Probabilistic modeling

Probabilistic modeling is a mathematical framework that uses probability theory to represent and quantify uncertainty in data, systems, and predictions. This approach models variables as probability distributions rather than fixed values, enabling systems to capture and reason about inherent randomness and incomplete information. Probabilistic models incorporate prior knowledge through Bayesian inference, updating beliefs as new evidence emerges. Core techniques include Markov Chain Monte Carlo (MCMC) sampling, variational inference, and expectation-maximization algorithms. In AI systems, probabilistic modeling enables robust decision-making under uncertainty, confidence estimation in predictions, and handling of noisy or missing data. Applications span machine learning algorithms like Gaussian processes, hidden Markov models, and Bayesian neural networks. For AI agents, probabilistic modeling provides frameworks for risk assessment, multi-armed bandit problems, and sequential decision-making in uncertain environments, making systems more reliable and interpretable.