Combining expert opinions in prior elicitation

We consider the problem of combining opinions from different experts in an explicitly model-based way to construct a valid subjective prior in a Bayesian statistical approach. We propose a generic approach by considering a hierarchical model accounting for various sources of variation as well as accounting for potential dependence between experts. We apply this approach to two problems. The first problem deals with a food risk assessment problem involving modelling dose-response for Listeria monocytogenes contamination of mice. Two hierarchical levels of variation are considered (between and within experts) with a complex mathematical situation due to the use of an indirect probit regression. The second concerns the time taken by PhD students to submit their thesis in a particular school. It illustrates a complex situation where three hierarchical levels of variation are modelled but with a simpler underlying probability distribution (log-Normal).

Optimal Bayesian experimental design for models with intractable likelihoods using indirect inference applied to biological process models

This paper addresses the problem of determining optimal designs for biological process models with intractable likelihoods, with the goal of parameter inference. The Bayesian approach is to choose a design that maximises the mean of a utility, and the utility is a function of the posterior distribution. Therefore, its estimation requires likelihood evaluations. However, many problems in experimental design involve models with intractable likelihoods, that is, likelihoods that are neither analytic nor can be computed in a reasonable amount of time. We propose a novel solution using indirect inference (II), a well established method in the literature, and the Markov chain Monte Carlo (MCMC) algorithm of Müller et al. (2004). Indirect inference employs an auxiliary model with a tractable likelihood in conjunction with the generative model, the assumed true model of interest, which has an intractable likelihood. Our approach is to estimate a map between the parameters of the generative and auxiliary models, using simulations from the generative model. An II posterior distribution is formed to expedite utility estimation. We also present a modification to the utility that allows the Müller algorithm to sample from a substantially sharpened utility surface, with little computational effort. Unlike competing methods, the II approach can handle complex design problems for models with intractable likelihoods on a continuous design space, with possible extension to many observations. The methodology is demonstrated using two stochastic models; a simple tractable death process used to validate the approach, and a motivating stochastic model for the population evolution of macroparasites.

Field validation of controlled Monte Carlo data generation for statistical damage identification employing Mahalanobis squared distance

This article presents the field applications and validations for the controlled Monte Carlo data generation scheme. This scheme was previously derived to assist the Mahalanobis squared distance–based damage identification method to cope with data-shortage problems which often cause inadequate data multinormality and unreliable identification outcome. To do so, real-vibration datasets from two actual civil engineering structures with such data (and identification) problems are selected as the test objects which are then shown to be in need of enhancement to consolidate their conditions. By utilizing the robust probability measures of the data condition indices in controlled Monte Carlo data generation and statistical sensitivity analysis of the Mahalanobis squared distance computational system, well-conditioned synthetic data generated by an optimal controlled Monte Carlo data generation configurations can be unbiasedly evaluated against those generated by other set-ups and against the original data. The analysis results reconfirm that controlled Monte Carlo data generation is able to overcome the shortage of observations, improve the data multinormality and enhance the reliability of the Mahalanobis squared distance–based damage identification method particularly with respect to false-positive errors. The results also highlight the dynamic structure of controlled Monte Carlo data generation that makes this scheme well adaptive to any type of input data with any (original) distributional condition.

Multivariate statistical analysis of hydrochemical data to assess alluvial aquifer–stream connectivity during drought and flood : Cressbrook Creek, southeast Queensland, Australia

A catchment-scale multivariate statistical analysis of hydrochemistry enabled assessment of interactions between alluvial groundwater and Cressbrook Creek, an intermittent drainage system in southeast Queensland, Australia. Hierarchical cluster analyses and principal component analysis were applied to time-series data to evaluate the hydrochemical evolution of groundwater during periods of extreme drought and severe flooding. A simple three-dimensional geological model was developed to conceptualise the catchment morphology and the stratigraphic framework of the alluvium. The alluvium forms a two-layer system with a basal coarse-grained layer overlain by a clay-rich low-permeability unit. In the upper and middle catchment, alluvial groundwater is chemically similar to streamwater, particularly near the creek (reflected by high HCO3/Cl and K/Na ratios and low salinities), indicating a high degree of connectivity. In the lower catchment, groundwater is more saline with lower HCO3/Cl and K/Na ratios, notably during dry periods. Groundwater salinity substantially decreased following severe flooding in 2011, notably in the lower catchment, confirming that flooding is an important mechanism for both recharge and maintaining groundwater quality. The integrated approach used in this study enabled effective interpretation of hydrological processes and can be applied to a variety of hydrological settings to synthesise and evaluate large hydrochemical datasets.

