Predictive confidence

Blood pressure numbers previously considered normal in the United States are now given the new designation prehypertension. Doctors began using that term in 2003 to denote patients whose seemingly okay levels predicted problems down the road. There s our crystal ball again. Doctors can now predict confidently those who will develop full-blown hypertension in the years to come. 

An optimal control strategy for batch processes using particle swam optimisation (PSO) and stacked neural networks is presented in this paper. Stacked neural networks are used to improve model generalisation capability, as well as provide model prediction confidence bounds. In order to improve the reliability of the calculated optimal control policy, an additional term is introduced in the optimisation objective function to penalise wide model prediction confidence bounds. PSO can cope with multiple local minima and could generally find the global minimum. Application to a simulated fed-batch process demonstrates that the proposed technique is very effective. 

A method to overcome the impact of model plant mismatch on optimisation performance was previously investigated by Zhang [8] where model prediction confidence bormds are incorporated as a penalty in the objective function. Therefore, the objective function can be modified as... 

The study demonstrates that particle swam optimisation is a powerful optimisation technique, especially when the objective function has several local rninirna. Conventional optimisation techniques could be trapped in local minima but PSO could in general find the global rninimrun. Stacked neural networks can not only given better prediction performance but also provide model prediction confidence bounds. In order to improve the reliability of neural network model based optimisation, an additional term is introduced in the optimisation objective to penalize wide model prediction confidence bormd. The proposed technique is successfully demonstrated on a simulated fed-batch reactor. 

The importance of validation has been generally acknowledged, and most QSAR models in the literature are validated either by cross validation or external test sets [13,46]. Model validation for classification models is typically specified by statistical quality measures of overall quality such as sensitivity, specificity, false positives, false negatives, and overall prediction. Unfortunately, it is often impossible to specify accuracy and prediction confidence for individual unknown chemicals, specifically those unknown chemicals with structures requiring the model to extend to, or beyond, the limits of chemistry space defined by the training set. 

Applicability Domain for DT-Based Models We describe applicability domain for QSAR models as being determined by two parameters (1) prediction confidence, or the certainty of a prediction for an unknown chemical, and (2) domain extrapolation, or the prediction accuracy of an unknown chemical that lies beyond the chemical space of the training set [60]. Both parameters can be quantitatively estimated in the consensus tree approaches, where individual models are constructed as DTs. Taken together, prediction confidence and domain extrapolation assess the applicability domain of a model for each prediction. 

A model s limitations should be assessed from three different perspectives (1) overall model predictivity (model validation), (2) individual prediction confidence (applicability domain), and (3) chance correlation. These attributes can be more readily assessed in the consensus tree modeling such as the DF method than in other QSAR methods. Using DF as an example, we have found the following ... 

The prediction confidence and domain extrapolation can be readily calculated and constitute the definition of the applicability domain for DF. 

Tong W, Xie Q, Hong H, Shi LM, Fang H, Perkins R. Assessment of prediction confidence and domain extrapolation of two structure-activity relationship models for predicting estrogen receptor binding activity. Environ Health Perspect 2004 112 1249-54. 

Predicted confidence intervals for treatment differences Section 7.4.3.2 outlined estimation of treatment differences by calculating a CI for the true difference between the treatments. It is possible to predict how wide such a CI will be when considering the issue of study size. Goodman and Berlin derived a simple equation which enables this calculation to be performed. 

Goodman SN, Berlin JA. The use of predicted confidence intervals when planning experiments and the misuse of power when interpreting results. Intern Med... 

This chapter is written primarily for a reader who wishes to carry out a low-water biotransformation, and requires some general advice on the selection of reaction conditions. It will be a long time before our understanding of these systems is sufficient to predict confidently the optimal conditions for a novel reaction. Of course, we cannot do this for an aqueous biotransformation, or, for that matter, most non-enzymic chemical transformations. However, it is possible to give recommenda-... 

To demonstrate this we use the simple example that was introduced in chapter 4, that of solubility in a mixed surfactant system. The treatment is in two stages, the first being a intuitive rather than mathematical demonstration of testing for lack of fit and curvature of a response surface. Then, in section Il.B, we will carry out a more detailed, statistical analysis of the same process, showing how prediction confidence limits are calculated and the use of ANOVA in validating a model. 

The use of LCM processes in the civil engineering industry is just in its infancy. The main hindrance to their wider use is a lack of knowledge of the behaviour of composite materials, and the mistrust of these materials due to bad experiences with the use of less repeatable processes such as wet hand lay-up or spraying of chopped fibres. However, advanced manufacturing methods such as LCM processes can allow a much improved repeatability of construction, and the mechanical performance can thus be accurately characterised and predicted. Confidence in the use of composites will also grow with growing use and experience. 

The 100( 1 —a)% predictive confidence intervals, that is, the region within which the actual value will lie 100(1—a)% of the time, for the point Xd is given by... 

---