Statistical models are, by design, stochastic models.

The purpose of a statistical model is to estimate the values of parameters describing a process with uncertain outcomes.

In contrast, deterministic models assume there are no, or more realistically negligible, statistical uncertainties in the model structure.

A familiar example of a deterministic model is a model predicting sunrise and sunset times for your location.

Stochastic models incorporate statistical uncertainty, either in the model structure itself or in the measurement of data that enter the model.

A familiar example of a stochastic model is weather forecasting, where predictions are usually associated with expressions of uncertainty.

Biologists use stochastic models to generate fishing or hunting harvest forecasts, or trends in population abundance, particularly for exploited or endangered species.

Stochastic models may be forward or inverse.

Forward models generate outcomes (data) from a specified deterministic model structure, error specification and parameter values.

Inverse (or estimation) models challenge data with hypothetical models in order to estimate parameter values and identify the underlying 'true' deterministic model structure, under an assumed error specification.