Parsimony, principle

It is advisable not to forget the parsimony principle, also called Occam razor, often paraphrased into... 

If the value F exceeds the tabulated value of Fischer s F-distribution for (F - F ) and (N - F ) degrees of freedom, and a confidence level of (usually) 95% (a = 0.05), then the complex model fits significantly better to the data than the simpler model. If not, the parsimony principle dictates that the simpler model should be accepted as the best model. 

Three different parsimony methods have been used for the analysis of restriction site data Wagner parsimony,25 Dollo parsimony,26 and weighted parsimony or generalized parsimony.27 As the names suggest, they all invoke a parsimony principle to select the best tree (or trees) from the set of all possible trees. Specifically, the trees selected are those that require the minimum amount of evolutionary change. The methods differ from one another in how the amount of evolutionary change is calculated. 

Simplest Base Model Is Backbone. The simplest base model that characterizes the underlying patterns in the data should form the backbone for developing a population model. The principle of simplicity stipulates that models with the minimum number of parameters should be used. This is called the parsimony principle. The model with the smallest number of parameters that describe the data well is the most parsimonious model. 

If a component model of the raw data requires, say, R + 1 components to describe the data well, whereas a model of the centered data requires only R components, then centering is sensible because the model of the centered data only has R(I + J) + J parameters. The J parameters pertain to the calculated averages, assuming that centering is performed across the first mode. The alternative of fitting the (R + l)-component model to the raw data would lead to a model with (R + 1)(7 + J) parameters and thus would violate the parsimony principle [Judge et al. 1985, Seasholtz Kowalski 1993, Weinberg 1964],... 

Seasholtz MB, Kowalski BR, The parsimony principle applied to multivariate calibration, Analytica Chimica Acta, 1993, 277, 165-177. 

M.B. Seasholtz and B. Kowalski, The Parsimony Principle Applied to Multivariate Calibration, Analylica Chimica Acta, 277(2) (1993), 165-177. 

The cladistic parsimony principle, as understood by most users of computer programs, is utilized only in the search for the shortest tree. I have frequently heard cladists say that it should be impossible to discover an optimal tree topology by hand when many species are being considered, because there are millions of alternative topologies to be considered (e.g., about two million unrooted topologies for only 10 terminal taxa). As there exist more than 900,000 known species of insects and the number of alternative topologies that... 

Recent research has shown that judicious variable selection can improve statistical predictions of models (Baroni et al, 1992 Brereton, 1995 Brereton and Elbergali, 1994 Broadhurst et aL, 1997 Brown, 1993 Cruciani and Watson, 1994 Defalguerolles and Jmel, 1993 Hazen, Arnold and Small, 1994 Heikka, Minkkinen and Taavitsainen, 1994 Kubinyi, 1994a, b, 1996 Lindgren et aL, 1995 Norinder, 1996 Shaw et al, 1996,1997 Sreerama and Woody, 1994) statistical theory, in particular the parsimony principle... 

To examine the quality of model predictions to observed data, in addition to visual inspection, various statistical tests on residuals are available to check for presence of systematic misfitting, nonrandomness of the errors, and accordance with assumed experimental noise. Model order estimation, that is, number of compartments in the model, is also relevant here, and for linear compartmental models, criteria such as F-test, and those based on the parsimony principle such as the Akaike and Schwarz criteria, can be used if measurement errors are Gaussian. 

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