DiscrimOD-package: Finding Optimal Discrimination Designs by Hybirdizing...

In PingYangChen/DiscrimOD: DiscrimOD: Finding Optimal Discrimination Designs by Hybridizing Particle Swarm and L-BFGS Algorithms

Description

The **DiscrimOD** package adopts a hybrid algorithm to search for the optimal discrimination designs when there are two or more than two competing models under normal or non-normal error assumption. This hybrid algorithm is chosen to efficiently solve the maximin design criteria in the optimal discrimination design problem which is usually a challenging task. It combines the particle swarm optimization (PSO) algorithm and the L-BFGS algorithm to tackle the outer and inner objectives of the maximin design criterion, respectively. The equivalence theorems for various discrimination criteria are also available for verifying the optimal discrimination designs.

Details

For the case of two competing models with normal errors, the package searches for T-optimal design introduced in Atkinson and Fedorov (1975). That is, we assume one of the competing models to be the true model and the fixed nominal values of the parameters. The another model is called the rival model and its parameter are assumed to be in a specifued parameter space. The T-optimal design maximizes the minimal squared distance between the true and the rival models among the parameter space of the latter.

If the errors are non-normal, the package searches for the KL-optimal design based on Lopez-Fidalgo et al. (2007). The approach is similar except that the distance measure for non-normal models is the Kullback-Leibler (KL) divergence. This package has equipped some commonly used KL-divergence functions for convenient uses and it also allows users to customize the distance measure function by themselves.

When there are more than two competing models, this package searches for the max-min optimal discrimination design in Tommasi et al. (2016). To find the max-min optimal design, we need a two-stpe approach. Similarly, we assume one true model, fix its nominal values and treat the remaining models as rival models. The first step is to identify the T/KL-optimal designs for each pair of true model and one rival model. The second step searches for the max-min optimal discrimination design by maximizing the minimal discriminaiton efficiency among the efficiencies relative to each T/KL-optimal design.

References

Our Discrimination design paper.

Atkinson, A. C. and Fedorov, V. V. (1975). The design of experiments for discriminating between two rival models. Biometrika, 62(1):57-70.

Lopez-Fidalgo, J., Tommasi, C., and Trandafir, P. C. (2007). An optimal experimental design criterion for discriminating between non-normal models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 69(2):231-242.

Tommasi, C., Martin-Martin, R., and Lopez-Fidalgo, J. (2016). Max-min optimal discriminating designs for several statistical models. Statistics and Computing, 26(6):1163-1172.

Eberhart, R. C. and Kennedy, J. (1995). A new optimizer using particle swarm theory. In Proceedings of the sixth international symposium on micro machine and human science, pages 39-43. IEEE.

Nocedal, J. and Wright, S. (2006). Numerical Optimization. Springer.

PingYangChen/DiscrimOD documentation built on Jan. 30, 2022, 5:25 p.m.