Bayesian methods for estimation, optimization and experimental design

Mathematical models often contain parameters that need to be calibrated from measured data. The emergence of efficient Markov Chain Monte Carlo (MCMC) methods has made the Bayesian approach a standard tool in quantifying the uncertainty in the parameters. With MCMC, the parameter estimation problem can be solved in a fully statistical manner, and the whole distribution of the parameters can be explored, instead of obtaining point estimates and using, e.g., Gaussian approximations. In this thesis, MCMC methods are applied to parameter estimation problems in chemical reaction engineering, population ecology, and climate modeling. Motivated by the climate model experiments, the methods are developed further to make them more suitable for problems where the model is computationally intensive. After the parameters are estimated, one can start to use the model for various tasks. Two such tasks are studied in this thesis: optimal design of experiments, where the task is to design the next measurements so that the parameter uncertainty is minimized, and model-based optimization, where a model-based quantity, such as the product yield in a chemical reaction model, is optimized. In this thesis, novel ways to perform these tasks are developed, based on the output of MCMC parameter estimation. A separate topic is dynamical state estimation, where the task is to estimate the dynamically changing model state, instead of static parameters. For example, in numerical weather prediction, an estimate of the state of the atmosphere must constantly be updated based on the recently obtained measurements. In this thesis, a novel hybrid state estimation method is developed, which combines elements from deterministic and random sampling methods.

Docosahexaenoic acid ethyl esther (DHAEE) microcapsule production by spray-drying: optimization by experimental design

Docosahexaenoic acid is an essential polyunsaturated fatty acid with important metabolic activities. Its conjugated double bonds make it susceptible to decomposition. Its stability may be improved through fatty acid entrapment with a spray-drying technique; however, the many parameters involved in this technique must be considered to avoid affecting the final product quality. Therefore, this study aimed to evaluate the entrapment conditions and yields of fish oil enriched with docosahexaenoic acid ethyl ester. Microcapsules were obtained from Acacia gum using a spray-drying technique. The experimental samples were analyzed by chromatography and delineated by Statistica software, which found the following optimum entrapment conditions: an inlet temperature of 188 °C; 30% core material; an N2 flow rate of 55 mm; and a pump flow rate of 12.5 mL/minute. These conditions provided a 66% yield of docosahexaenoic acid ethyl ester in the oil, corresponding to 19.8% of entrapped docosahexaenoic acid ethyl ester (w/w). This result was considered significant since 30% corresponded to wall material.

Application of Doehlert experimental design in the optimization of experimental variables for the Pseudozyma sp. (CCMB 306) and Pseudozyma sp. (CCMB 300) cell lysis

This study aimed to verify the influence of pH and temperature on the lysis of yeast using experimental design. In this study, the enzymatic extract containing β-1,3-glucanase and chitinase, obtained from the micro-organism Moniliophthora perniciosa, was used. The experiment showed that the best conditions for lysis of Pseudozyma sp. (CCMB 306) and Pseudozyma sp. (CCMB 300) by lytic enzyme were pH 4.9 at 37 ºC and pH 3.9 at 26.7 ºC, respectively. The lytic enzyme may be used for obtaining various biotechnology products from yeast.

Inactivation of Staphylococcus aureus in raw salmon with supercritical CO2 using experimental design

Abstract Considering the microbial safety of consumption of raw foods (Asian food), this study aimed to explore the inactivation S. aureus in raw salmon by supercritical CO2 treatment (SC-CO2). For this purpose, experimental design methodology was employed as a tool to evaluate the effects of pressure (120-220 bar), the depressurization rate (10 to 100 bar.min–1) and the salmon:CO2 mass relation (1:0.2 to 1:1.0). It was observed that the pressure and the depressurization rate was statistically significant, i.e. the higher the system pressure and depressurization rate, the greater the microbial inactivation. The salmon: CO2 mass relation did not influence the S. aureus inactivation in raw salmon. There was a total reduction in S. aureus with 225 bar, a depressurizing rate of 100 bar.min–1, a salmon: CO2 mass relation of 1:0.6, for 2 hours at 33 °C.

Extracellular β-glucosidase Production by a Marine Aspergillus sydowii BTMFS 55 under Solid State Fermentation Using Statistical Experimental Design

A potential fungal strain producing extracellular β-glucosidase enzyme was isolated from sea water and identified as ^ëéÉêJ Öáääìë=ëóÇçïáá BTMFS 55 by a molecular approach based on 28S rDNA sequence homology which showed 93% identity with already reported sequences of ^ëéÉêÖáääìë=ëóÇçïáá in the GenBank. A sequential optimization strategy was used to enhance the production of β-glucosidase under solid state fermentation (SSF) with wheat bran (WB) as the growth medium. The two-level Plackett-Burman (PB) design was implemented to screen medium components that influence β-glucosidase production and among the 11 variables, moisture content, inoculums, and peptone were identified as the most significant factors for β-glucosidase production. The enzyme was purified by (NH4)2SO4 precipitation followed by ion exchange chromatography on DEAE sepharose. The enzyme was a monomeric protein with a molecular weight of ~95 kDa as determined by SDS-PAGE. It was optimally active at pH 5.0 and 50°C. It showed high affinity towards éNPG and enzyme has a hã and sã~ñ of 0.67 mM and 83.3 U/mL, respectively. The enzyme was tolerant to glucose inhibition with a há of 17 mM. Low concentration of alcohols (10%), especially ethanol, could activate the enzyme. A considerable level of ethanol could produce from wheat bran and rice straw after 48 and 24 h, respectively, with the help of p~ÅÅÜ~êçãóÅÉë=ÅÉêÉîáëá~É in presence of cellulase and the purified β-glucosidase of ^ëéÉêÖáääìë=ëóÇçïáá BTMFS 55.

