Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Variation in biomass related variables of reed canary grass

Selostus: Ruokohelven biomassan tuotantoon vaikuttavien ominaisuuksien vaihtelu

Stratified estimation of forest inventory variables using spatially summarized stratifications

Abstract

The effects of some variables on CO2 laser-MAG hybrid welding

The CO2-laser-MAG hybrid welding process has been shown to be a productive choice for the welding industry, being used in e.g. the shipbuilding, pipe and beam manufacturing, and automotive industries. It provides an opportunity to increase the productivity of welding of joints containing air gaps compared with autogenous laser beam welding, with associated reductions in distortion and marked increases in welding speeds and penetration in comparison with both arc and autogenous laser welding. The literature study indicated that the phenomena of laser hybrid welding are mostly being studied using bead-on-plate welding or zero air gap configurations. This study shows it very clearly that the CO2 laser-MAG hybrid welding process is completely different, when there is a groove with an air gap. As in case of industrial use it is excepted that welding is performed for non-zero grooves, this study is of great importance for industrial applications. The results of this study indicate that by using a 6 kW CO2 laser-MAG hybrid welding process, the welding speed may also be increased if an air gap is present in the joint. Experimental trials indicated that the welding speed may be increased by 30-82% when compared with bead-on-plate welding, or welding of a joint with no air gap i.e. a joint prepared as optimum for autogenous laser welding. This study demonstrates very clearly, that the separation of the different processes, as well as the relative configurations of the processes (arc leading or trailing) affect welding performance significantly. These matters influence the droplet size and therefore the metal transfer mode, which in turn determined the resulting weld quality and the ability to bridge air gaps. Welding in bead-onplate mode, or of an I butt joint containing no air gap joint is facilitated by using a leading torch. This is due to the preheating effect of the arc, which increases the absorptivity of the work piece to the laser beam, enabling greater penetration and the use of higher welding speeds. With an air gap present, air gap bridging is more effectively achieved by using a trailing torch because of the lower arc power needed, the wider arc, and the movement of droplets predominantly towards the joint edges. The experiments showed, that the mode of metal transfer has a marked effect on gap bridgeability. Transfer of a single droplet per arc pulse may not be desirable if an air gap is present, because most of the droplets are directed towards the middle of the joint where no base material is present. In such cases, undercut is observed. Pulsed globular and rotational metal transfer modes enable molten metal to also be transferred to the joint edges, and are therefore superior metal transfer modes when bridging air gaps. It was also found very obvious, that process separation is an important factor in gap bridgeability. If process separation is too large, the resulting weld often exhibits sagging, or no weld may be formed at all as a result of the reduced interaction between the component processes. In contrast, if the processes are too close to one another, the processing region contains excess molten metal that may create difficulties for the keyhole to remain open. When the distance is optimised - i.e. a separation of 0-4 mm in this study, depending on the welding speed and beam-arc configuration - the processes act together, creating beneficial synergistic effects. The optimum process separation when using a trailing torch was found to be shorter (0-2 mm) than when a leading torch is used (2-4 mm); a result of the facilitation of weld pool motion when the latter configuration is adopted. This study demonstrates, that the MAG process used has a strong effect on the CO2-laser-MAG hybrid welding process. The laser beam welding component is relatively stable and easy to manage, with only two principal processing parameters (power and welding speed) needing to be adjusted. In contrast, the MAG process has a large number of processing parameters to optimise, all of which play an important role in the interaction between the laser beam and the arc. The parameters used for traditional MAG welding are often not optimal in achieving the most appropriate mode of metal transfer, and weld quality in laser hybrid welding, and must be optimised if the full range of benefits provided by hybrid welding are to be realised.

Advanced chemometric methods: Applicability on industrial data

Recent years have produced great advances in the instrumentation technology. The amount of available data has been increasing due to the simplicity, speed and accuracy of current spectroscopic instruments. Most of these data are, however, meaningless without a proper analysis. This has been one of the reasons for the overgrowing success of multivariate handling of such data. Industrial data is commonly not designed data; in other words, there is no exact experimental design, but rather the data have been collected as a routine procedure during an industrial process. This makes certain demands on the multivariate modeling, as the selection of samples and variables can have an enormous effect. Common approaches in the modeling of industrial data are PCA (principal component analysis) and PLS (projection to latent structures or partial least squares) but there are also other methods that should be considered. The more advanced methods include multi block modeling and nonlinear modeling. In this thesis it is shown that the results of data analysis vary according to the modeling approach used, thus making the selection of the modeling approach dependent on the purpose of the model. If the model is intended to provide accurate predictions, the approach should be different than in the case where the purpose of modeling is mostly to obtain information about the variables and the process. For industrial applicability it is essential that the methods are robust and sufficiently simple to apply. In this way the methods and the results can be compared and an approach selected that is suitable for the intended purpose. Differences in data analysis methods are compared with data from different fields of industry in this thesis. In the first two papers, the multi block method is considered for data originating from the oil and fertilizer industries. The results are compared to those from PLS and priority PLS. The third paper considers applicability of multivariate models to process control for a reactive crystallization process. In the fourth paper, nonlinear modeling is examined with a data set from the oil industry. The response has a nonlinear relation to the descriptor matrix, and the results are compared between linear modeling, polynomial PLS and nonlinear modeling using nonlinear score vectors.

Interdependence of Macroeconomics Variables, Stock Market Returns and Stock Market Volatility in Latin America

This thesis examines the interdependence of macroeconomic variables, stock market returns and stock market volatility in Latin America between 2000 and 2015. Argentina, Brazil, Chile, Colombia, Mexico and Peru were chosen as the sample markets, while inflation, interest rate, exchange rate, money supply, oil and gold were chosen as the sample macroeconomic variables. Bivariate VAR (1) model was applied to examine the mean return spillovers between the variables, whereas GARCH (1, 1) – BEKK model was applied to capture the volatility spillovers. The sample was divided into two smaller sub-periods, where the first sub-period covers from 2000 to 2007, and the second sub-period covers from 2007 to 2015. The empirical results report significant shock transmissions and volatility spillovers between inflation, interest rate, exchange rate, money supply, gold, oil and the selected markets, which suggests interdependence between the variables.