Probabilistic generative models (PGMs) play a crucial role in mathematically representing human cognitive functions. PGMs are mathematical models designed to capture latent structures and patterns underlying observed data. The advantages of PGMs include their ability to handle uncertainty, incorporating prior knowledge, and adapting flexibly to new data. These characteristics make them highly useful for mimicking human cognition and decision-making processes. Generative models describe the process of generating observed data and capture latent structures or patterns underlying them. PGMs introduce probability distributions into the generative process, enabling the representation of uncertainty and variability in data. This capability allows for accurate predictions when encountering new data while enhancing the understanding of the overall characteristics of an observed dataset. The concepts of PGMs and Bayesian inference extend beyond cognitive modeling for symbol emergence in robotics and are widely applied in constructing world models and computational neuroscience. PGMs can mathematically define internal representations that generate and predict observed data as brain and cognitive models. Additionally, Bayesian inference facilitates the computation of arbitrary probability distributions under given model definitions, functioning as a concrete processing mechanism for cognitive functions.