Analytic Convergence Rates and Parameterization Issues for the Gibbs Sampler Applied to State Space Models

In this paper we obtain a closed form expression for the convergence rate of the Gibbs sampler applied to the unobserved states of a first-order autoregression plus noise model. The rate is expressed in terms of the parameters of the model, which are regarded as fixed. For the case where the unconditional mean of the states is a parameter of interest we provide evidence that a 'centred' parameterization of a state space model is preferable for the performance of the Gibbs sampler. These two results provide guidance when the Gaussianity or linearity of the state space form is lost. We illustrate this by examining the performance of a Markov chain Monte Carlo sampler for the stochastic volatility model.     

Model Development and Parameter Estimation for the Oxidation of Pyrrhotite‐Containing Rock Surfaces

A novel experimental method was developed for the evaluation of the biotic oxidation rate of waste rock containing sulphide minerals. Sized waste rock samples were inoculated with an Acidithiobacillus ferrooxidans suspension and sparged with discontinuing humidified air to yield the oxygen consumption rate. A kinetic/mass transport model was proposed based on oxidation of pyrrhotite. Bayesian statistical analysis using the Metropolis‐Hastings algorithm showed that at ambient oxygen concentration the mean (i.e., estimated) values of the initial oxygen flux, the reaction order, the oxygen diffusion coefficient through the oxidation product layer, and the surface reaction rate constant were 1.3×10^?7 mol/m².s, 0.55, 2.91×10^?13 m²/s and 3.23×10^?7 mol^0.45/m^0.35.s, respectively.     

Likelihood‐based Analysis of a Class of Generalized Long‐Memory Time Series Models

Abstract. This article introduces a family of ‘generalized long‐memory time series models’, in which observations have a specified conditional distribution, given a latent Gaussian fractionally integrated autoregressive moving‐average (ARFIMA) process. The observations may have discrete or continuous distributions (or a mixture of both). The family includes existing models such as ARFIMA models themselves, long‐memory stochastic volatility models, long‐memory censored Gaussian models and others. Although the family of models is flexible, the latent long‐memory process poses problems for analysis. Therefore, we introduce a Markov chain Monte Carlo sampling algorithm and develop a set of recursions which makes it feasible. This makes it possible, among other things, to carry out exact likelihood‐based analysis of a wide range of non‐Gaussian long‐memory models without resorting to the use of likelihood approximations. The procedure also yields predictive distributions that take into account model parameter uncertainty. The approach is demonstrated in two case studies.     

Demystifying the estimation of reactivity ratios for terpolymerization systems

In typical practice for terpolymerizations so far, binary reactivity ratios have been used directly in the instantaneous Alfrey and Goldfinger (AG) model, effectively ignoring the presence of the third monomer. In addition, the use of the AG model leads to severe estimation problems, if one would like to estimate reactivity ratios from experimental data. Due to the above reasons, the AG model was recast and was subsequently used with terpolymerization data directly to estimate ternary reactivity ratios under the error‐in‐variables‐model framework, based both on instantaneous (low conversion) and cumulative composition data (medium and high conversions). Several examples and counter examples highlight such important issues as the choice of the correct number of responses, accounting for the appropriate error structure, and incorporating the right information content, all with diagnostic checks whose target is the eventual reliability of the reactivity ratio estimates. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1752–1766, 2014     

Spatio‐temporal models for big multinomial data using the conditional multivariate logit‐beta distribution

We introduce a Bayesian approach for analyzing high‐dimensional multinomial data that are referenced over space and time. In particular, the proportions associated with multinomial data are assumed to have a logit link to a latent spatio‐temporal mixed effects model. This strategy allows for covariances that are nonstationarity in both space and time, asymmetric, and parsimonious. We also introduce the use of the conditional multivariate logit‐beta distribution into the dependent multinomial data setting, which leads to conjugate full‐conditional distributions for use in a collapsed Gibbs sampler. We refer to this model as the multinomial spatio‐temporal mixed effects model (MN‐STM). Additionally, we provide methodological developments including: the derivation of the associated full‐conditional distributions, a relationship with a latent Gaussian process model, and the stability of the non‐stationary vector autoregressive model. We illustrate the MN‐STM through simulations and through a demonstration with public‐use quarterly workforce indicators data from the longitudinal employer household dynamics program of the US Census Bureau.     

Interaction Parameter Method for Investigating BTEX Extraction Using the Hollow‐Fiber Microporous Membrane Liquid/Liquid Extraction Technique

This work focused on the extraction of BTEX from aqueous solution by a hollow‐fiber microporous membrane liquid/liquid extraction (HF‐MMLLE) technique. A simple and rapid method based on the Hansen solubility parameters (HSP) theory was adopted to theoretically determine the interaction parameter (χ₁₂) between the extractants and BTEX. Experiments were carried out to establish the relationship between the interaction parameter and the extraction performance. Furthermore, the distribution coefficient and permeability coefficient related to the extraction performance were also discussed, which verified the relationship from a quantitative idea. It was observed that the liquid/liquid extraction was based on the strong affinities between the extractants and the target pollutants. This method should be paid more attention for its potential application in other solvent‐sensitive processes.     

The Effect of the Estimation on Goodness‐of‐Fit Tests in Time Series Models

Abstract. We analyze, by simulation, the finite‐sample properties of goodness‐of‐fit tests based on residual autocorrelation coefficients (simple and partial) obtained using different estimators frequently used in the analysis of autoregressive moving‐average time‐series models. The estimators considered are unconditional least squares, maximum likelihood and conditional least squares. The results suggest that although the tests based on these estimators are asymptotically equivalent for particular models and parameter values, their sampling properties for samples of the size commonly found in economic applications can differ substantially, because of differences in both finite‐sample estimation efficiencies and residual regeneration methods.     

