Sampling (statistics)

Sampling is the procedure of drawing values from a probability distribution, often to approximate probabilities, expectations, or the distribution itself.

Inverse transform sampling: A method that generates random values by applying a distribution’s inverse cumulative distribution function to uniform random values. It converts uniform draws into samples from a target distribution when its inverse cumulative distribution is available.
Probability distribution: A mathematical description assigning probabilities to possible outcomes of a random variable. Sampling takes its target and the relative likelihoods of its possible outcomes from this object.
Monte Carlo method: A computational approach that uses random sampling to estimate quantities or solve problems. It uses repeated samples to approximate integrals, probabilities, and other quantities.
Simple random sampling: A sampling design in which every possible sample of a fixed size has equal probability of selection. It is a specific population-sampling design, distinct from algorithms that draw from a specified distribution.
Rejection sampling: A method for sampling from a target distribution by accepting or rejecting draws from a proposal distribution. It handles distributions that are difficult to sample directly by filtering easier proposal draws.
Random variable: A function that assigns a numerical value to each outcome in a probabilistic experiment. Each draw produces a value that can be interpreted as an outcome of a random variable.
Bootstrap method: A statistical procedure that estimates uncertainty by repeatedly resampling observations from an observed dataset. It substitutes resampling from data for repeated sampling from an unknown population.
Stratified sampling: A sampling design that divides a population into groups and selects samples separately within each group. It allocates draws across defined population groups rather than relying on an undivided selection process.
Markov chain Monte Carlo: A family of algorithms that uses Markov chains to generate samples from complex probability distributions. Its chains produce dependent samples when direct independent draws are impractical.
Cumulative distribution function: A function giving the probability that a random variable is less than or equal to each specified value. Inverse transform sampling uses it to map uniform draws onto target-distribution values.

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