Predicting random level and seasonality of hotel prices. A structural equation growth curve approach

This article examines the effect on price of different characteristics of holiday hotels in the sun-and-beach segment, under the hedonic function perspective. Monthly prices of the majority of hotels in the Spanish continental Mediterranean coast are gathered from May to October 1999 from the tour operator catalogues. Hedonic functions are specified as random-effect models and parametrized as structural equation models with two latent variables, a random peak season price and a random width of seasonal fluctuations. Characteristics of the hotel and the region where they are located are used as predictors of both latent variables. Besides hotel category, region, distance to the beach, availability of parking place and room equipment have an effect on peak price and also on seasonality. 3- star hotels have the highest seasonality and hotels located in the southern regions the lowest, which could be explained by a warmer climate in autumn

Application of the european customer satisfaction index to postal services. Structural equation models versus partial least squars

Customer satisfaction and retention are key issues for organizations in today’s competitive market place. As such, much research and revenue has been invested in developing accurate ways of assessing consumer satisfaction at both the macro (national) and micro (organizational) level, facilitating comparisons in performance both within and between industries. Since the instigation of the national customer satisfaction indices (CSI), partial least squares (PLS) has been used to estimate the CSI models in preference to structural equation models (SEM) because they do not rely on strict assumptions about the data. However, this choice was based upon some misconceptions about the use of SEM’s and does not take into consideration more recent advances in SEM, including estimation methods that are robust to non-normality and missing data. In this paper, both SEM and PLS approaches were compared by evaluating perceptions of the Isle of Man Post Office Products and Customer service using a CSI format. The new robust SEM procedures were found to be advantageous over PLS. Product quality was found to be the only driver of customer satisfaction, while image and satisfaction were the only predictors of loyalty, thus arguing for the specificity of postal services

Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model and the design region. The talk will consider the design of experiments for regression models in which there is a single response with the explanatory variables lying in a simplex. One example is experiments on various compositions of glass such as those considered by Martin, Bursnall, and Stillman (2001). Because of the highly symmetric nature of the simplex, the class of models that are of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather different from those of standard regression analysis. The optimum designs are also rather different, inheriting a high degree of symmetry from the models. In the talk I will hope to discuss a variety of modes for such experiments. Then I will discuss constrained mixture experiments, when not all the simplex is available for experimentation. Other important aspects include mixture experiments with extra non-mixture factors and the blocking of mixture experiments. Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007). If time and my research allows, I would hope to finish with a few comments on design when the responses, rather than the explanatory variables, lie in a simplex. References Atkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum Experimental Designs, with SAS. Oxford: Oxford University Press. Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results on optimal and efficient designs for constrained mixture experiments. In A. C. Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000, pp. 225–239. Dordrecht: Kluwer. Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal Statistical Society, Ser. B 20, 344–360. 1

Psychosocial sources of stress and burnout in the consruction sector : a structural equation model. 'Fuentes psicosociales de estr??s y burnout en el sector de la construcci??n : un modelo de ecuaciones estructurales'

Resumen tomado de la publicaci??n. Resumen tambi??n en ingl??s

Simultaneous estimation of indirect and interaction effects using structural equation models

Interaction effects are usually modeled by means of moderated regression analysis. Structural equation models with non-linear constraints make it possible to estimate interaction effects while correcting for measurement error. From the various specifications, Jöreskog and Yang's (1996, 1998), likely the most parsimonious, has been chosen and further simplified. Up to now, only direct effects have been specified, thus wasting much of the capability of the structural equation approach. This paper presents and discusses an extension of Jöreskog and Yang's specification that can handle direct, indirect and interaction effects simultaneously. The model is illustrated by a study of the effects of an interactive style of use of budgets on both company innovation and performance

Psychological contract breach and outcomes : Combining meta-analysis and structural equation models. 'Ruptura de contrato psicol??gico : combinando meta-an??lisis y modelos de ecuaciones estructurales'

Resumen tomado de la publicaci??n

IQ heritability estimation : analyzing genetically-informative data with structural equation models. 'Estimaci??n de la heredabilidad del CI : analizando datos gen??ticamente informativos con modelos de ecuaciones estructurales'

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Sparse kernel density estimator using orthogonal regression based on D-optimality experimental design

A novel sparse kernel density estimator is derived based on a regression approach, which selects a very small subset of significant kernels by means of the D-optimality experimental design criterion using an orthogonal forward selection procedure. The weights of the resulting sparse kernel model are calculated using the multiplicative nonnegative quadratic programming algorithm. The proposed method is computationally attractive, in comparison with many existing kernel density estimation algorithms. Our numerical results also show that the proposed method compares favourably with other existing methods, in terms of both test accuracy and model sparsity, for constructing kernel density estimates.

Sparse kernel regression modeling using combined locally regularized orthogonal least squares and D-optimality experimental design

The note proposes an efficient nonlinear identification algorithm by combining a locally regularized orthogonal least squares (LROLS) model selection with a D-optimality experimental design. The proposed algorithm aims to achieve maximized model robustness and sparsity via two effective and complementary approaches. The LROLS method alone is capable of producing a very parsimonious model with excellent generalization performance. The D-optimality design criterion further enhances the model efficiency and robustness. An added advantage is that the user only needs to specify a weighting for the D-optimality cost in the combined model selecting criterion and the entire model construction procedure becomes automatic. The value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values.