Determination of the Joint Confidence Region of Optimal Operating Conditions in Robust Design by Bootstrap Technique

Robust design has been widely recognized as a leading method in reducing variability and improving quality. Most of the engineering statistics literature mainly focuses on finding "point estimates" of the optimum operating conditions for robust design. Various procedures for calculating point estimates of the optimum operating conditions are considered. Although this point estimation procedure is important for continuous quality improvement, the immediate question is "how accurate are these optimum operating conditions?" The answer for this is to consider interval estimation for a single variable or joint confidence regions for multiple variables. In this paper, with the help of the bootstrap technique, we develop procedures for obtaining joint "confidence regions" for the optimum operating conditions. Two different procedures using Bonferroni and multivariate normal approximation are introduced. The proposed methods are illustrated and substantiated using a numerical example.Comment: Two tables, Three figure

Synthetic LISA: Simulating Time Delay Interferometry in a Model LISA

We report on three numerical experiments on the implementation of Time-Delay Interferometry (TDI) for LISA, performed with Synthetic LISA, a C++/Python package that we developed to simulate the LISA science process at the level of scientific and technical requirements. Specifically, we study the laser-noise residuals left by first-generation TDI when the LISA armlengths have a realistic time dependence; we characterize the armlength-measurements accuracies that are needed to have effective laser-noise cancellation in both first- and second-generation TDI; and we estimate the quantization and telemetry bitdepth needed for the phase measurements. Synthetic LISA generates synthetic time series of the LISA fundamental noises, as filtered through all the TDI observables; it also provides a streamlined module to compute the TDI responses to gravitational waves according to a full model of TDI, including the motion of the LISA array and the temporal and directional dependence of the armlengths. We discuss the theoretical model that underlies the simulation, its implementation, and its use in future investigations on system characterization and data-analysis prototyping for LISA.Comment: 18 pages, 14 EPS figures, REVTeX 4. Accepted PRD version. See http://www.vallis.org/syntheticlisa for information on the Synthetic LISA software packag

A Bayesian spatio-temporal model of panel design data: airborne particle number concentration in Brisbane, Australia

This paper outlines a methodology for semi-parametric spatio-temporal modelling of data which is dense in time but sparse in space, obtained from a split panel design, the most feasible approach to covering space and time with limited equipment. The data are hourly averaged particle number concentration (PNC) and were collected, as part of the Ultrafine Particles from Transport Emissions and Child Health (UPTECH) project. Two weeks of continuous measurements were taken at each of a number of government primary schools in the Brisbane Metropolitan Area. The monitoring equipment was taken to each school sequentially. The school data are augmented by data from long term monitoring stations at three locations in Brisbane, Australia. Fitting the model helps describe the spatial and temporal variability at a subset of the UPTECH schools and the long-term monitoring sites. The temporal variation is modelled hierarchically with penalised random walk terms, one common to all sites and a term accounting for the remaining temporal trend at each site. Parameter estimates and their uncertainty are computed in a computationally efficient approximate Bayesian inference environment, R-INLA. The temporal part of the model explains daily and weekly cycles in PNC at the schools, which can be used to estimate the exposure of school children to ultrafine particles (UFPs) emitted by vehicles. At each school and long-term monitoring site, peaks in PNC can be attributed to the morning and afternoon rush hour traffic and new particle formation events. The spatial component of the model describes the school to school variation in mean PNC at each school and within each school ground. It is shown how the spatial model can be expanded to identify spatial patterns at the city scale with the inclusion of more spatial locations.Comment: Draft of this paper presented at ISBA 2012 as poster, part of UPTECH projec

Application of Bayesian model averaging to measurements of the primordial power spectrum

Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for assessing parameter uncertainties in situations where there is also uncertainty in the underlying model. We apply model averaging to the estimation of the parameters associated with the primordial power spectra of curvature and tensor perturbations. We use CosmoNest and MultiNest to compute the model Evidences and posteriors, using cosmic microwave data from WMAP, ACBAR, BOOMERanG and CBI, plus large-scale structure data from the SDSS DR7. We find that the model-averaged 95% credible interval for the spectral index using all of the data is 0.940 < n_s < 1.000, where n_s is specified at a pivot scale 0.015 Mpc^{-1}. For the tensors model averaging can tighten the credible upper limit, depending on prior assumptions.Comment: 7 pages with 7 figures include

Retrodiction as a tool for micromaser field measurements

We use retrodictive quantum theory to describe cavity field measurements by successive atomic detections in the micromaser. We calculate the state of the micromaser cavity field prior to detection of sequences of atoms in either the excited or ground state, for atoms that are initially prepared in the excited state. This provides the POM elements, which describe such sequences of measurements.Comment: 20 pages, 4(8) figure

Redshifts and Velocity Dispersions of Galaxy Clusters in the Horologium-Reticulum Supercluster

