Design Of Experiments For Discrimination Research Articles

Sequential Markov Chain Monte Carlo (MCMC) model discrimination

AbstractIn this paper a new approach to model discrimination is presented that takes advantage of Markov Chain Monte Carlo (MCMC) methods. It combines an experimental criterion first proposed by Roth (Roth, Design of Experiments for Discrimination Among rival Models, PhD, Thesis, Princeton University, New Jersey, USA, 1965) with an adaptation of a model selection method described by Chib and Jeliazkov [Chib and Jeliazkov, Stat. Neerl. 59, 30–44 (2005)], which uses an Acceptance–Rejection Metropolis–Hastings algorithm to evaluate the model marginal likelihood thus enabling the calculation of model posterior probabilities. It does so without requiring any linearisation of nonlinear models. In designing model discrimination experiments using the Roth criterion, MCMC methods are again used to find the mean of the predicted values by integrating over the entire parameter probability density function. The method is illustrated using the well‐known chemical reaction kinetics example first discussed by Box and Hill [Box and Hill, Technometrics 9, 57–71 (1967)]. The results indicate that the method is very successful in identifying the correct model. Higher error levels and more complex kinetics require on average more model discrimination experiments. © 2012 Canadian Society for Chemical Engineering

Design of experiments for discrimination of rival models based on the expected number of eliminated models

This work presents a new design criterion for discrimination of rival models, taking into account the number of models that are expected to be discriminated after execution of the experimental design (ξ⁎). The potential for model discrimination at ξ⁎ can be calculated by assuming that model m is the true one. In this case, responses can be predicted with model m at ξ⁎, parameters of the remaining models can be re-estimated and model adequacy tests can be performed in order to compute the number of discriminated models. Since several rival models are considered simultaneously and the true model is not known a priori, the potential for model discrimination at ξ⁎ should be evaluated for pair-wise comparisons of the plausible models. As a consequence, Maxmin, Bayesian or Equal Model Weights optimization criteria must be adopted to select the best experimental conditions in the Pareto set for discrimination of rival models within the scope of a sequential design procedure. The proposed approach leads to formulation of an informative design criterion, where the discriminant value can be easily interpreted in terms of the expected number of eliminated models.

Development of an optimized random amplified polymorphic DNA protocol for fingerprinting of Klebsiella pneumoniae

To develop an optimized random amplified polymorphic DNA (RAPD) protocol for fingerprinting clinical isolates of Klebsiella pneumoniae. Employing factorial design of experiments, repeatable amplification patterns were obtained for 54 nosocomial isolates using 1 μmol 1(-1) primer, 4 mmol 1(-1) MgCl(2), 0·4 mmol 1(-1) dNTPs, 2·5 U Taq DNA polymerase and 90 ng DNA template in a total volume of 25 μl. The optimum thermocycling program was: initial denaturation at 94°C for 4 min followed by 50 cycles of 1 min at 94°C, 2 min at 34°C, 2 min at 72°C and a final extension at 72°C for 10 min. The optimized RAPD protocol was highly discriminatory (Simpson's diversity index, 0·982), and all isolates were typable with repeatable patterns (Pearson's similarity coefficient ≈ 100%). Seven main clusters were obtained on a similarity level of 70% and 32 distinct clusters on a similarity level of 85%, reflecting the heterogeneity of the isolates. Systematic optimization of RAPD generated reliable DNA fingerprints for nosocomial isolates of K. pneumoniae. This is the first report on RAPD optimization based on factorial design of experiments for discrimination of K. pneumoniae.

Nonlinear regression methods in design of experiments and mathematical modelling. Applications to the analysis of the steady-state kinetics of glutathione reductase

A branching reaction pathway involving a ping pong and a sequential loop has been proposed for glutathione reductase (Biochem. Biophys. Res. Commun. 53 (1973) 1151). In the present investigation nonlinear regression methods have been applied in the fitting of rate equations to experimental data to test the validity of the model proposed and to discriminate between alternative mathematical models (cf. FEBS Lett. 26 (1972) 252). In the best rate law, some of the parameters were numerically redundant. Therefore, a feature-wise analysis of the rate equation was carried out by varying one substrate concentration at a time. The overall strategy used was a cyclic procedure involving: experimentation — analysis of data — modelling — design of experiments — new experimentation etc. Consideration was given to the experimental error structure and to the importance of weighting in the regression analysis. In the design of experiments for discrimination between rival models, a previously defined discrimination function was used. The results of the analysis support the branching reaction scheme proposed for glutathione reductase.