Bayesian model

Such Bayesian models could be couched in terms of parametric distributions, but the mathematics for real problems becomes intractable, so discrete distributions, estimated with the aid of computers, are used instead. The calculation of probability of outcomes from assumptions (inference) can be performed through exhaustive multiplication of conditional probabilities, or with large problems estimates can be obtained through stochastic methods (Monte Carlo techniques) that sample over possible futures. 

AIME Ol Workshop Bayesian Models in Medicine. The European Conference on Artificial Intelligence in Medicine (AIME Ol). Cascais, Portugal, 2001. 

The standard of testability (vulnerability to negation in the framework of a working hypothesis in the hypothetico-deductive mode or of simultaneous adjustment in the framework of Bayesian modeling) is probably the toughest standard demanded in science. Ideas as old as the monad are not necessarily tested and validated by repeated corroboration. Indeed, they may be untested and powered by inertia. Ideas which are testable are those for which there are alternatives otherwise ideas are either unnecessary or untestable. Since Dennett has already asserted that reductionism permits no alternative, monophyly as such would have to be untestable, but, before condemning it to the rank of scientific dogma, let me cite two cases in which monophyly was tested as the alternative to a different (polyphylic) hypothesis. 

Advocates of polyphylism have indeed been harmed professionally by the attitudes and actions of monophylists. Moreover, the study of evolution has been harmed. Evolution, like weather and climate, should be studied by modeling - Bayesian modeling with multiple, simultaneous hypotheses - but because the study of polyphylic alternatives is stifled, modeling evolution is set back and all but killed. 

Elicitation of jndgment may be involved in the selection of a prior distribution for Bayesian analysis. However, particularly because of developments in Bayesian computing, Bayesian modeling may be useful in data-rich situations. In those situations the priors may contain little prior information and may be chosen in such a way that the results will be dominated by the data rather than by the prior. The results may be acceptable from a frequentist viewpoint, if not actually identical to some frequentist results. 

Klon, A.E., Lowrie, J.E. and Ddler, D.J. (2006) Improved naive Bayesian modeling of numerical data for absorption, distribution, metabobsm and excretion (ADME) property prediction. Journal of Chemical Information and Modeling, 46, 1945-1956. 

Nidhi, G.M., Davies, J.W. and Jenkins, J.L. (2006) Prediction of biological targets for compounds using multiple-category bayesian models trained on chemo-genomics databases. Journal of Chemical Information and Modeling, 46 (3), 1124-1133. 

Xia, X., Maliski, E.G., Gallant, P. and Rogers, D. (2004) Classification of kinase inhibitors using a Bayesian model. Journal of Medicinal Chemistry, 47 (18), 4463-4470. 

Thus, multilinear models were introduced, and then a wide series of tools, such as nonlinear models, including artificial neural networks, fuzzy logic, Bayesian models, and expert systems. A number of reviews deal with the different techniques [4-6]. Mathematical techniques have also been used to keep into account the high number (up to several thousands) of chemical descriptors and fragments that can be used for modeling purposes, with the problem of increase in noise and lack of statistical robustness. Also in this case, linear and nonlinear methods have been used, such as principal component analysis (PCA) and genetic algorithms (GA) [6]. 

Fig. 6 Test set receiver operator characteristic curves for M. tuberculosis Bayesian models, (a) Southern Research Institute data for >100,000 molecules (1,702 actives), (b) Novartis data for 248 molecules (34 actives), (c) FDA-approved drugs, 2,108 molecules (21 actives) (17,29)...

Key words Bayesian models, Collaborative Drug Discovery Tuberculosis database, Docking, Mycobacterium tuberculosis, Quantitative structure-activity relationship, Tuberculosis... 

Inspired by this work (24), we used Bayesian methods (24) with molecular function class fingerprints of maximum diameter 6 (53) to identify substructures that were shown to be important in recent TB screening datasets (21-23). Bayesian models were built with the previously described Molecular Libraries Small Molecule Repository (MLSMR) 220,463 library (4,096 active compounds) (15) and dose-response data using 2,273 molecules (475 active compounds). In addition, these models were tested (15) with the National Institute of Allergy and Infectious Diseases (NIAID) data and GVK Biosciences (Hyderabad, India) datasets used by Prathipati et al. (24). We have validated the models with compounds left out of the original models, in some cases showing up to tenfold enrichments in finding active compounds in the top-ranked 600 molecules (22). 

The large-scale whole-cell screening efforts have created large training sets for TB models such as the Bayesian models described by us and others. The caveat with these models is they are likely limited to predicting compound activity under the exact in vitro conditions used (15). However, by considering data from different groups, we have shown that this may not be a major issue (21). Hence such models can be used to filter vendor libraries of molecules and natural products (21). 

Prathipati P, Ma NL, Keller TH (2008) Global Bayesian models for the prioritization of anti-tubercular agents. J Chem Inf Model 48 2362-2370... 

Hoeting, J. A., Madigan, D., Raftery, A. E., and Volinsky, C. T. (1999). Bayesian model averaging A tutorial (with discussion). Statistical Science, 14, 382-417. 

Ibrahim, J. G., Chen, M. H., and Gray, R. J. (2002). Bayesian models for gene expression with DNA microarray data. Journal of the American Statistical Association, 97, 88-99. 

Stochastic simulation methods for fitting Bayesian models are now discussed and illustrated using the two examples that were described earlier in the chapter. 

Chipman, H. A., George, E. I., and McCulloch, R. E. (2001). The practical implementation of Bayesian model selection. In Model Selection. Editor R Lahiri, pages 65-116. Volume 38 of IMS Lecture Notes—Monograph Series, Institute of Mathematical Statistics, Beachwood. 

George, E. I., McCulloch, R. E., and Tsay, R. S. (1995). Two approaches to Bayesian model selection with applications. In Bayesian Analysis in Statistics and Econometrics Essays in Honor of Arnold Zellner. Editors D. A. Berry, K. A. Chaloner, and J. K. Geweke, pages 339-348. John Wiley and Sons, New York. 

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