Probability & Statistics

Statistical independence is the property that joint probabilities factor into the product of the corresponding individual probabilities.

Statistical interaction occurs when the association between a predictor and an outcome depends on another predictor, on a specified measurement or model scale.

Statistical power is the probability that a hypothesis test rejects the null hypothesis under a specified alternative, measuring its ability to detect an effect.

Statistics is the science of collecting, analyzing, interpreting and presenting data under uncertainty.

A stochastic process is a family of random variables indexed by time or another parameter, used to describe uncertain systems and their dependence structure.

A family of symmetric, heavy-tailed probability distributions central to inference about normally distributed populations with unknown variance.

A sufficient statistic preserves all information in a sample about an unknown parameter within a specified statistical model.

A test statistic is a numerical function of sample data used to assess a statistical hypothesis against a reference distribution.

A time series is a sequence of observations indexed by time, studied to describe temporal patterns, model dependence, and forecast future values.

A matrix encoding probabilities of movement between states, or, in linear algebra, conversion between coordinate bases.

Type I and Type II errors are the two ways a statistical hypothesis test can reach an incorrect decision about a null hypothesis.

A probability distribution assigning equal probabilities to outcomes in a finite set, or constant density over a region of finite positive measure.

Variance measures dispersion by averaging squared deviations from a mean, providing a foundation for probability theory, statistical inference, and predictive modeling.

Variational inference approximates complex probability distributions by optimizing a tractable family of distributions, enabling scalable Bayesian computation.

A Wiener process is a continuous-time stochastic process with continuous paths and independent Gaussian increments, providing the standard mathematical model of Brownian motion.