Statistical Model Selection Task
A Statistical Model Selection Task is a selection task that requires the selection a statistical model family.
- Context:
- It can (typically) be a Statistical Modeling Task.
- It can be solved by a Model Selection System.
- …
- Counter-Example(s):
- See: Function Fitting Task, AIC, BIC.
References
2013
- http://en.wikipedia.org/wiki/Model_selection
- Model selection is the task of selecting a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered. However, the task can also involve the design of experiments such that the data collected is well-suited to the problem of model selection. Given candidate models of similar predictive or explanatory power, the simplest model is most likely to be correct.
2009
- http://en.wikipedia.org/wiki/Model_selection
- … Of the endless number of possible models that could have produced the data, how can one even begin to choose the correct model? The mathematical approach commonly taken decides among a set of possible models; this set must be selected by the researcher. Often simple models such as polynomials or quadrics are used as a starting point. Burnham and Anderson (2002) emphasize the importance of selecting models based on sound scientific principles modeling the underlying data throughout their book on model selection[1].
Once the set of possible models has been selected, the mathematical analysis allows us to determine the best of these models. What is meant by best is controversial. A good model selection technique will balance goodness of fit with simplicity. More complex models will be better able to adapt their shape to fit the data (for example, a fifth-order polynomial can exactly fit six points), but the additional parameters may not represent anything useful. (Perhaps those six points are really just randomly distributed about a line.) Goodness of fit is generally determined using a likelihood ratio approach, or an approximation of this, leading to a chi-squared test. The complexity is generally measured by counting the number of free parameters in the model.
Model selection techniques can be considered as estimators of some physical quantity, such as the probability of the model producing the given data. The bias and variance are both important measures of the quality of this estimator.
- … Of the endless number of possible models that could have produced the data, how can one even begin to choose the correct model? The mathematical approach commonly taken decides among a set of possible models; this set must be selected by the researcher. Often simple models such as polynomials or quadrics are used as a starting point. Burnham and Anderson (2002) emphasize the importance of selecting models based on sound scientific principles modeling the underlying data throughout their book on model selection[1].
- http://www.nature.com/nrg/journal/v5/n4/glossary/nrg1318_glossary.html
- MODEL SELECTION The process of choosing among different models given their posterior probability.