Bayesian data analysis

A Gelman, JB Carlin, HS Stern, DB Rubin. Bayesian Data Analysis. London Chapman Hall, 1995. 

Gelman A, Carlin JB, Stem HS, Rubin DB. 1997. Bayesian data analysis. Boca Raton (FL) Chapman and Hall/CRC. 

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2003). Bayesian Data Analysis, second edition. Chapman Hall/CRC, Boca Raton, FL. 

Paola Sebastiani is Associate Professor in the Department of Biostatistics and adjunct Associate Professor in the Bioinformatics and Systems Biology Program of Boston University. Her research interests are in Bayesian data analysis and experimental design, and the automation of statistical methods. 

Gelman, A., et al. (2003). Bayesian Data Analysis. Boca Raton, FL Chapman Hah. 

Gelman, A. 2004. Bayesian Data Analysis (Second Edition). USA Chapman Hall/CRC. 

A. Gelman, J.B. Carlin, H.S. Stem, D.B. Rubin, Bayesian Data Analysis. Chapman and Hall, Boca Raton, FL, 2004. 

Dale A (1986) A newly-discovered result of Thomas Bayes. Arch Hist Exact Sci 35(2) 101-113 Edwards A (1978) Commentary on the arguments of Thomas Bayes. Scand J Stat 5(2) 116-118 Esteva L (1969) Seismicity prediction a Bayesian approach. In Proceedings of the fourth world conference on earthquake engineering, Santiago de Chile Gelman A, Cariin JB, Shan HS, Rubin DB (2003) Bayesian data analysis, 2nd edn. Texts in statistical sciences. Chapman Hall CRC, Boca Raton Gillies D (1987) Was Bayes a Bayesian Hist Math 14 325-346... 

Mixmre models have come up frequently in Bayesian statistical analysis in molecular and structural biology [16,28] as described below, so a description is useful here. Mixture models can be used when simple forms such as the exponential or Dirichlet function alone do not describe the data well. This is usually the case for a multimodal data distribution (as might be evident from a histogram of the data), when clearly a single Gaussian function will not suffice. A mixture is a sum of simple forms for the likelihood ... 

Sivia, D. S., Data Analysis. A Bayesian Tutorial, Clarendon Oxford, 1996... 

Many scientists ignore the prior information, and for cases where data are fairly good, this can be perfectly acceptable. However, chemical data analysis is most useful where the answer is not so obvious, and the data are difficult to analyse. The Bayesian method allows prior information or measurements to be taken into account. It also allows continuing experimentation, improving a model all the time. 

A few programs are now available that allow the efficient simultaneous data analysis from a population of subjects. This approach has the significant advantage that the number of data points per subject can be small. However, using data from many subjects, it is possible to complete the analyses and obtain both between- and within-subject variance information. These programs include NONMEM and WinNON-MIX for parametric (model dependent) analyses and NPEM when non-parametric (model independent) analyses are required. This approach nicely complements the Bayesian approach. Once the population values for the pharmacokinetic parameters are obtained, it is possible to use the Bayesian estimation approach to obtain estimates of the individual patient s pharmacokinetics and optimize their drug therapy. 

The three disadvantages of MI when compared with other imputation methods are (a) more effort to create the multiple imputations, (b) more time to run the analyses, and (c) more computer storage space for Ml-created data sets (6). These are hardly issues with current development in computer technology. The MI approach is computationally simpler than the ML and Bayesian approaches for most practical situations. Once the imputed data is generated, the data can be analyzed with any data analysis software of choice. 

G. Graham, S. Gupta, and L. Aarons, Determination of an optimal dosage regimen using a Bayesian decision analysis of efficacy and adverse effect data. J Pharmacokinet Pharmacodyn 29 67-88 (2002). 

Sivia D., and Skilling J., Data Analysis A Bayesian Tutorial, Oxford University Press isbn 978-0-19-856832-2 (2006)... 

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