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.

Software for design of experiments and response modelling of cake ltration applications

Filtration is a widely used unit operation in chemical engineering. The huge variation in the properties of materials to be ltered makes the study of ltration a challenging task. One of the objectives of this thesis was to show that conventional ltration theories are di cult to use when the system to be modelled contains all of the stages and features that are present in a complete solid/liquid separation process. Furthermore, most of the ltration theories require experimental work to be performed in order to obtain critical parameters required by the theoretical models. Creating a good overall understanding of how the variables a ect the nal product in ltration is somewhat impossible on a purely theoretical basis. The complexity of solid/liquid separation processes require experimental work and when tests are needed, it is advisable to use experimental design techniques so that the goals can be achieved. The statistical design of experiments provides the necessary tools for recognising the e ects of variables. It also helps to perform experimental work more economically. Design of experiments is a prerequisite for creating empirical models that can describe how the measured response is related to the changes in the values of the variable. A software package was developed that provides a ltration practitioner with experimental designs and calculates the parameters for linear regression models, along with the graphical representation of the responses. The developed software consists of two software modules. These modules are LTDoE and LTRead. The LTDoE module is used to create experimental designs for di erent lter types. The lter types considered in the software are automatic vertical pressure lter, double-sided vertical pressure lter, horizontal membrane lter press, vacuum belt lter and ceramic capillary action disc lter. It is also possible to create experimental designs for those cases where the variables are totally user de ned, say for a customized ltration cycle or di erent piece of equipment. The LTRead-module is used to read the experimental data gathered from the experiments, to analyse the data and to create models for each of the measured responses. Introducing the structure of the software more in detail and showing some of the practical applications is the main part of this thesis. This approach to the study of cake ltration processes, as presented in this thesis, has been shown to have good practical value when making ltration tests.

Software for design of experiments and response modelling of cake filtration applications

Filtration is a widely used unit operation in chemical engineering. The huge variation in the properties of materials to be ltered makes the study of ltration a challenging task. One of the objectives of this thesis was to show that conventional ltration theories are di cult to use when the system to be modelled contains all of the stages and features that are present in a complete solid/liquid separation process. Furthermore, most of the ltration theories require experimental work to be performed in order to obtain critical parameters required by the theoretical models. Creating a good overall understanding of how the variables a ect the nal product in ltration is somewhat impossible on a purely theoretical basis. The complexity of solid/liquid separation processes require experimental work and when tests are needed, it is advisable to use experimental design techniques so that the goals can be achieved. The statistical design of experiments provides the necessary tools for recognising the e ects of variables. It also helps to perform experimental work more economically. Design of experiments is a prerequisite for creating empirical models that can describe how the measured response is related to the changes in the values of the variable. A software package was developed that provides a ltration practitioner with experimental designs and calculates the parameters for linear regression models, along with the graphical representation of the responses. The developed software consists of two software modules. These modules are LTDoE and LTRead. The LTDoE module is used to create experimental designs for di erent lter types. The lter types considered in the software are automatic vertical pressure lter, double-sided vertical pressure lter, horizontal membrane lter press, vacuum belt lter and ceramic capillary action disc lter. It is also possible to create experimental designs for those cases where the variables are totally user de ned, say for a customized ltration cycle or di erent piece of equipment. The LTRead-module is used to read the experimental data gathered from the experiments, to analyse the data and to create models for each of the measured responses. Introducing the structure of the software more in detail and showing some of the practical applications is the main part of this thesis. This approach to the study of cake ltration processes, as presented in this thesis, has been shown to have good practical value when making ltration tests.

The usage of experimental research in business-to-business marketing context in academic marketing journals

The aim of this master’s thesis is to introduce what is experimental research and how the researcher is able to use this researching method in business-to-business context. This work has been done with analyzing articles of four academic marketing journals from years 1992-2012. In the literature part there is introduction of the nature of the experimental research, its terminology and design. There is also discussion about limitations of experimental research and comparison of experimental research to quasi-experimental design. In the results part there is a review how experimental research has been used in the business-to-business context in the past two decades. In the analysis there is introduction of themes, samplings, different kinds of variables and main findings. The work offers a good understanding to nature of experimental research and useful data for organizing a real experimental study.