In the context of modeling, the terms "stochastic model," "probabilistic model," and "deterministic model" have specific meanings and differences:
Stochastic Model:A stochastic model is a mathematical model that incorporates randomness or uncertainty into its representation of a system or a process. Stochastic models assume that certain aspects of the system are governed by random variables or probabilistic events. Stochastic models are used to describe situations where outcomes are not completely predictable and where randomness plays a significant role. Examples of stochastic models include Markov chains, stochastic differential equations, and Monte Carlo simulations.
Probabilistic Model:A probabilistic model is a type of stochastic model that explicitly uses probability distributions to describe uncertainty. In probabilistic models, the randomness is quantified using probability distributions, and the model makes probabilistic predictions about the outcomes. These models are used when there is a clear understanding of the underlying probability distributions that govern the system. Examples of probabilistic models include Gaussian (normal) distributions, Poisson distributions, and Bayesian models.
Deterministic Model:A deterministic model is a mathematical model that does not consider randomness or uncertainty in its representation. In deterministic models, the outcome is entirely determined by the initial conditions and the model's equations or rules. These models assume that there is no inherent randomness in the system being modeled. Differential equations, algebraic equations, and logical models are often deterministic.
In summary, the main difference between stochastic and probabilistic models is that stochastic models introduce randomness or uncertainty into the modeling process, while probabilistic models specifically use probability distributions to quantify and predict outcomes. On the other hand, deterministic models do not account for randomness and assume that outcomes are entirely predictable based on known inputs and equations. It's important to choose the appropriate type of model based on the nature of the system being studied and the level of uncertainty or randomness involved.
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I think that Chakit Arora provides a good way of defining those three terms. However, I would caution against assuming that those definitions are applied consistently across different fields of study.