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

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

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

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

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

Optical, physical and chemical characteristics of Australian continental aerosols: results from a field experiment

Mineral dust is one of the major components of the world's aerosol mix, having a number of impacts within the Earth system. However, the climate forcing impact of mineral dust is currently poorly constrained, with even its sign uncertain. As Australian deserts are more reddish than those in the Northern Hemisphere, it is important to better understand the physical, chemical and optical properties of this important aerosol. We have investigated the properties of Australian desert dust at a site in SW Queensland, which is strongly influenced by both dust and biomass burning aerosol. &lt;br&gt;&lt;br&gt; Three years of ground-based monitoring of spectral optical thickness has provided a statistical picture of gross aerosol properties. The aerosol optical depth data showed a clear though moderate seasonal cycle with an annual mean of 0.06 &amp;plusmn; 0.03. The Angstrom coefficient showed a stronger cycle, indicating the influence of the winter-spring burning season in Australia's north. AERONET size distributions showed a generally bimodal character, with the coarse mode assumed to be mineral dust, and the fine mode a mixture of fine dust, biomass burning and marine biogenic material. &lt;br&gt;&lt;br&gt; In November 2006 we undertook a field campaign which collected 4 sets of size-resolved aerosol samples for laboratory analysis – ion beam analysis and ion chromatography. Ion beam analysis was used to determine the elemental composition of all filter samples, although elemental ratios were considered the most reliable output. Scatter plots showed that Fe, Al and Ti were well correlated with Si, and Co reasonably well correlated with Si, with the Fe/Al ratio somewhat higher than values reported from Northern Hemisphere sites (as expected). Scatter plots for Ca, Mn and K against Si showed clear evidence of a second population, which in some cases could be identified with a particular sample day or size fraction. These data may be used to attempt to build a signature of soil in this region of the Australian interior. &lt;br&gt;&lt;br&gt; Ion chromatography was used to quantify water soluble ions for 2 of our sample sets, complementing the picture provided by ion beam analysis. The strong similarities between the MSA and SO&lt;sub&gt;4&lt;/sub&gt;&lt;sup&gt;2&amp;minus;&lt;/sup&gt; size distributions argue strongly for a marine origin of much of the SO&lt;sub&gt;4&lt;/sub&gt;&lt;sup&gt;2&amp;minus;&lt;/sup&gt;. The similarity of the Na&lt;sup&gt;+&lt;/sup&gt;, Cl&lt;sup&gt;&amp;minus;&lt;/sup&gt; and Mg&lt;sup&gt;2+&lt;/sup&gt; size distributions also argue for a marine contribution. Further, we believe that both NO&lt;sub&gt;3&lt;/sub&gt;&lt;sup&gt;&amp;minus;&lt;/sup&gt; and NH&lt;sub&gt;4&lt;/sub&gt;&lt;sup&gt;+&lt;/sup&gt; are the result of surface reactions with appropriate gases

Role of loop entropy in the force induced melting of DNA hairpin

Dynamics of a single stranded DNA, which can form a hairpin have been studied in the constant force ensemble. Using Langevin dynamics simulations, we obtained the force-temperature diagram, which differs from the theoretical prediction based on the lattice model. Probability analysis of the extreme bases of the stem revealed that at high temperature, the hairpin to coil transition is entropy dominated and the loop contributes significantly in its opening. However, at low temperature, the transition is force driven and the hairpin opens from the stem side. It is shown that the elastic energy plays a crucial role at high force. As a result, the phase diagram differs significantly with the theoretical prediction.Comment: 9 pages, 8 figures; J. Chem. Phys (2011

Modeling and Optimization of Lactic Acid Synthesis by the Alkaline Degradation of Fructose in a Batch Reactor

The present work deals with the determination of the optimal operating conditions of lactic acid synthesis by the alkaline degradation of fructose. It is a complex transformation for which detailed knowledge is not available. It is carried out in a batch or semi-batch reactor. The ‘‘Tendency Modeling’’ approach, which consists of the development of an approximate stoichiometric and kinetic model, has been used. An experimental planning method has been utilized as the database for model development. The application of the experimental planning methodology allows comparison between the experimental and model response. The model is then used in an optimization procedure to compute the optimal process. The optimal control problem is converted into a nonlinear programming problem solved using the sequencial quadratic programming procedure coupled with the golden search method. The strategy developed allows simultaneously optimizing the different variables, which may be constrained. The validity of the methodology is illustrated by the determination of the optimal operating conditions of lactic acid production