Probabilistic modeling is a branch of mathematics and statistics that aims to represent and manipulate uncertainty in a systematic and mathematically rigorous way. It involves the use of probability theory to model and analyze complex systems or processes that involve random variables. Probabilistic modeling is widely used in various fields such as machine learning, artificial intelligence, economics, biology, and finance, among others. It allows researchers to make predictions or decisions based on uncertain or incomplete information, and to evaluate the likelihood of different outcomes. In probabilistic modeling, a probabilistic model is constructed based on observed data and prior knowledge, and is used to make inferences about the underlying system or process. This can involve fitting a model to data, estimating parameters, simulating data, and making predictions. Overall, probabilistic modeling provides a powerful framework for reasoning under uncertainty and making informed decisions in a wide range of applications.