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Data and ModelsThis section examines data values and models to learn lessons for some generalised software being developed in the CSSE. CSE454
2005
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This document is online at
http://www.csse.monash.edu.au/~lloyd/tilde/CSC4/CSE454/
and contains hyperlinks to other resources

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Some Types of Values:TypeScalarDiscreteInts & 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... 
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Some distributions / models:ModelDiscreteUniform    Multistate etc.  ContinuousUniform    Normal(m,s) etc.  StructuredIndependent    Factors etc.  Vectorset (independent)  seriesMarkov  etc. A Model should be able to
give (log) probability of data value,
generate (sample) data,
... 
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e.g. A classification (decision) tree T models
life expectancy as N(m,s) given
diet, gender and weight,
where m and s depend on diet, gender and weight. 
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MixtureCan form a mixture (weighted average) of models M_{1}, ..., M_{n}, given weightsI.e. Input spaces, parameter spaces, and data spaces are the same across the M_{i}. 
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(Time) SeriesA 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 1storder Markov model can be thought of as S 0order MM's, one for each "context". (A 0order Markov model is ~ a multistate distribution.) A timeseries model can produce a model of the next value given (conditional on) the context of previous values. 
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Complex ModelsPeople 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.
© 2005 L. Allison, School of Computer Science and Software Engineering, 