Three‐dimensional CFD‐PBM coupled model of the temperature fields in fluidized‐bed polymerization reactors

A three‐dimensional (3‐D) computational fluid dynamics model, coupled with population balance (CFD‐PBM), was developed to describe the gas–solid two‐phase flow in fluidized‐bed polymerization reactors. The model considered the Eulerian–Eulerian two‐fluid model, the kinetic theory of granular flow, the population balance, and heat exchange equations. First, the model was validated by comparing simulation results with the classical calculated data. The entire temperature fields in the reactor were also obtained numerically. Furthermore, two case studies, involving constant solid particle size and constant polymerization heat or evolving particle‐size distribution, polymerization kinetics, and polymerization heat, were designed to identify the model. The results showed that the calculated results in the second case were in good agreement with the reality. Finally, the model of the second case was used to investigate the influences of operational conditions on the temperature field. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

The use of CO2 for reversible pH shifting,and the removal of succinic acid in a polymer‐based two‐phase partitioning bioreactor

BACKGROUND: Succinic acid (SA) is an intermediate in the production of commodity chemicals, but SA bioproduction has not yet been commercialized due to end product inhibition and high product separation costs. Two‐phase partitioning bioreactors (TPPBs) can increase volumetric productivity through in situ product removal, although SA uptake by polymers requires a pH below the pK_A2 of SA (4.2). It was proposed to reversibly reduce the pH with CO₂ sparging for absorption of SA, followed by nitrogen stripping to allow continued bioproduction after returning to metabolic pH levels. RESULTS: At 1 atm CO₂ sparging lowered the pH of RO water to 3.8 but only to 4.75 in medium, requiring acid/base pH adjustment in subsequent experiments. Actinobacillus succinogenes was temporarily exposed to pH 4.2 for between 5 min and 4 h to observe the effect on subsequent growth; cells could grow after up to 4 h of low pH exposure, sufficient time for SA uptake. Because atmospheric CO₂ could not adequately lower the pH of medium, a TPPB was operated with the pH being shifted using strong acid/base; SA was recovered in situ, however, the accumulation of salts hindered further cell growth. CONCLUSION: Several key elements of this novel processing strategy were successfully demonstrated, and work is continuing with high pressure CO₂ to achieve the desired pH adjustment levels. Copyright © 2011 Society of Chemical Industry     

Melt processing of poly(L‐lactic acid) in the presence of organomodified anionic or cationic clays

Poly(L ‐lactic acid) (PLA) films are in use for various types of food packaging; however, a wider range of applications would be possible if the barrier properties of these films could be improved. To make such improvements, combinations of PLA with two nanofillers, laurate‐intercalated Mg‐Al layered double hydroxide (LDH‐C₁₂) and a cationic organomodified montmorillonite (MMT) clay (Cloisite® 30B), were investigated. The dispersion of these fillers in PLA by melt processing was explored using two methods, either by mixing the nanofillers with PLA granulate immediately before extrusion or by preparation and subsequent dilution of PLA‐nanofiller masterbatches. After melt processing of these materials, PLA molecular weight, thermal stability, film transparency, morphology, and permeability characteristics were determined. Direct addition of LDH‐C₁₂ drastically reduced the PLA molecular weight. Although this reduction in molecular weight was still very significant, it was less when a PLA/LDH‐C₁₂ masterbatch was processed. In contrast, there was no significant reduction in PLA molecular weight when processing with Cloisite® 30B. However, film transparency was compromised when either LDH or MMT nanofillers were used. Evidence from DSC analyses showed a significant increase in heat of fusion when LDH‐C₁₂ was dispersed in PLA compared with Cloisite® 30B, likely indicating a difference in nucleating properties. Complementary optical purity analyses suggested that racemization as a result of processing could influence the PLA crystallinity as determined by DSC in certain cases. A reduction in thermal stability when incorporating LDH‐C₁₂ could be a direct result of PLA molecular weight reduction. XRD and TEM analyses showed that both Cloisite® 30B‐ and LDH‐C₁₂‐based PLA composites yielded exfoliated and intercalated morphologies, but nanofiller agglomeration was also seen when LDH‐C₁₂ was used. PLA/Cloisite® 30B nanocomposite films exhibited significant enhancement in oxygen and water vapor barrier properties, but no such improvement was found in PLA/LDH‐C₁₂ nanocomposite films. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Effects of Orlistat on white adipose tissue (WAT) in the γ‐irradiated mouse model

In this study, we showed that γ‐irradiation could trigger biological response like the fat accumulation of gonadal white adipose tissue (gWAT) in mice. The irradiated animal can be used as a useful model for evaluation of anti‐obesity drugs. To induce the fat accumulation by γ‐irradiation, 2‐months‐old female C57BL/6 mice were irradiated at 5 Gy and further raised for 6 months. Subsequently, the mice were i.p. injected daily with Orlistat (25 mg/kg) or vehicle for 3 wk and analyzed for the adipose tissue weight and serum triglyceride and T‐cholesterol levels. The abdominal WAT of the γ‐irradiated mice weighed an average of 3.9/100 g body weight, 1.7‐fold higher than what was seen in normal mice (2.3/100 g body weight), indicating that γ‐irradiation induced the fat accumulation in the adipose tissue. However, the administration of Orlistat, a well‐known anti‐obesity agent, significantly reduced the adipose tissue weight to 1.7/100 g body weight in irradiated mice. In addition, in these Orlistat‐treated mice, a significant reduction of serum triglyceride and T‐cholesterol was observed up to 14% and 27%, respectively.