Are stochastic methods classified under empirical models?

Answer 1

It really depends on what exactly you are referring to when you use the term "stochastic method". Stochastic implies randomness. A stochastic method could involve a random search for the correct interaction, a random search for a set of possible outcomes, or even guided guessing for a nearly exact or likely solution, just to list a few.

The model used in a stochastic method could be first principles, or empirical. In a first principles model the interactions are governed by equations which have been determined by the most basic physics. Any approximations are justified and accounted for. In an empirical model, the interaction is either approximated, guessed at, or completely ignored with a simple input to output mapping. The approximations are unknown, and the errors must be accounted for by comparing the model to a real event, and then crossing ones fingers in the hopes that the errors hold true for all similar events.

For examples:

* Most weather models are a mix of first principles, empirical and stochastic methods. They use first principles to govern air and heat flow, but use empirical approximations to account for the surface of the Earth and the effects of rain fall. They are stochastic in that they use slightly randomized sets of data to reflect errors in the data gathering, and in the model itself.

* Climate models are empirical and stochastic. The basic interactions have been either guessed at or ignored in favor of a simple input to output mapping. The "most likely" outcome is then guessed at by feeding the model a range of inputs. * Calculation of electron exchange and correlation potentials are first principles and stochastic. The interactions of the electrons are dictated strictly by quantum mechanics and electrostatics, but the ground states of many random configurations need to be investigated.