A Bayesian analysis of experiments with small numbers of events

Within the framework of Bayesian statistics we derive a distribution for the posterior degree of belief both for the difference and ratio of small numbers of events, when the background mean in each case is known with finite precision.     

Estimation of kinetic parameters in neopentyl glycol esterification with propionic acid

The reaction kinetics of neopentyl glycol esterification with propionic acid is studied in a batch reactor at different temperatures. The reaction is catalyzed by a heterogeneous resin (DOWEX 50 WX 2). The parameters of the kinetic model are estimated by non-linear regression by minimizing the difference between the measured and predicted concentrations. The reliability of the estimated parameters is analyzed using the Markov chain Monte Carlo (MCMC) method. The MCMC method is an advanced statistical approach, which is well suited for the analysis of complex multiparametric non-linear models. The potential of the MCMC method is further demonstrated by optimizing the product yield in CSTR using the estimated parameters from the batch experiments.     

Skeletal isomerization kinetics of 1-pentene over an HZSM-22 catalyst

Synthesis of the oxygenate fuel additive TAME (tertiary amyl methyl ether) is based on the reaction between reactive isopentene compounds (2-methyl-1-butene and 2-methyl-2-butene) and methanol. Skeletal isomerization of n-pentenes is an important reaction route in production of the raw material for TAME synthesis. In this work the kinetics of skeletal isomerization of 1-pentene was studied using HZSM-22 as a catalyst, and the effect of temperature (523–598 K) and WHSV (weight hourly space velocity) on product composition were investigated. The observed main reaction products were cis- and trans-2-pentenes, 2-methyl-2-butene, 2-methyl-1-butene and 3-methyl-1-butene. Minor products found in the output stream were C₂, C₃, C₄, C₆, C₇, C₈ and C₁₀ – alkenes and – alkanes. Only traces of methane and C₉ compounds were detected. Two different reaction mechanisms have been proposed in literature for skeletal isomerization of n-pentenes and their side reactions (dimerization and fragmentation); the monomolecular and the bimolecular skeletal isomerization mechanisms. In the current work a pseudohomogeneous reaction model for both mechanisms is fitted to experimental data. The fitting results show that both reaction mechanisms explain the skeletal isomerization of 1-pentene to isopentenes well. However, the monomolecular reaction mechanism explained the formation of dimerization and fragmentation products slightly better. The reliability of the estimated Arrhenius parameters was analyzed using Bayesian inference and Markov chain Monte Carlo methods (MCMC) which are rarely used in chemical engineering.     

Determination of the Henry's Coefficient and Mass Transfer for Ozone in a Bubble Column at Different pH Values of Water

In this study, the ozone gas-liquid mass transfer into water in a bubble column was investigated for different pH values. The ozone volumetric mass transfer coefficient and the Henry's coefficient were determined simultaneously by parameter estimation using a nonlinear optimization method. A sensitivity analysis was conducted to obtain information on the reliability and identifiability of the estimated parameters. A minor dependence of the Henry's law constant on pH was detected at the pH range 4 to 9.     

Kalman filtering of traffic fluctuations for real-time network management

Discrete- time stochastic models of sequential traffic records in telephone networks are considered. They appear to be well suited for a use of the Kaiman filter. A version of the filtering algorithm is adopted to deal with traffic fluctuations. The overall approach is tested against the real data gathered by the supervisor of the French toll network. The adaptive traffic estimator is inserted into a simulator of a testbed network operated in the urban zone of Paris. The traffic estimations provided by the filter are used to decide an overflow hierarchy.     

Serum beta-carotene deficiency in HIV-infected children

Representative levels of serum micronutrients specifically, beta-carotene and vitamins A and E, were studied in symptomatic human immunodeficiency virus (HIV)-infected children. The nutritional status of 23 symptomatic African-American and Hispanic HIV-infected children were compared with an appropriate control group comprised of 36 uninfected children matched for age and sex, using body mass index. Serum beta-carotene and vitamin A and E levels were randomly determined on 15 of the infected children. Beta-carotene concentration was 4.9-fold reduced in symptomatic HIV-infected children when compared with the control group. There was a 6.5-fold decrease in the serum level for children without acquired immunodeficiency syndrome (AIDS) and a 13-fold reduction in children with AIDS. No differences in the mean values for serum vitamins A and E were observed in the groups studied. Although the nutritional status of the symptomatic HIV-infected children was not different from that of the control population, their serum beta-carotene levels were profoundly deficient. This finding may have immunologic and clinical implications for children with rapidly progressing HIV disease.     

Inference about long run canonical correlations

This article proposes methods for testing the null hypothesis that a number of so‐called long run canonical correlations (LRCCs) are zero. Two test statistics are proposed and their limiting distributions are derived under the null hypothesis. The finite sample properties of the tests are illustrated via a number of simulation studies that reveal the asymptotic theory provides a good guidance to behaviour in moderate or large sized samples. It is shown that the statistics provide a natural way for testing the asymptotic independence of two standardized sums. The usefulness of the tests is illustrated via the following examples: inference about cointegrating vector in a particular cointegration model; inference about break points in a cointegration model; moment estimation; parameter estimation in Generalized Method of Moments estimation.