Regression Models and Experimental Designs: A Tutorial for Simulation Analaysts

This tutorial explains the basics of linear regression models. especially low-order polynomials. and the corresponding statistical designs. namely, designs of resolution III, IV, V, and Central Composite Designs (CCDs).This tutorial assumes 'white noise', which means that the residuals of the fitted linear regression model are normally, independently, and identically distributed with zero mean.The tutorial gathers statistical results that are scattered throughout the literature on mathematical statistics, and presents these results in a form that is understandable to simulation analysts.metamodels;fractional factorial designs;Plackett-Burman designs;factor interactions;validation;cross-validation

Experimental investigation of consumer price evaluations

We develop a procedure to collect experimental choice data for estimating consumer preferences with a special focus on consumer price evaluations. For this purpose we employ a heteroskedastic mixed logit model that measures the effect of the way prices are specified on the variance of choice. Our procedure is based on optimal design ideas from the statistics literature and on some algorithms for constructing choice designs published in marketing journals. In an empirical application on mobile phone preferences we find evidence that the way prices are specified significantly affects the variance of choice. In a simulation study we show that our design is significantly more efficient than randomly generated designs., which can be regarded as equivalent to most commonly used experimental designs in the literature.heterogeneity;Bayesian design;demand;quasi-random;task complexity

Stochastic Gradient Bayesian Optimal Experimental Designs for Simulation-based Inference

Simulation-based inference (SBI) methods tackle complex scientific models with challenging inverse problems. However, SBI models often face a significant hurdle due to their non-differentiable nature, which hampers the use of gradient-based optimization techniques. Bayesian Optimal Experimental Design (BOED) is a powerful approach that aims to make the most efficient use of experimental resources for improved inferences. While stochastic gradient BOED methods have shown promising results in high-dimensional design problems, they have mostly neglected the integration of BOED with SBI due to the difficult non-differentiable property of many SBI simulators. In this work, we establish a crucial connection between ratio-based SBI inference algorithms and stochastic gradient-based variational inference by leveraging mutual information bounds. This connection allows us to extend BOED to SBI applications, enabling the simultaneous optimization of experimental designs and amortized inference functions. We demonstrate our approach on a simple linear model and offer implementation details for practitioners.Comment: Presented at ICML 2023 workshop on Differentiable Everythin

Helical channel design and technology for cooling of muon beams

Novel magnetic helical channel designs for capture and cooling of bright muon beams are being developed using numerical simulations based on new inventions such as helical solenoid (HS) magnets and hydrogen-pressurized RF (HPRF) cavities. We are close to the factor of a million six-dimensional phase space (6D) reduction needed for muon colliders. Recent experimental and simulation results are presented.Comment: 6 pp. 14th Advanced Accelerator Concepts Workshop 13-19 Jun 2010: Annapolis, Marylan

An experimental evaluation of a loop versus a reference design for two-channel microarrays

Motivation: Despite theoretical arguments that socalled "loop designs" of two-channel DNA microarray experiments are more efficient, biologists keep on using "reference designs". We describe two sets of microarray experiments with RNA from two different biological systems (TPA-stimulated mammalian cells and Streptomyces coelicor). In each case, both a loop and a reference design were performed using the same RNA preparations with the aim to study their relative efficiency. Results: The results of these experiments show that (1) the loop design attains a much higher precision than the reference design, (2) multiplicative spot effects are a large source of variability, and if they are not accounted for in the mathematical model, for example by taking log-ratios or including spot-effects, then the model will perform poorly. The first result is reinforced by a simulation study. Practical recommendations are given on how simple loop designs can be extended to more realistic experimental designs and how standard statistical methods allow the experimentalist to use and interpret the results from loop designs in practice

Simulation of non-linear bearing forces for post-stability investigation

Different types of bearing designs were developed to improve dynamic properties of rotor-bearing systems. Elliptical bearings, multisleeve bearings, tilting pad and other designs such as herringbone groove were utilized to increase resistance to the onset of self excited vibrations. Experimental trials are costly, two alternative methods are used to gain a qualitative insight. The first one creates mathematical model and applies both a digital or an analog computer simulation. The second one investigates phenomena occurring on the laboratory rig with the bearing replaced by an electronic simulating device, working in a feedback loop, which produces forces,which are functions of journal displacement and velocity. The simulated hydrodynamic forces are produced according to assumed characteristics matched to the bearing type. The principal benefit of the analog simulation is that nonlinear characteristics of a subsystem are precisely identified and mathematical methods applied for a wide class of problems are checked on the experimental installation

Validation of the GATE Monte Carlo simulation platform for modelling a CsI(Tl) scintillation camera dedicated to small animal imaging

Monte Carlo simulations are increasingly used in scintigraphic imaging to model imaging systems and to develop and assess tomographic reconstruction algorithms and correction methods for improved image quantitation. GATE (GEANT 4 Application for Tomographic Emission) is a new Monte Carlo simulation platform based on GEANT4 dedicated to nuclear imaging applications. This paper describes the GATE simulation of a prototype of scintillation camera dedicated to small animal imaging and consisting of a CsI(Tl) crystal array coupled to a position sensitive photomultiplier tube. The relevance of GATE to model the camera prototype was assessed by comparing simulated 99mTc point spread functions, energy spectra, sensitivities, scatter fractions and image of a capillary phantom with the corresponding experimental measurements. Results showed an excellent agreement between simulated and experimental data: experimental spatial resolutions were predicted with an error less than 100 mu m. The difference between experimental and simulated system sensitivities for different source-to-collimator distances was within 2%. Simulated and experimental scatter fractions in a [98-182 keV] energy window differed by less than 2% for sources located in water. Simulated and experimental energy spectra agreed very well between 40 and 180 keV. These results demonstrate the ability and flexibility of GATE for simulating original detector designs. The main weakness of GATE concerns the long computation time it requires: this issue is currently under investigation by the GEANT4 and the GATE collaboration

Experimental designs for multiple-level responses, with application to a large-scale educational intervention

Educational research often studies subjects that are in naturally clustered groups of classrooms or schools. When designing a randomized experiment to evaluate an intervention directed at teachers, but with effects on teachers and their students, the power or anticipated variance for the treatment effect needs to be examined at both levels. If the treatment is applied to clusters, power is usually reduced. At the same time, a cluster design decreases the probability of contamination, and contamination can also reduce power to detect a treatment effect. Designs that are optimal at one level may be inefficient for estimating the treatment effect at another level. In this paper we study the efficiency of three designs and their ability to detect a treatment effect: randomize schools to treatment, randomize teachers within schools to treatment, and completely randomize teachers to treatment. The three designs are compared for both the teacher and student level within the mixed model framework, and a simulation study is conducted to compare expected treatment variances for the three designs with various levels of correlation within and between clusters. We present a computer program that study designers can use to explore the anticipated variances of treatment effects under proposed experimental designs and settings.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS216 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org