicts future solar irradiance or photovoltaic power output as a probability distribution rather than a single value, quantifying uncertainty for grid operators, utilities, and market decisions.
Probability
Probability is a numerical measure, between 0 and 1, of how likely an event is, with its mathematical theory tracing to Pascal and Fermat's 1654 correspondence on gambling problems.
Probability amplitude
A probability amplitude, also called a complex probability amplitude, is a complex number whose squared modulus gives a quantum event's probability; the rule is the Born rule, stated by Max Born in 1926.
Probability axioms
The probability axioms, or Kolmogorov axioms, are three rules defining probability, introduced by Andrey Kolmogorov in 1933 and now the standard foundation of probability theory.
Probability current
Probability current, or probability current density, is a vector field in quantum mechanics measuring the local flow of probability, satisfying a continuity equation with the probability density.
Probability density function
A probability density function (PDF) is a function describing the relative likelihood of values of a continuous random variable, where probabilities are areas under the curve.
Probability distribution
A probability distribution, also known as a probability frequency distribution, is the rule that assigns probabilities to events involving a random variable, such as the chance that X falls between two values.
Probability hypothesis density filter
The probability hypothesis density (PHD) filter is a recursive Bayesian algorithm for multi-target tracking, introduced by R.P.S. Mahler in 2003, that propagates the first-order moment of the multi-target posterior and avoids data association.
Probability integral transform
The probability integral transform (PIT) is a result in probability theory: if X has a continuous CDF F, then F(X) follows the uniform distribution on [0, 1].
Probability interpretations
Probability interpretations, also called interpretations of probability, are accounts of what probability statements mean; all share Kolmogorov's 1933 formal calculus but divide over whether probability is physical chance or degree of belief.
Probability mass function
The probability mass function (PMF), also known as the discrete density function, gives the probability that a discrete random variable equals each of its possible values, with all probabilities summing to 1.
Probability measure
A probability measure is a function assigning each event a number between 0 and 1, with total 1 on the whole space, axiomatized by Kolmogorov in 1933.
Probability of default
Probability of default (PD) is the likelihood that a borrower fails to meet payment obligations over a stated horizon, typically one year, used in credit risk analysis.
Probability sampling
Probability sampling is a survey sampling method in which every population element has a known, nonzero selection probability, allowing unbiased estimates and measurable sampling error.
Probability space
A probability space, or probability triple, is the mathematical object on which probability theory is built: a sample space of outcomes, a collection of events, and a probability measure.
Probability theory
Probability theory is the branch of mathematics that models randomness by assigning numbers between 0 and 1 to events, axiomatized by Andrey Kolmogorov in 1933 using measure theory.