This section examines data values and models to learn lessons for some generalised software being developed in the CSSE.
CSE454 2003 : This document is online at http://www.csse.monash.edu.au/~lloyd/tilde/CSC4/CSE454/ and contains hyper-links to other resources - Lloyd Allison ©.
Type--|--Scalar--|--Discrete--|--Ints & subranges | | | | | |--Symbolic | | | |--Continuous & subranges | |--Structured i.e. multivariate | |--Vector N.B. homogenous | |--Union i.e. either S1 or S2 | |--Function i.e. S1->S2 | |--Model...
Model--|--Discrete----|--Uniform | | | |--Multistate etc. | |--Continuous--|--Uniform | | | |--Normal(m,s) etc. | |--Structured--|--Independent | | | |--Factors etc. | |--Vector------|--set (independent) | |--series--|--Markov | etc.
A Model should be able to
give (-log) probability of data value,
generate (sample) data,
...
parameters | | | v | ||||
input space exogenous variables | -----> | "Model" | -----> |
(output) Sample (Data) Space endogenous variables |
Note, input space and/or parameter space may be trivial.
e.g. A classification- (decision-) tree T models
blood-pressure as N(m,s) given
age, gender and weight where m and s depend on age, gender and weight.
i.e. input spaces, parameter spaces, and data spaces are the same across the Mi.
A model M with data space S trivially induces a model on S* if the elements of the series are modelled as being independent.
There are more interesting models in S*: A 1st-order Markov model can be thought of as |S| 0-order MM's, one for each "context".
(A 0-order Markov model is just a multi-state distribution.)
People use the word "model" to cover anything from a simple probability distribution to "a model of the Australian economy" (MAE). At its most general the word is too general to program with although any instance, such as MAE, can be programmed from a collection of functions, data structures and simpler models.