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.

A Bayesian Approach for Forecasting Heat Load in a District Heating System

The growing population in cities increases the energy demand and affects the environment by increasing carbon emissions. Information and communications technology solutions which enable energy optimization are needed to address this growing energy demand in cities and to reduce carbon emissions. District heating systems optimize the energy production by reusing waste energy with combined heat and power plants. Forecasting the heat load demand in residential buildings assists in optimizing energy production and consumption in a district heating system. However, the presence of a large number of factors such as weather forecast, district heating operational parameters and user behavioural parameters, make heat load forecasting a challenging task. This thesis proposes a probabilistic machine learning model using a Naive Bayes classifier, to forecast the hourly heat load demand for three residential buildings in the city of Skellefteå, Sweden over a period of winter and spring seasons. The district heating data collected from the sensors equipped at the residential buildings in Skellefteå, is utilized to build the Bayesian network to forecast the heat load demand for horizons of 1, 2, 3, 6 and 24 hours. The proposed model is validated by using four cases to study the influence of various parameters on the heat load forecast by carrying out trace driven analysis in Weka and GeNIe. Results show that current heat load consumption and outdoor temperature forecast are the two parameters with most influence on the heat load forecast. The proposed model achieves average accuracies of 81.23 % and 76.74 % for a forecast horizon of 1 hour in the three buildings for winter and spring seasons respectively. The model also achieves an average accuracy of 77.97 % for three buildings across both seasons for the forecast horizon of 1 hour by utilizing only 10 % of the training data. The results indicate that even a simple model like Naive Bayes classifier can forecast the heat load demand by utilizing less training data.

Structure learning of context-specific graphical models

Abstract The ultimate problem considered in this thesis is modeling a high-dimensional joint distribution over a set of discrete variables. For this purpose, we consider classes of context-specific graphical models and the main emphasis is on learning the structure of such models from data. Traditional graphical models compactly represent a joint distribution through a factorization justi ed by statements of conditional independence which are encoded by a graph structure. Context-speci c independence is a natural generalization of conditional independence that only holds in a certain context, speci ed by the conditioning variables. We introduce context-speci c generalizations of both Bayesian networks and Markov networks by including statements of context-specific independence which can be encoded as a part of the model structures. For the purpose of learning context-speci c model structures from data, we derive score functions, based on results from Bayesian statistics, by which the plausibility of a structure is assessed. To identify high-scoring structures, we construct stochastic and deterministic search algorithms designed to exploit the structural decomposition of our score functions. Numerical experiments on synthetic and real-world data show that the increased exibility of context-specific structures can more accurately emulate the dependence structure among the variables and thereby improve the predictive accuracy of the models.

Clinical Learning Environment and Supervision. Development and Validation of the CLES Evaluation Scale

The purpose of the study is: (1) to describe how nursing students' experienced their clinical learning environment and the supervision given by staff nurses working in hospital settings; and (2) to develop and test an evaluation scale of Clinical Learning Environment and Supervision (CLES). The study has been carried out in different phases. The pilot study (n=163) explored the association between the characteristics of a ward and its evaluation as a learning environment by students. The second version of research instrument (which was developed by the results of this pilot study) were tested by an expert panel (n=9 nurse teachers) and test-retest group formed by student nurses (n=38). After this evaluative phase, the CLES was formed as the basic research instrument for this study and it was tested with the Finnish main sample (n=416). In this phase, a concurrent validity instrument (Dunn & Burnett 1995) was used to confirm the validation process of CLES. The international comparative study was made by comparing the Finnish main sample with a British sample (n=142). The international comparative study was necessary for two reasons. In the instrument developing process, there is a need to test the new instrument in some other nursing culture. Other reason for comparative international study is the reflecting the impact of open employment markets in the European Union (EU) on the need to evaluate and to integrate EU health care educational systems. The results showed that the individualised supervision system is the most used supervision model and the supervisory relationship with personal mentor is the most meaningful single element of supervision evaluated by nursing students. The ward atmosphere and the management style of ward manager are the most important environmental factors of the clinical ward. The study integrates two theoretical elements - learning environment and supervision - in developing a preliminary theoretical model. The comparative international study showed that, Finnish students were more satisfied and evaluated their clinical placements and supervision with higher scores than students in the United Kingdom (UK). The difference between groups was statistical highly significant (p= 0.000). In the UK, clinical placements were longer but students met their nurse teachers less frequently than students in Finland. Arrangements for supervision were similar. This research process has produced the evaluation scale (CLES), which can be used in research and quality assessments of clinical learning environment and supervision in Finland and in the UK. CLES consists of 27 items and it is sub-divided into five sub-dimensions. Cronbach's alpha coefficient varied from high 0.94 to marginal 0.73. CLES is a compact evaluation scale and user-friendliness makes it suitable for continuing evaluation.