### theory | model:

Descriptive model
* are the precursors of generative model.
* use experimental data to calculate parameters which fit the model to the data.

Dynamic model
* are an essential tool for understanding complex biological systems
  - critical tools in the analysis of time-dependent systems
* can include different types of physical systems.

Ecological model
* can be deterministic or stochastic.
* have to consider both a scale in time and space.

Economic model
* Many economic models involve a trade-off between current and future rewards.
* are abstract and rely on mathematics and mathematical reasoning
  - small-scale versions of the economy
* can aid policy makers in formulating policy and avoiding costly mistakes.
* differ in a number of ways.
* have tradition ally used indicators of the production volume.
* treat two kinds of learning activities, distinguished by the subject being learned.

### theory | model:

Mathematical model
* are a rigorous way of posing questions
  - at their best when humans are trying as hard as they can
  - caricatures of systems made from mathematical equations
  - especially useful in making sense of complicated systems
  - helpful in determining the effect of process variables
  - key components of the safety assessment of waste disposal options
  - of great importance in the natural sciences, particularly in physics
  - ordinary or partial differential equations
  - used to provide evidence and to prove the validity of a solution
  - valuable tools in the study of trauma
  - very important for solving many problems
* can address specific predictions about modes of speciation
  - include logical models
  - take many forms
* come in all shapes and sizes.
* describe how signalling can contribute to an evolutionarily stable strategy.
* help elucidate the factors that influence such processes.
* play an increasingly important role in economic science.
* provide the basis for much of the theoretical evaluation of statistical tools.
* rely on accurate experimental measurements of the soil moisture characteristic.
* show that it requires millions of years for a gene to change significantly.
  * These and other types of models can overlap, with a given model involving a variety of abstract structures. Mathematical models can include logical models. In many cases, the quality of a scientific field depends on how well the mathematical models built on theory agree with results of repeatable experiments. When theoretical mathematical models do not match experimental measurements, scientists try to correct the model. Such corrections lead the way to better theories to explain the facts.

Physical model
* Many physical models involve motion which is called harmonic.
* are generally simplifications of the real world.

Probability model
* describe the likelihoods of specific events associated with specific processes.
* exist in a theoretical world where complete information is unavailable.

Scientific model
* are hypotheses set forth to explain experimental observations
  - metaphors for the physical universe
  - used as a basis for scientific work
* make it easier to understand cells.
  * A 'scientific model' simplified abstract view of a complex reality. Scientific models are used as a basis for scientific work. They can be used to explain, predict, and test, or to develop computer programs or mathematical equations.

Stochastic model
* assume probabilistic distributions for the values of variables in models.
* predict variable outcomes based on probabilities of occurrence.
* provide a zero-order theory of the decadal variations in North Pacific.

Stochastic process
* are especially important for small populations
  - important in non-equilibrium statistical mechanics and disordered solids
* arise from the study of fluctuations in physical systems.