Forecasting Election Results in the Czech Republic Kateřina Doskočilová In this thesis, a forecasting model for the 2017 legislative election in the Czech Republic is built. As the Czech Republic has a multi-party system, the outcomes of the model are the expected vote shares for each party. There are two types of forecasts calculated. Firstly, a poll-based forecast using a dynamic linear model and Kalman filter to weigh the information in the polls. Secondly, the prices on betting markets are translated into probabilistic forecasts for the expected vote shares. This is a novel approach as prediction markets were previously used to forecasts only the probabilities of winning an election. Finally, the two types of forecasts are combined into one and weighed by their variance. Comparing the forecasts, we conclude that the betting market is able to predict the exact vote shares the most accurately right before the election.

The time it takes an athlete to recover from an injury can be highly influenced by training procedures as well as the medical care and physical therapy received. When an injury occurs to the muscles or tendons of an athlete, it is desirable to cool the muscles and tendons within the body to reduce inflammation, thereby reducing the recovery time. Consequently, finding a method of treatment that is effective in reducing tendon temperatures is beneficial to increasing the speed at which the athlete is able to recover. In this project, Bayesian inference with Gaussian processes will be used to model the effect that different treatments have in reducing tendon temperature within the ankle. Gaussian processes provide a powerful methodology for modeling data that exhibit complex characteristics such as nonlinear behavior while retaining mathematical simplicity.

A main objective of Departments of Transportation is to improve the safety of the roadways over which they have jurisdiction. Safety projects, such as cable barriers and raised medians, are utilized to reduce both crash frequency and crash severity. The efficacy of these projects must be evaluated in order to use resources in the best way possible. Five models are proposed for the evaluation of traffic projects: (1) a Bayesian Poisson regression model; (2) a hierarchical Poisson regression model building on model (1) by adding hyperpriors; (3) a similar model correcting for overdispersion; (4) a dynamic linear model; and (5) a traditional before-after study model. Evaluation of these models is discussed using various metrics including DIC. Using the models selected for analysis, it was determined that cable barriers are quite effective at reducing severe crashes and cross-median crashes on Utah highways. Raised medians are also largely effective at reducing severe crashes. The results of before and after analyses are highly valuable to Departments of Transportation in identifying effective projects and in determining which roadway segments will benefit most from their implementation.

The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the "classical" approach and the "inverse" regression approach. Both of these models are static models and are used to estimate "exact" measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe the measurement. The Bayesian time series analysis method of Dynamic Linear Models (DLM) can be used to monitor the evolution of the measures, thus introducing a dynamic approach to statistical calibration. The research presented employs the use of Bayesian methodology to perform statistical calibration. The DLM framework is used to capture the time-varying parameters that may be changing or drifting over time. Dynamic based approaches to the linear, nonlinear, and multivariate calibration problem are presented in this dissertation. Simulation studies are conducted where the dynamic models are compared to some well known "static'" calibration approaches in the literature from both the frequentist and Bayesian perspectives. Applications to microwave radiometry are given.

In solving target tracking problems, the Kalman filter (KF) is a systematic estimation algorithm. Whether the state of a moving target adapts to the changes in the observations depends on the model assumptions. The interacting multiple model (IMM) algorithm uses interaction of a bank of parallel KFs by updating associated model probabilities. Every parallel KF has its model probability adjusted by the dynamic system. For moving targets of different dynamic linear models, an IMM with two KFs generally performs well. In this thesis, in order to improve the performance of target tracking and state estimation, multi-sensor data fusion technique will be used. Same types of IMMs can be incorporated in the cooperative IMM-based algorithm. The IMM-based estimators exchange with each other the estimates, model robabilities and model transition probabilities. A distributed algorithm for multi-sensor tracking usually needs a fusion center that integrates decisions or estimates, but the proposed cooperative IMM-based algorithm does not use the architecture. Cooperative IMM estimator structures exchange weights and estimates on the platforms to avoid accumulation of errors. Performance of data fusion may degrade due to different kinds of undesirable environmental effects. The simulations show that an IMM estimator with smaller measurement noise level can be used to compensate the other IMM, which is affected by larger measurement noise. In addition, failure of a sensor will cause the problem that model probabilities can not be updated in the corresponding estimator. Kalman filters will not be able to perform state correction for the moving target. To tackle the problem, we can use the estimates from other IMM estimators by adjusting the corresponding weights and model probabilities. The simulations show that the proposed cooperative IMM structure effectively improve the tracking performance.