Ion impact distribution over plasma exposed nanocone arrays

The effect of an ordered array of nanocones on a conducting substrate immersed in the plasma on the transport of the plasma ions is investigated. The real conical shape of the cones is rigorously incorporated into the model. The movement of 10^5 CH3+ ions in the plasma sheath modified by the nanocone array is simulated. The ions are driven by the electric fields produced by the sheath and the nanostructures. The surface charge density and the total charge on the nanotips with different aspect ratios are computed. The ion transport simulation provides important characteristics of the displacement and velocity of the ions. The relative ion distribution along the lateral surfaces of the carbon nanotips is computed as well. It is shown that a rigorous account of the realistic nanostructure shape leads to very different distribution of the ion fluxes on the nanostructured surfaces compared to the previously reported works. The ion flux distribution is a critical factor in the nucleation process on the substrate and determines the nanostructure growth patterns.

Control of ion density distribution by magnetic traps for plasma electrons

The effect of a magnetic field of two magnetic coils on the ion current density distribution in the setup for low-temperature plasma deposition is investigated. The substrate of 400 mm diameter is placed at a distance of 325 mm from the plasma duct exit, with the two magnetic coils mounted symmetrically under the substrate at a distance of 140 mm relative to the substrate centre. A planar probe is used to measure the ion current density distribution along the plasma flux cross-sections at distances of 150, 230, and 325 mm from the plasma duct exit. It is shown that the magnetic field strongly affects the ion current density distribution. Transparent plastic films are used to investigate qualitatively the ion density distribution profiles and the effect of the magnetic field. A theoretical model is developed to describe the interaction of the ion fluxes with the negative space charge regions associated with the magnetic trapping of the plasmaelectrons. Theoretical results are compared with the experimental measurements, and a reasonable agreement is demonstrated.

Thin single-walled carbon nanotubes with narrow chirality distribution : constructive interplay of plasma and Gibbs–Thomson effects

Multiscale, multiphase numerical modeling is used to explain the mechanisms of effective control of chirality distributions of single-walled carbon nanotubes in direct plasma growth and suggest effective approaches to further improvement. The model includes an unprecedented combination of the plasma sheath, ion/radical transport, species creation/loss, plasma–surface interaction, heat transfer, surface/bulk diffusion, graphene layer nucleation, and bending/lift-off modules. It is shown that the constructive interplay between the plasma and the Gibbs–Thomson effect can lead to the effective nucleation and lift-off of small graphene layers on small metal catalyst nanoparticles. As a result, much thinner nanotubes with narrower chirality distributions can nucleate at much lower process temperatures and pressures compared to thermal CVD. This approach is validated by a host of experimental results, substantially reduces the amounts of energy and atomic matter required for the nanotube growth, and can be extended to other nanoscale structures and materials systems, thereby nearing the ultimate goal of energy- and matter-efficient nanotechnology.

Plasma-controlled adatom delivery and (re)distribution: Enabling uninterrupted, low-temperature growth of ultralong vertically aligned single walled carbon nanotubes

Large-scale (∼109 atoms) numerical simulations reveal that plasma-controlled dynamic delivery and redistribution of carbon atoms between the substrate and nanotube surfaces enable the growth of ultralong single walled carbon nanotubes (SWCNTs) and explain the common experimental observation of slower growth at advanced stages. It is shown that the plasma-based processes feature up to two orders of magnitude higher growth rates than equivalent neutral-gas systems and are better suited for the SWCNT synthesis at low nanodevice friendly temperatures. © 2008 American Institute of Physics.

