Abhyuday Mandal

Multi-objective optimal experimental designs for event-related fMRI studies

In this article, we propose an efficient approach to find optimal experimental designs for event-related functional magnetic resonance imaging (ER-fMRI). We consider multiple objectives, including estimating the hemodynamic response function (HRF), detecting activation, circumventing psychological confounds and fulfilling customized requirements. Taking into account these goals, we formulate a family of multi-objective design criteria and develop a genetic-algorithm-based technique to search for optimal designs. Our proposed technique incorporates existing knowledge about the performance of fMRI designs, and its usefulness is shown through simulations. Although our approach also works for other linear combinations of parameters, we primarily focus on the case when the interest lies either in the individual stimulus effects or in pairwise contrasts between stimulus types. Under either of these popular cases, our algorithm outperforms the previous approaches. We also find designs yielding higher estimation efficiencies than m-sequences. When the underlying model is with white noise and a constant nuisance parameter, the stimulus frequencies of the designs we obtained are in good agreement with the optimal stimulus frequencies derived by Liu and Frank, 2004, NeuroImage 21: 387-400. In addition, our approach is built upon a rigorous model formulation.

Model Selection by Testing for the Presence of Small-Area Effects, and Application to Area-Level Data

The models used in small-area inference often involve unobservable random effects. While this can significantly improve the adaptivity and flexibility of a model, it also increases the variability of both point and interval estimators. If we could test for the existence of the random effects, and if the test were to show that they were unlikely to be present, then we would arguably not need to incorporate them into the model, and thus could significantly improve the precision of the methodology. In this article we suggest an approach of this type. We develop simple bootstrap methods for testing for the presence of random effects, applicable well beyond the conventional context of the natural exponential family. If the null hypothesis that the effects are not present is not rejected then our general methodology immediately gives us access to estimators of unknown model parameters and estimators of small-area means. Such estimators can be substantially more effective, for example, because they enjoy much faster convergence rates than their counterparts when the model includes random effects. If the null hypothesis is rejected then the next step is either to make the model more elaborate (our methodology is available quite generally) or to turn to existing random effects models. This article has supplementary material online.

Estimation of Process Parameters to Determine the Optimum Diagnosis Interval for Control of Defective Items

The online quality monitoring procedure for attributes proposed by Taguchi has been critically studied and extended by a few researchers. Determination of the optimum diagnosis interval requires estimation of some parameters related to the process failure mechanism. Improper estimates of these parameters may lead to an incorrect choice of the diagnosis interval and thus huge economic penalties. We propose a Bayesian approach to estimate the process parameters under two different process models, commonly called as the case II and case III models in the literature. We discuss a systematic way to use available engineering knowledge in eliciting the prior for the parameters, and demonstrate the performance of the proposed method using extensive simulation and a case study from a hot rolling mill.

Small Area Estimation With Uncertain Random Effects

Random effects models play an important role in model-based small area estimation. Random effects account for any lack of fit of a regression model for the population means of small areas on a set of explanatory variables. In a recent article, Datta, Hall, and Mandal showed that if the random effects can be dispensed with via a suitable test, then the model parameters and the small area means may be estimated with substantially higher accuracy. The work of Datta, Hall, and Mandal is most useful when the number of small areas, m, is moderately large. For large m, the null hypothesis of no random effects will likely be rejected. Rejection of the null hypothesis is usually caused by a few large residuals signifying a departure of the direct estimator from the synthetic regression estimator. As a flexible alternative to the Fay–Herriot random effects model and the approach in Datta, Hall, and Mandal, in this article we consider a mixture model for random effects. It is reasonably expected that small areas with population means explained adequately by covariates have little model error, and the other areas with means not adequately explained by covariates will require a random component added to the regression model. This model is a useful alternative to the usual random effects model and the data determine the extent of lack of fit of the regression model for a particular small area, and include a random effect if needed. Unlike the Datta, Hall, and Mandal approach which recommends excluding random effects from all small areas if a test of null hypothesis of no random effects is not rejected, the present model is more flexible. We used this mixture model to estimate poverty ratios for 5–17-year-old-related children for the 50 U.S. states and Washington, DC. This application is motivated by the SAIPE project of the U.S. Census Bureau. We empirically evaluated the accuracy of the direct estimates and the estimates obtained from our mixture model and the Fay–Herriot random effects model. These empirical evaluations and a simulation study, in conjunction with a lower posterior variance of the new estimates, show that the new estimates are more accurate than both the frequentist and the Bayes estimates resulting from the standard Fay–Herriot model. Supplementary materials for this article are available online.

OPTIMAL DESIGNS FOR 2(k) FACTORIAL EXPERIMENTS WITH BINARY RESPONSE.

We consider the problem of obtaining D-optimal designs for factorial experiments with a binary response and

D-optimal Factorial Designs under Generalized Linear Models

k

Maximin and maximin-efficient event-related fMRI designs under a nonlinear model

qualitative factors each at two levels. We obtain a characterization for a design to be locally D-optimal. Based on this characterization, we develop efficient numerical techniques to search for locally D-optimal designs. Using prior distributions on the parameters, we investigate EW D-optimal designs, which are designs that maximize the determinant of the expected information matrix. It turns out that these designs can be obtained very easily using our algorithm for locally D-optimal designs and are very good surrogates for Bayes D-optimal designs. We also investigate the properties of fractional factorial designs and study the robustness with respect to the assumed parameter values of locally D-optimal designs.

Efficient Designs for Event-Related Functional Magnetic Resonance Imaging with Multiple Scanning Sessions

Generalized linear models (GLMs) have been used widely for modeling the mean response both for discrete and continuous random variables with an emphasis on categorical response. Recently Yang, Mandal and Majumdar (2013) considered full factorial and fractional factorial locally D-optimal designs for binary response and two-level experimental factors. In this article, we extend their results to a general setup with response belonging to a single-parameter exponential family and for multilevel predictors.

d-QPSO: A Quantum-Behaved Particle Swarm Technique for Finding D-Optimal Designs with Discrete and Continuous Factors and a Binary Response

Previous studies on event-related functional magnetic resonance imaging experimental designs are primarily based on linear models, in which a known shape of the hemodynamic response function (HRF) is assumed. However, the HRF shape is usually uncertain at the design stage. To address this issue, we consider a nonlinear model to accommodate a wide spectrum of feasible HRF shapes, and propose efficient approaches for obtaining maximin and maximin-efficient designs. Our approaches involve a reduction in the parameter space and a search algorithm that helps to efficiently search over a restricted class of designs for good designs. The obtained designs are compared with traditional designs widely used in practice. We also demonstrate the usefulness of our approaches via a motivating example.

Antibacterial and Drug Elution Performance of Thermoplastic Blends

Event-related functional magnetic resonance imaging (ER-fMRI) is a leading technology for studying brain activity in response to mental stimuli. Due to the popularity and high cost of this pioneering technology, efficient experimental designs are in great demand. However, the complex nature of ER-fMRI makes it difficult to obtain such designs; it requires careful consideration regarding both statistical and practical issues as well as major computational efforts. In this article, we obtain efficient designs for ER-fMRI. In contrast to previous studies, we take into account a common practice where subjects undergo multiple scanning sessions in an experiment. To the best of our knowledge, this important reality has never been studied systematically for design selection. We compare several approaches to obtain efficient designs and propose a novel algorithm for this problem. Our simulation results indicate that, using our algorithm, highly efficient designs can be obtained.