Bayesian assessments

A very powerful idea behind Bayesian inference is that statistical inference is simply updating a previous knowledge, assessed by a prior distribution. The obtained posterior distribution, which encodes the current state of knowledge, can be sequentially updated by adding more and more data. To exemphfy this idea, let us consider a very simple problem the Bayesian assessment of an exponential lifetime model, of failure rate X ... 

It should be noted that the Bayesian conception of probability of a hypothesis and the Bayesian procedure for assessing this probability is the original paradigm for probabilistic... 

Bruneau, P., McElroy, N. R. Log D " modeling using Bayesian regularised neural networks. Assessment and correction of errors of prediction. 

The authors also evaluated the performance of various DES-T and DES cutoffs for detecting taxon members defined by Bayesian probabilities. Waller and Ross found that DES-T cutoffs work much better than the cutoffs on the DES because they have higher sensitivity, specificity, and positive and negative predictive values. One could say that the authors stacked the deck in favor of the DES-T, as the Bayesian probabilities and DES-T scores are based on the same data. However, this redundancy is unavoidable, since there is no other method of assessing taxon membership. It is important to evaluate the qualities of DES-T cutoffs for studies that will use the DES-T, rather than the Bayesian scoring scheme. 

Table 15.12 Hand-held Bayesian ADR assessment data and scoring sheet ...

Lane DA, Hutchinson TA, Jones JK, et al. A Bayesian Approach to Causality Assessment. University of Minnesota School of Statistics Tech Reps No 472 (no date available). 

Lane DA, Kramer MS, Hutchinson TA, et al. The causality assessment of adverse drug reactions using a Bayesian approach. Pharm Med 1987 2 265-83. 

Before deciding to treat a line of evidence separately, consideration shonld be given to whether it can in fact be directly incorporated into the quantitative assessment. For example, it may be possible to use Bayesian updating to incorporate information from field studies or monitoring if they provide direct measurements of the assessment endpoint, or of the intermediate model. 

The topic of eliciting probability distributions that are based purely on judgment (professional or otherwise) is discussed in texts on risk assessment (e.g., Moore 1983 Vose 2000) and decision theory or Bayesian methodology (e.g., Berger 1985). Elicitation methods may be considered with ID models in case no data are available for htting a model. In the 2D situation, elicitation may be used for the parameter uncertainty distribntions. In that situation, it may happen that no kind of relative fre-qnency data wonld be relevant, simply because the distributions represent subjective uncertainty and not relative frequency. 

In conclusion, we believe that error propagation methods like Monte Carlo, Bayesian Monte Carlo, and Ist-order error analysis should be promoted and extensively used in pesticide risk assessments implemented in both the United States and Europe. 

Erdy DM. 1989. The confidence profile method a Bayesian method for assessing health technologies. Operations Res 37 210-228. 

Warren-Hicks WJ, Butcher B. 1996. Monte Carlo analysis classical and Bayesian applications. Human Ecol Risk Assess 2 643-649. 

Bayesian approaches are discussed throughout this book. Unfortunately, because frequentist methods are typically presented in introductory statistics courses, most environmental scientists do not clearly understand the basic premises of Bayesian methods. This lack of understanding could hamper appreciation for Bayesian approaches and delay the adaptation of these valuable methods for analyzing uncertainty in risk assessments. 

Bayesian statistics are applicable to analyzing uncertainty in all phases of a risk assessment. Bayesian or probabilistic induction provides a quantitative way to estimate the plausibility of a proposed causality model (Howson and Urbach 1989), including the causal (conceptual) models central to chemical risk assessment (Newman and Evans 2002). Bayesian inductive methods quantify the plausibility of a conceptual model based on existing data and can accommodate a process of data augmentation (or pooling) until sufficient belief (or disbelief) has been accumulated about the proposed cause-effect model. Once a plausible conceptual model is defined, Bayesian methods can quantify uncertainties in parameter estimation or model predictions (predictive inferences). Relevant methods can be found in numerous textbooks, e.g., Carlin and Louis (2000) and Gelman et al. (1997). 

Bayesian fundamentals are reviewed here because several chapters in this volume apply these methods in complex ways to assessing uncertainty. The goal is to create enough understanding so that methods described in later chapters can be fully appreciated. 

Central to any risk assessment is a model of causality. At the onset, a conceptual model is needed that identifies a plausible cause-effect relationship linking stressor exposure to some effect. Most ecological risk assessments rely heavily on weight-of-evidence or expert opinion methods to foster plausibility of the causal model. Unfortunately, such methods are prone to considerable error (Lane et al. 1987 Hutchinson and Lane 1989 Lane 1989), and attempts to quantify that error are rare. Although seldom used in risk assessment, Bayesian methods can explicitly quantify the plausibility of a causal model. 

For the normal distribution there are analytical solutions allowing the assessment of both FA and HC using frequentist statistics. In contrast, Bayesian solutions are numerical. This highlights the flexibility of the Bayesian approach since it can easily deal with any distribution, which is not always possible with the frequentist approach. 

Newman MC, Evans DA. 2002. Causal inference in risk assessments cognitive idols or Bayesian theory In Newman MC, Roberts M, Hale R, editors. Coastal and estuarine risk assessment. Boca Raton (FL) CRC Press, p 73-96. 

Determine whether there are more cost-effective alternatives to additional data generation and risk assessment refinements. What-if analyses can be used to examine the savings in risk management that might result from additional data generation. Techniques that may be suitable for this include Bayesian Monte Carlo and expected value of information (EVOI) analysis (Dakins et al. 1996). 

Regardless of the method used, the basis of the final risk characterization must be explicit. All components and sources of evidence should be described. The explicit linkage between the analysis results and the assessment endpoints must be clearly but adequately stated. Tandem presentation of conventional methods (e.g., ad hoc weight of evidence) and formal methods (e.g., Bayesian, meta-anal-ysis) are recommended to enhance understanding. This is intended to facilitate acceptance of unfamiliar approaches, not to imply that the conventional methods are a touchstone. 

Methods for evaluating the performance and utility of uncertainty analysis in the context of probabilistic pesticide assessments are needed. This should include comparisons between assessment outputs and existing field data (e.g., avian field studies) to evaluate whether decision makers can rely on the assessment methods. Consideration should also be given to existing field data to refine generic assessment models, using Bayesian updating methods. 

Brrmeau, P. and McElroy, N.R. (2006) logD(7.4) modeling using Bayesian regularized neural networks. Assessment and correction of the errors of prediction. Journal of Chemical Information and Modeling, 46, 1379-1387. 

Expand modeling approaches and case examples in which nonsteady-state biomonitoring data are simulated to explore the exposure conditions responsible for biomonitoring results this may provide exposure estimates that can be used in risk assessment (for example, Bayesian inference techniques and population behavior-exposure models). 

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