Probabilistlik

Probabilistlik is an Estonian term for anything relating to probability theory and probabilistic methods. In mathematics and statistics, probabilistlik approaches model uncertainty by assigning probabilities to events and by using random variables and stochastic processes.

Key concepts include random variables, probability distributions (discrete and continuous), expectation and variance, independence and identical distribution assumptions, conditional probability, joint distributions, and relevant theorems such as Bayes' theorem and the law of total probability. Inference uses these tools to update beliefs or to estimate parameters from data, producing point estimates, intervals, or predictive distributions.

Two broad philosophical interpretations frame probabilistlik reasoning: Bayesian and frequentist. Bayesian probability treats probability as a degree of belief and updates it via Bayes' rule using priors, likelihoods, and posteriors. Frequentist probability views probability as a long-run frequency of outcomes in repeatable experiments, focusing on sampling distributions, confidence intervals, and hypothesis testing. In practice, many models blend ideas or use computational methods to approximate intractable integrals.

Common methods associated with probabilistlik modelling include Monte Carlo simulation, Markov chain Monte Carlo, and variational inference. Probabilistic programming languages enable specifying complex probabilistic models and automatically performing inference.

Applications span science, engineering, economics, finance, risk assessment, and data science. Probabilistlik thinking supports forecasting under uncertainty, decision making under risk, and the development of machine learning models such as Bayesian networks and probabilistic graphical models.