Bayesian sensitivity analysis

Bayesian networks for multivariate reasoning about cause and effect within R D with a flow bottleneck model (Fig. 11.6) to help combine scientific and economic aspects of decision making. This model can, where research process decisions affect potential candidate value, further incorporate simple estimation of how the candidate value varies based on the target product profile. Factors such as ease of dosing in this profile can then be causally linked to the relevant predictors within the research process (e.g., bioavailability), to model the value of the predictive methods that might be used and to perform sensitivity analysis of how R D process choices affect the expected added... 

In all analyses, there is uncertainty about the accuracy of the results that may be dealt with via sensitivity analyses [1, 2]. In these analyses, one essentially asks the question What if These allow one to vary key values over clinically feasible ranges to determine whether the decision remains the same, that is, if the strategy initially found to be cost-effective remains the dominant strategy. By performing sensitivity analyses, one can increase the level of confidence in the conclusions. Sensitivity analyses also allow one to determine threshold values for these key parameters at which the decision would change. For example, in the previous example of a Bayesian evaluation embedded in a decision-analytic model of pancreatic cancer, a sensitivity analysis (Fig. 24.6) was conducted to evaluate the relationship... 

Equation (4.11) is a useful form of the Bayesian acceptance-rejection procedure for generalized sensitivity analysis, in that it applies whenever one s model is predicting an average of a measured quantity. 

Fig. 8.11. The classifier development process. Clinical knowledge provides us with a set of classes for supervised classification (top, right). Large numbers of spectra from large sample numbers are reduced to a set of potentially useful features (top, left) or metrics. A modified Bayesian algorithm operates on the metrics to provide predictions that are compared to a gold standard. The end result of the training and validation process is an optimized algorithm, metric set, calibration and validation statistics, and sensitivity analysis of the data...

Sensitivity analysis is about asking how sensitive your model is to perturbations of assumptions in the underlying variables and structure. Models developed under any platform should be subject to some form of sensitivity analysis. Those constructed under a Bayesian framework may be subject to further sensitivity analysis associated with assumptions that may be made in the specihcation of the prior information. In general, therefore, a sensitivity analysis will involve some form of perturbation of the priors. There are generally scenarios where this may be important. First, the choice of a noninformative prior could lead to an improper posterior distribution that may be more informative than desired (see Gelman (18) for some discussion on this). Second, the use of informative priors for PK/PD analysis raises the issue of introduction of bias to the posterior parameter estimates for a specihed subject group that is, the prior information may not have been exchangeable with the current data. 

Greenland, S. (2001). Sensitivity analysis, Monte Carlo risk analysis, and Bayesian uncertainty assessment. Risk Anal 21, 579-583. 

Thus, we take advantage of the accuracy, robustness and efficiency of the direct problem solution, to tackle the associated inverse heat transfer problem analysis [26, 27] towards the simultaneous estimation of momentum and thermal accommodation coefficients in micro-channel flows with velocity slip and temperature jump. A Bayesian inference approach is adopted in the solution of the identification problem, based on the Monte Carlo Markov Chain method (MCMC) and the Metropolis-Hastings algorithm [28-30]. Only simulated temperature measurements at the external faces of the channel walls, obtained for instance via infrared thermography [30], are used in the inverse analysis in order to demonstrate the capabilities of the proposed approach. A sensitivity analysis allows for the inspection of the identification problem behavior when the external wall Biot number is also included among the parameters to be estimated. 

A) Define decision problem Decision alternatives Select quanlilics of Interest —> (B> Traditiojial analysis Selection of models) Bayesian updating and assessments Sensitivity analysis and importance mnkina - (O QvalUativc uncertainty analysis Assessment of uneertainty factors Assessment of sensitivity Assessment of unocriaintics Summari/ation of importance... 

Oakley, J.E., O Hagan, A. Probabilistic sensitivity analysis of complex models a Bayesian approach. J. R. Slat. Soc. Ser. B (Stat. Methodol.) 66, 751-769 (2004)... 

In a further large-scale analysis on the same database, gene expression and biological screening data were used to identify a correlation between gene expression and cell sensitivity to compounds [83]. Sixty cancer cell lines were exposed to numerous compounds at the National Cancer Institute, and were determined to be either sensitive or resistant to each compound. Using a Bayesian statistical classifier, Staunton et al. 

A comment needs to be made on the form of the uncertainty assessment suggested here. The uncertainty assessment in Table 1 is semi-quantitative, in the sense that qualitatively described conditions are established for the classification of uncertainty factors. However, the classification itself involves quantitative analysis, for example in classifying the sensitivity of an uncertainty factor. The alternative would be a completely quantitative uncertainty assessment, say a standard Bayesian analysis. As an example, uncertainty factor 8 in Table 1 relates to the duration of annual planned/scheduled maintenance. In the traditional analysis this duration is assumed to be a fixed quantity. Alternatively, we could introduce it as an unknown quantity and assess uncertainty about it quantitatively. Two points can be made here. Firstly, such an uncertainty assessment would also be based on a number of assumptions. Secondly, there is a balance to be made between the effort put into such an assessment and its usefulness, which is questionable if the backgroimd knowledge is poor. 

Nikolaev, E.V., Atlas, J.C., Shuler, M.L. Sensitivity and cmitFol analysis of periodically forced reaction networks using the Green s function method. J. Theor. Biol. 247,442-461 (2007) Oakley, J., O Hagan, A. Bayesian inference for the uncertainty distribution of computer model outputs. Biometrika 89, 769-784 (2002)... 

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