Deterministic vs. stochastic models
Statistical models are, by design, stochastic models.
Linear vs non-linear models
A statistical model is linear with respect to a parameter
if an estimate of that parameter can be obtained in a single
There may be more than one way to express a particular deterministic
model (i.e., functional relationship).
The error specification of a stochastic model is equal in
importance to the deterministic formulation.
Most statistical models drawing conclusions from data utilize
the principle of maximum-likelihood as their basis for statistical
Linear models can be solved for explicit analytical expressions
of the maximum-likelihood parameter estimates, given a model
A statistical model should be rejected if it fails a posteriori
Models with more free parameters typically 'fit' the data
better, i.e., model error variance is reduced, but at a cost
that has to be considered.
A underlying premise of stochastic models is that exact outcomes
cannot be predicted with certainty.
Typically, maximum-likelihood estimates are asymptotically
How well does a particular model work?
For many biological considerations, the concept of an underlying
'true', point, value for a parameter as a premise for statistical
inference is somewhat artificial.