The error specification of a stochastic model is equal in importance to the deterministic formulation.

Using simple linear regression as an example, it is imperative to realize that all inferences regarding the estimates for a and b, and their uncertainty, stem from the assumptions made concerning the error term (epsilon) in the following stochastic model.

For simple linear regression the assumption is that each of the error terms has a Gaussian (normal) distribution with a mean of zero (0) and finite variance.

It is also assumed that each of the error terms (epsilons) are independent of each other.

Thus in general, statistical model results can heavily depend upon the nature of model error (e.g., random sampling error, measurement error, process error) and the probability distributions chosen to represent it (e.g., Gaussian, Poisson, binomial, etc.).

Clearly, carefully consideration must be given to the mode error specification when constructing a statistical model.

Too frequently error specification gets much less consideration by analysts than it warrants.

There are three basic elements of error that may enter a statistical model: (1) measurement error - the data are imperfect; (2) process error - the model is imperfect; and (3) Bernoulli (and binomial or multinomial) error - stochastic frequency outcomes such as are observed when coin flipping.

Typically, Gaussian (normal) error is associated with continuous variables, while binomial or multinomial error is associated with frequency data.

However, many biological models and processes may demand alternative simple, complex or correlated error structures that include all of measurement, process and/or Bernoulli family errors.