Probabilistically

Probabilistically is an adverb used to indicate that a statement, method, or outcome is considered, modeled, or inferred using probability theory and the mathematics of uncertainty. It is used when results are not certain but described in terms of likelihoods or distributions.

In mathematics and statistics, reasoning or analysis that is probabilistic is based on models of random variation. Probabilistic models specify probability distributions for variables, allowing predictions of the frequency of outcomes, not exact values. Practices include inference from data using likelihoods or Bayes’ rule, computation of expected values, and assessment of uncertainty.

In computation and data science, probabilistic approaches underpin algorithms and simulations. Monte Carlo methods estimate integrals or probabilities by random sampling. Probabilistic programming languages enable models to be specified and inferred automatically. In machine learning, probabilistic methods provide uncertainty estimates and principled decision-making under risk.

Usage notes: probabilistically should not be confused with probabilistic as an adjective; the former modifies verbs or constructions (for example, “we estimated probabilistically”), while the latter describes the model itself (for example, “a probabilistic model”). Related concepts include stochasticity, random processes, and Bayesian inference.