Distribution of ion-current density on substrate between carbon nanotubes grown from low-temperature plasma

Using Monte Carlo simulation technique, we have calculated the distribution of ion current extracted from low-temperature plasmas and deposited onto the substrate covered with a nanotube array. We have shown that a free-standing carbon nanotube is enclosed in a circular bead of the ion current, whereas in square and hexagonal nanotube patterns, the ion current is mainly concentrated along the lines connecting the nearest nanotubes. In a very dense array (with the distance between nanotubes/nanotube-height ratio less than 0.05), the ions do not penetrate to the substrate surface and deposit on side surfaces of the nanotubes.

Behavior of the electron temperature in nonuniform complex plasmas

The response of complex ionized gas systems to the presence of nonuniform distribution of charged grains is investigated using a kinetic model. Contrary to an existing view that the electron temperature inevitably increases in the grain-occupied region because of enhanced ionization to compensate for the electrons lost to the grains, it is shown that this happens only when the ionizing electric field increases in the electron depleted region. The results for two typical plasma systems suggest that when the ionizing electric field depends on the spatially averaged electron density, the electron temperature in the grain containing region can actually decrease.

Effect of an internal rotating current on low-frequency inductively coupled plasmas

The effects of an inductively rotating current were observed on low-frequency inductively coupled plasmas. The spatial distribution of electromagnetic fields was investigated in a cylindrical metallic chamber filled with dense plasma. The distribution of the magnetic field in plasma chamber was observed for rarefied and dense plasmas. The plasma was assumed as uniform in the electromagnetic fields. The results showed the plasma density increased with power and the electron density increased with pressure.

Angular distribution of carbon ion flux in a nanotube array during the plasma process by the Monte Carlo technique

Angular distribution of microscopic ion fluxes around nanotubes arranged into a dense ordered pattern on the surface of the substrate is studied by means of multiscale numerical simulation. The Monte Carlo technique was used to show that the ion current density is distributed nonuniformly around the carbon nanotubes arranged into a dense rectangular array. The nonuniformity factor of the ion current flux reaches 7 in dense (5× 1018 m-3) plasmas for a nanotube radius of 25 nm, and tends to 1 at plasma densities below 1× 1017 m-3. The results obtained suggest that the local density of carbon adatoms on the nanotube side surface, at areas facing the adjacent nanotubes of the pattern, can be high enough to lead to the additional wall formation and thus cause the single- to multiwall structural transition, and other as yet unexplained nanoscience phenomena.

Simulation of ion flux distribution in conductive and nonconductive nanotip patterns

The distribution of flux of carbon-bearing cations over nanopatterned surfaces with conductive nanotips and nonconductive nanoislands is simulated using the Monte-Carlo technique. It is shown that the ion current is focused to nanotip surfaces when the negative substrate bias is low and only slightly perturbed at higher substrate biases. In the low-bias case, the mean horizontal ion displacement caused by the nanotip electric field exceeds 10 nm. However, at higher substrate biases, this value reduces down to 2 nm. In the nonconductive nanopattern case, the ion current distribution is highly nonuniform, with distinctive zones of depleted current density around the nanoislands. The simulation results suggest the efficient means to control ion fluxes in plasma-aided nanofabrication of ordered nanopatterns, such as nanotip microemitter structures and quantum dot or nanoparticle arrays. © World Scientific Publishing Company.

Effect of pupil dilation and constriction on the distribution of bit errors within the iris

Texture information in the iris image is not uniform in discriminatory information content for biometric identity verification. The bits in an iris code obtained from the image differ in their consistency from one sample to another for the same identity. In this work, errors in bit strings are systematically analysed in order to investigate the effect of light-induced and drug-induced pupil dilation and constriction on the consistency of iris texture information. The statistics of bit errors are computed for client and impostor distributions as functions of radius and angle. Under normal conditions, a V-shaped radial trend of decreasing bit errors towards the central region of the iris is obtained for client matching, and it is observed that the distribution of errors as a function of angle is uniform. When iris images are affected by pupil dilation or constriction the radial distribution of bit errors is altered. A decreasing trend from the pupil outwards is observed for constriction, whereas a more uniform trend is observed for dilation. The main increase in bit errors occurs closer to the pupil in both cases.