Statistical model

A statistical model uses probability distributions and parameters to describe relationships in data or represent a process that could have generated the data. It is an approximation whose assumptions can be tested against observations.

Probability distribution: A mathematical function describing the probabilities of possible outcomes of a random variable. Models specify distributions for observed data, latent quantities, or both.
Statistical inference: The process of using data to estimate unknown quantities or assess claims about a population or process. Inference uses a model to connect observed samples with unknown data-generating quantities.
Linear regression: A model that represents a response's conditional mean as a linear combination of predictors. It models continuous outcomes with a simple, interpretable relationship between predictors and response.
Deterministic model: A model that produces a fixed output from given inputs without representing randomness. Unlike a statistical model, it does not describe variability through probability distributions.
Random variable: A variable whose possible values are assigned probabilities by a probability model. Statistical models describe uncertain observations through random variables.
Maximum likelihood estimation: A method that estimates parameters by maximizing the likelihood of the observed data. It selects parameter values that make the observed data most likely under the model.
Logistic regression: A regression model that relates predictors to the log-odds of a binary outcome. It extends regression to outcomes recorded in two categories.
Machine learning: A field developing methods that learn patterns from data for prediction, decision-making, or representation. Machine-learning methods often fit statistical models, though the fields are not identical.
Parameter: A fixed but often unknown quantity that indexes a family of probability distributions or mathematical relationships. Parameters distinguish particular distributions and relationships within a model.
Bayesian inference: A method that updates prior probability distributions with data to obtain posterior distributions. Bayesian fitting represents uncertainty about model parameters with probability distributions.

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