Designing experiments for estimating an appropriate outlet size for a silo type problem

The problem of jam formation during the discharge by gravity of granular material through a two-dimensional silo has a number of practical applications. In many problems the estimation of the minimum outlet size which guarantees that the time to the next jamming event is long enough is crucial. Assuming that the time is modeled by an exponential distribution with two unknown parameters, this goal translates to the optimal estimation of a non-linear transformation of the parameters. We obtain $c$-optimum experimental designs with that purpose, applying the graphic Elfving method. Since the optimal designs depend on the nominal values of the parameters, a sensitivity study is additionally provided. Finally, a simulation study checks the performance of the approximations made, first with the Fisher Information matrix, then with the linearization of the function to be estimated. The results are useful for experimenting in a laboratory and translating then the results to a larger scenario. Apart from the application a general methodology is developed in the paper for the problem of precise estimation of a one-dimensional parametric transformation in a non-linear model

Designing experiments for estimating an appropriate outlet size for a silo type problem

The problem of jam formation during the discharge by gravity of granular material through a two-dimensional silo has a number of practical applications. In many problems the estimation of the minimum outlet size which guarantees that the time to the next jamming event is long enough is crucial. Assuming that the time is modeled by an exponential distribution with two unknown parameters, this goal translates to the optimal estimation of a non-linear transformation of the parameters. We obtain $c$-optimum experimental designs with that purpose, applying the graphic Elfving method. Since the optimal designs depend on the nominal values of the parameters, a sensitivity study is additionally provided. Finally, a simulation study checks the performance of the approximations made, first with the Fisher Information matrix, then with the linearization of the function to be estimated. The results are useful for experimenting in a laboratory and translating then the results to a larger scenario. Apart from the application a general methodology is developed in the paper for the problem of precise estimation of a one-dimensional parametric transformation in a non-linear model.Comment: 11 Figure

A comparison of general-purpose optimization algorithms forfinding optimal approximate experimental designs

Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs

Comparison of seven prognostic tools to identify low-risk pulmonary embolism in patients aged <50 years

publishersversionPeer reviewe

Optimal designs for longitudinal studies with fractional polynomial models

Fractional polynomials (FP) have been shown to be much more flexible than polynomials for fitting continuous outcomes in the biological and health sciences. Despite their increasing popularity, design issues for FP models have never been addressed. D- and I-optimal experimental designs will be computed for prediction using FP models. Their properties will be evaluated and a catalogue of design points useful for FP models will be provided. As applications, we consider linear mixed effects models for longitudinal studies. To provide greater flexibility in modeling the shape of the response, we use fractional polynomials and not polynomials to approximate the mean response. An example using gene expression data will be considered comparing the designs used in practice. An additional an interesting problem is finding designs for effective model discrimination for FP models. This will be explored from the KL-optimality point of view.Non UBCUnreviewedAuthor affiliation: University of NavarreFacult

Minimax designs for a particolar parametrization of binary response models

Maximum variance (MV) and Standarized maximum variance (SMV) optimum designs for binary response models have already been studied in the literature. In this work, some theoretical results, useful for researchers working on a specific binary model, are given. The MV- and SMV-optimum designs are also compared with a classical real-life design and with other optimum designs. These comparisons are possible because of explicit formulas for local optimum designs and their efficiencies computed here

Bayesian optimal designs for discriminating between non-Normal models

Designs are found for discriminating between two non-Normal models in the presence of prior information. The KL-optimality criterion, where the true model is assumed to be completely known, is extended to a criterion where prior distributions of the parameters and a prior probability of each model to be true are assumed. Concavity of this criterion is proved. Thus, the results of optimal design theory apply in this context and optimal designs can be constructed and checked by the General Equivalence Theorem. Some illustrative examples are provided.KL-optimum designs, discrimination between models,

Optimal Designs for Discriminating Between some Extensions of the Michaelis-Menten Model

In this paper some results on the problem of computing optimal designs for discriminating between rival models are provided. Using T-optimality for two rival models a compound criterion is developed to discriminate between more than two models. Surprising results arise when T-optimal designs are compared with classical c-optimal designs for nonlinear models. In particular, some practical deviations of the Michaelis-Menten model are considered in order to measure and compare efficiencies of different designs.Optimal design, compound designs, pharmacokinetic models, T-optimality,