We present 118 new optical redshifts for galaxies in 12 clusters in the Horologium-Reticulum supercluster (HRS) of galaxies. For 76 galaxies, the data were obtained with the Dual Beam Spectrograph on the 2.3m telescope of the Australian National University at Siding Spring Observatory. After combining 42 previously unpublished redshifts with our new sample, we determine mean redshifts and velocity dispersions for 13 clusters, in which previous observational data were sparse. In six of the 13 clusters, the newly determined mean redshifts differ by more than 750 km/s from the published values. In the case of three clusters, A3047, A3109, and A3120, the redshift data indicate the presence of multiple components along the line of sight. The new cluster redshifts, when combined with other reliable mean redshifts for clusters in the HRS, are found to be distinctly bi-modal. Furthermore, the two redshift components are consistent with the bi-modal redshift distribution found for the inter-cluster galaxies in the HRS by Fleenor et al. (2005).Comment: 13 pages, 3 figures, Accepted to A

Design and analysis of fractional factorial experiments from the viewpoint of computational algebraic statistics

We give an expository review of applications of computational algebraic statistics to design and analysis of fractional factorial experiments based on our recent works. For the purpose of design, the techniques of Gr\"obner bases and indicator functions allow us to treat fractional factorial designs without distinction between regular designs and non-regular designs. For the purpose of analysis of data from fractional factorial designs, the techniques of Markov bases allow us to handle discrete observations. Thus the approach of computational algebraic statistics greatly enlarges the scope of fractional factorial designs.Comment: 16 page

The Kinetic Sunyaev-Zel'dovich Effect from Radiative Transfer Simulations of Patchy Reionization

We present the first calculation of the kinetic Sunyaev-Zel'dovich (kSZ) effect due to the inhomogeneous reionization of the universe based on detailed large-scale radiative transfer simulations of reionization. The resulting sky power spectra peak at l=2000-8000 with maximum values of l^2C_l~1\times10^{-12}. The peak scale is determined by the typical size of the ionized regions and roughly corresponds to the ionized bubble sizes observed in our simulations, ~5-20 Mpc. The kSZ anisotropy signal from reionization dominates the primary CMB signal above l=3000. This predicted kSZ signal at arcminute scales is sufficiently strong to be detectable by upcoming experiments, like the Atacama Cosmology Telescope and South Pole Telescope which are expected to have ~1' resolution and ~muK sensitivity. The extended and patchy nature of the reionization process results in a boost of the peak signal in power by approximately one order of magnitude compared to a uniform reionization scenario, while roughly tripling the signal compared with that based upon the assumption of gradual but spatially uniform reionization. At large scales the patchy kSZ signal depends largely on the ionizing source efficiencies and the large-scale velocity fields: sources which produce photons more efficiently yield correspondingly higher signals. The introduction of sub-grid gas clumping in the radiative transfer simulations produces significantly more power at small scales, and more non-Gaussian features, but has little effect at large scales. The patchy nature of the reionization process roughly doubles the total observed kSZ signal for l~3000-10^4 compared to non-patchy scenarios with the same total electron-scattering optical depth.Comment: 14 pages, 13 figures (some in color), submitted to Ap

Retrodiction with two-level atoms: atomic previvals

In the Jaynes-Cummings model a two-level atom interacts with a single-mode electromagnetic field. Quantum mechanics predicts collapses and revivals in the probability that a measurement will show the atom to be excited at various times after the initial preparation of the atom and field. In retrodictive quantum mechanics we seek the probability that the atom was prepared in a particular state given the initial state of the field and the outcome of a later measurement on the atom. Although this is not simply the time reverse of the usual predictive problem, we demonstrate in this paper that retrodictive collapses and revivals also exist. We highlight the differences between predictive and retrodictive evolutions and describe an interesting situation where the prepared state is essentially unretrodictable.Comment: 15 pages, 3 (5) figure

Causal connectivity of evolved neural networks during behavior

To show how causal interactions in neural dynamics are modulated by behavior, it is valuable to analyze these interactions without perturbing or lesioning the neural mechanism. This paper proposes a method, based on a graph-theoretic extension of vector autoregressive modeling and 'Granger causality,' for characterizing causal interactions generated within intact neural mechanisms. This method, called 'causal connectivity analysis' is illustrated via model neural networks optimized for controlling target fixation in a simulated head-eye system, in which the structure of the environment can be experimentally varied. Causal connectivity analysis of this model yields novel insights into neural mechanisms underlying sensorimotor coordination. In contrast to networks supporting comparatively simple behavior, networks supporting rich adaptive behavior show a higher density of causal interactions, as well as a stronger causal flow from sensory inputs to motor outputs. They also show different arrangements of 'causal sources' and 'causal sinks': nodes that differentially affect, or are affected by, the remainder of the network. Finally, analysis of causal connectivity can predict the functional consequences of network lesions. These results suggest that causal connectivity analysis may have useful applications in the analysis of neural dynamics