Journal:Informatica
Volume 22, Issue 4 (2011), pp. 537–558
Abstract
The FDA's Quality by Design initiative and associated design space construct (ICH, 2009), have stimulated the use of quantitative methods, mathematical and statistical models, and designed experiments in the process of drug development and manufacture. For a given drug product, the design space may be interpreted as the constrained region of the manufacturing operating variable space within which assurance can be provided that drug product quality specifications will be met. It is now understood, at least conceptually, that this assurance is not deterministic, rather it must be stated in probabilistic terms. In this paper, we report on the use of Bayesian methods to develop a suitable risk metric based on both mathematical and statistical models of the manufacturing processes and product properties. The Bayesian estimation is carried out to determine the joint posterior distribution of the probability of the product meeting quality specifications. The computations are executed using a novel Variational Bayes approximation. In this paper the direct computational approach using this approximation is compared to the widely used but computationally very intensive Markov Chain Monte Carlo method. The approach is illustrated using experimental data and models drawn from a recent QbD study on the drug gabapentin in which the authors were participants.
Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 123–166
Abstract
We consider here the average deviation as the most important objective when designing numerical techniques and algorithms. We call that a Bayesian approach.
We start by describing the Bayesian approach to the continuous global optimization. Then we show how to apply the results to the adaptation of parameters of randomized techniques of optimization. We assume that there exists a simple function which roughly predicts the consequences of decisions. We call it heuristics. We define the probability of a decision by a randomized decision function depending on heuristics. We fix this decision function, except for some parameters that we call the decision parameters.
We repeat the randomized decision procedure several times given the decision parameters and regard the best outcome as a result. We optimize the decision parameters to make the search more efficient. Thus we replace the original optimization problem by an auxiliary problem of continuous stochastic optimization. We solve the auxiliary problem by the Bayesian methods of global optimization. Therefore we call the approach as the Bayesian one.
We discuss the advantages and disadvantages of the Bayesian approach. We describe the applications to some of discrete programming problems, such as optimization of mixed Boolean bilinear functions including the scheduling of batch operations and the optimization of neural networks.
Journal:Informatica
Volume 1, Issue 1 (1990), pp. 71–88
Abstract
In the paper the global optimization is described from the point of an interactive software design. The interactive software that implements numeric methods and other techniques to solve global optimization problems is presented. Some problems of such a software design are formulated and discussed.