<p>Financial stock market data, for various reasons, frequently contain missing values. One reason for this is that, because the markets close for holidays, daily stock prices are not always observed. This creates gaps in information, making it difficult to predict the following day’s stock prices. In this situation, information during the holiday can be “borrowed” from other countries’ stock market, since global stock prices tend to show similar movements and are in fact highly correlated. The main goal of this study is to combine stock index data from various markets around the world and develop an algorithm to impute the missing values in individual stock index using “information-sharing” between different time series. To develop imputation algorithm that accommodate time series-specific features, we take multiple imputation approach using dynamic linear model for time-series and panel data. This algorithm assumes ignorable missing data mechanism, as which missingness due to holiday. The posterior distributions of parameters, including missing values, is simulated using Monte Carlo Markov Chain (MCMC) methods and estimates from sets of draws are then combined using Rubin’s combination rule, rendering final inference of the data set. Specifically, we use the Gibbs sampler and Forward Filtering and Backward Sampling (FFBS) to simulate joint posterior distribution and posterior predictive distribution of latent variables and other parameters. A simulation study is conducted to check the validity and the performance of the algorithm using two error-based measurements: Root Mean Square Error (RMSE), and Normalized Root Mean Square Error (NRMSE). We compared the overall trend of imputed time series with complete data set, and inspected the in-sample predictability of the algorithm using Last Value Carried Forward (LVCF) method as a bench mark. The algorithm is applied to real stock price index data from US, Japan, Hong Kong, UK and Germany. From both of the simulation and the application, we concluded that the imputation algorithm performs well enough to achieve our original goal, predicting the stock price for the opening price after a holiday, outperforming the benchmark method. We believe this multiple imputation algorithm can be used in many applications that deal with time series with missing values such as financial and economic data and biomedical data.</p> / Thesis

Modelling of complex corroding industrial systems is ritical to effective inspection and maintenance for ssurance of system integrity. Wall thickness and corrosion rate are modelled for multiple dependent corroding omponents, given observations of minimum wall thickness per component. At each inspection, partial observations of the system are considered. A Bayes Linear approach is adopted simplifying parameter estimation and avoiding often unrealistic distributional assumptions. Key system variances are modelled, making exchangeability assumptions to facilitate analysis for sparse inspection time-series. A utility based criterion is used to assess quality of inspection design and aid decision making. The model is applied to inspection data from pipework networks on a full-scale offshore platform.

<p>This dissertation explores how consumers learn from repeated experiences with a product offering. It develops a new Bayesian consumer learning model, the unstable learning model. This model expands on existing models that explore learning when quality is stable, by considering when quality is changing. Further, the dissertation examines situations in which consumers may act as if quality is changing when it is stable or vice versa. This examination proceeds in two essays.</p><p>The first essay uses two experiments to examine how consumers learn when product quality is stable or changing. By collecting repeated measures of expectation data and experiences, more information enables estimation to discriminate between stable and unstable learning. The key conclusions are that (1) most consumers act as if quality is unstable, even when it is stable, and (2) consumers respond to the environment they face, adjusting their learning in the correct direction. These conclusions have important implications for the formation and value of brand equity.</p><p>Based on the conclusions of this first essay, the second essay develops a choice model of consumer learning when consumers believe quality is changing, even though it is not. A Monte Carlo experiment tests the efficacy of this model versus the standard model. The key conclusion is that both models perform similarly well when the model assumptions match the way consumers actually learn, but with a mismatch the existing model is biased, while the new model continues to perform well. These biases could lead to suboptimal branding decisions.</p> / Dissertation

Understanding the effect of human-induced pollution on the environment is an important precursor to promoting public health and environmental stability. One aspect of understanding pollution is understanding pollution sources. Various methods have been used and developed to understand pollution sources and the amount of pollution those sources emit. Multivariate receptor modeling seeks to estimate pollution source profiles and pollution emissions from concentrations of pollutants such as particulate matter (PM) in the air. Previous approaches to multivariate receptor modeling make the following two key assumptions: (1) PM measurements are independent and (2) source profiles are constant through time. Notwithstanding these assumptions, the existence of temporal correlation among PM measurements and time-varying source profiles is commonly accepted. In this thesis an approach to multivariate receptor modeling is developed in which the temporal structure of PM measurements is accounted for by modeling source profiles as a time-dependent Dirichlet process. The Dirichlet process (DP) pollution model developed herein is evaluated using several simulated data sets. In the presence of time-varying source profiles, the DP model more accurately estimates source profiles and source contributions than other multivariate receptor model approaches. Additionally, when source profiles are constant through time, the DP model outperforms other pollution receptor models by more accurately estimating source profiles and source contributions.

In the recent scenario of climate change, the natural variability and uncertainty associated with the hydrologic variables is of great concern to the community. This thesis opens up a new area of multi-disciplinary research. It is a promising field of research in hydrology and water resources that uses the information from the field of atmospheric science. A new way to identify and capture the variability and uncertainty associated with the hydrologic variables is established through this thesis. Assessment of hydroclimatic teleconnection for Indian subcontinent and its use in basin-scale hydrologic time series analysis and forecasting is the broad aim of this PhD thesis. The initial part of the thesis is devoted to investigate and establish the dependence of Indian summer monsoon rainfall (ISMR) on large-scale Oceanic-atmospheric circulation phenomena from tropical Pacific Ocean and Indian Ocean regions. El Niño-Southern Oscillation (ENSO) is the well established coupled Ocean-atmosphere mode of tropical Pacific Ocean whereas Indian Ocean Dipole (IOD) mode is the recently identified coupled Ocean-atmosphere mode of tropical Indian Ocean. Equatorial Indian Ocean Oscillation (EQUINOO) is known as the atmospheric component of IOD mode. The potential of ENSO and EQUINOO for predicting ISMR is investigated by Bayesian dynamic linear model (BDLM). A major advantage of this method is that, it is able to capture the dynamic nature of the cause-effect relationship between large-scale circulation information and hydrologic variables, which is quite expected in the climate change scenario. Another new method, proposed to capture the dependence between the teleconnected hydroclimatic variables is based on the theory of copula, which itself is quite new to the field of hydrology. The dependence of ISMR on ENSO and EQUINOO is captured and investigated for its potential use to predict the monthly variation of ISMR using the proposed method. The association of monthly variation of ISMR with the combined information of ENSO and EQUINOO, denoted by monthly composite index (MCI), is also investigated and established. The spatial variability of such association is also investigated. It is observed that MCI is significantly associated with monthly rainfall variation all over India, except over North-East (NE) India, where it is poor. Having established the hydroclimatic teleconnection at a comparatively larger scale, the hydroclimatic teleconnection for basin-scale hydrologic variables is then investigated and established. The association of large-scale atmospheric circulation with inflow during monsoon season into Hirakud reservoir, located in the state of Orissa in India, has been investigated. The strong predictive potential of the composite index of ENSO and EQUINOO is established for extreme inflow conditions. So the methodology of inflow prediction using the information of hydroclimatic teleconnection would be very suitable even for ungauged or poorly gauged watersheds as this approach does not use any information about the rainfall in the catchment. Recognizing the basin-scale hydroclimatic association with both ENSO and EQUINOO at seasonal scale, the information of hydroclimatic teleconnection is used for streamflow forecasting for the Mahanadi River basin in the state of Orissa, India, both at seasonal and monthly scale. It is established that the basin-scale streamflow is influenced by the large-scale atmospheric circulation phenomena. Information of streamflow from previous month(s) alone, as used in most of the traditional modeling approaches, is shown to be inadequate. It is successfully established that incorporation of large-scale atmospheric circulation information significantly improves the performance of prediction at monthly scale. Again, the prevailing conditions/characteristics of watershed are also important. Thus, consideration of both the information of previous streamflow and large-scale atmospheric circulations are important for basin-scale streamflow prediction at monthly time-scale. Adopting the developed approach of using the information of hydroclimatic teleconnection, hydrologic variables can be predicted with better accuracy which will be a very useful input for better management of water resources.