Kalman Filter Algorithm for Rating and Prediction in Basketball

The Thesis presents a state-space model for a basketball league and a Kalman filter algorithm for the estimation of the state of the league. In the state-space model, each of the basketball teams is associated with a rating that represents its strength compared to the other teams. The ratings are assumed to evolve in time following a stochastic process with independent Gaussian increments. The estimation of the team ratings is based on the observed game scores that are assumed to depend linearly on the true strengths of the teams and independent Gaussian noise. The team ratings are estimated using a recursive Kalman filter algorithm that produces least squares optimal estimates for the team strengths and predictions for the scores of the future games. Additionally, if the Gaussianity assumption holds, the predictions given by the Kalman filter maximize the likelihood of the observed scores. The team ratings allow probabilistic inference about the ranking of the teams and their relative strengths as well as about the teams’ winning probabilities in future games. The predictions about the winners of the games are correct 65-70% of the time. The team ratings explain 16% of the random variation observed in the game scores. Furthermore, the winning probabilities given by the model are concurrent with the observed scores. The state-space model includes four independent parameters that involve the variances of noise terms and the home court advantage observed in the scores. The Thesis presents the estimation of these parameters using the maximum likelihood method as well as using other techniques. The Thesis also gives various example analyses related to the American professional basketball league, i.e., National Basketball Association (NBA), and regular seasons played in year 2005 through 2010. Additionally, the season 2009-2010 is discussed in full detail, including the playoffs.

Methods and applications for improving parameter prediction models for stand structures in Finland

This thesis report attempts to improve the models for predicting forest stand structure for practical use, e.g. forest management planning (FMP) purposes in Finland. Comparisons were made between Weibull and Johnson s SB distribution and alternative regression estimation methods. Data used for preliminary studies was local but the final models were based on representative data. Models were validated mainly in terms of bias and RMSE in the main stand characteristics (e.g. volume) using independent data. The bivariate SBB distribution model was used to mimic realistic variations in tree dimensions by including within-diameter-class height variation. Using the traditional method, diameter distribution with the expected height resulted in reduced height variation, whereas the alternative bivariate method utilized the error-term of the height model. The lack of models for FMP was covered to some extent by the models for peatland and juvenile stands. The validation of these models showed that the more sophisticated regression estimation methods provided slightly improved accuracy. A flexible prediction and application for stand structure consisted of seemingly unrelated regression models for eight stand characteristics, the parameters of three optional distributions and Näslund s height curve. The cross-model covariance structure was used for linear prediction application, in which the expected values of the models were calibrated with the known stand characteristics. This provided a framework to validate the optional distributions and the optional set of stand characteristics. Height distribution is recommended for the earliest state of stands because of its continuous feature. From the mean height of about 4 m, Weibull dbh-frequency distribution is recommended in young stands if the input variables consist of arithmetic stand characteristics. In advanced stands, basal area-dbh distribution models are recommended. Näslund s height curve proved useful. Some efficient transformations of stand characteristics are introduced, e.g. the shape index, which combined the basal area, the stem number and the median diameter. Shape index enabled SB model for peatland stands to detect large variation in stand densities. This model also demonstrated reasonable behaviour for stands in mineral soils.

Chemical Characterization of Urban Background Aerosol Using Online And Filter Methods

In order to evaluate the influence of ambient aerosol particles on cloud formation, climate and human health, detailed information about the concentration and composition of ambient aerosol particles is needed. The dura-tion of aerosol formation, growth and removal processes in the atmosphere range from minutes to hours, which highlights the need for high-time-resolution data in order to understand the underlying processes. This thesis focuses on characterization of ambient levels, size distributions and sources of water-soluble organic carbon (WSOC) in ambient aerosols. The results show that in the location of this study typically 50-60 % of organic carbon in fine particles is water-soluble. The amount of WSOC was observed to increase as aerosols age, likely due to further oxidation of organic compounds. In the boreal region the main sources of WSOC were biomass burning during the winter and secondary aerosol formation during the summer. WSOC was mainly attributed to a fine particle mode between 0.1 - 1 μm, although different size distributions were measured for different sources. The WSOC concentrations and size distributions had a clear seasonal variation. Another main focus of this thesis was to test and further develop the high-time-resolution methods for chemical characterization of ambient aerosol particles. The concentrations of the main chemical components (ions, OC, EC) of ambient aerosol particles were measured online during a year-long intensive measurement campaign conducted on the SMEAR III station in Southern Finland. The results were compared to the results of traditional filter collections in order to study sampling artifacts and limitations related to each method. To achieve better a time resolution for the WSOC and ion measurements, a particle-into-liquid sampler (PILS) was coupled with a total organic carbon analyzer (TOC) and two ion chromatographs (IC). The PILS-TOC-IC provided important data about diurnal variations and short-time plumes, which cannot be resolved from the filter samples. In summary, the measurements made for this thesis provide new information on the concentrations, size distribu-tions and sources of WSOC in ambient aerosol particles in the boreal region. The analytical and collection me-thods needed for the online characterization of aerosol chemical composition were further developed in order to provide more reliable high-time-resolution measurements.

Investigating online reading with eye tracking and EEG : The influence of text format, reading task and parafoveal stimuli on reading processes

Research on reading has been successful in revealing how attention guides eye movements when people read single sentences or text paragraphs in simplified and strictly controlled experimental conditions. However, less is known about reading processes in more naturalistic and applied settings, such as reading Web pages. This thesis investigates online reading processes by recording participants eye movements. The thesis consists of four experimental studies that examine how location of stimuli presented outside the currently fixated region (Study I and III), text format (Study II), animation and abrupt onset of online advertisements (Study III), and phase of an online information search task (Study IV) affect written language processing. Furthermore, the studies investigate how the goal of the reading task affects attention allocation during reading by comparing reading for comprehension with free browsing, and by varying the difficulty of an information search task. The results show that text format affects the reading process, that is, vertical text (word/line) is read at a slower rate than a standard horizontal text, and the mean fixation durations are longer for vertical text than for horizontal text. Furthermore, animated online ads and abrupt ad onsets capture online readers attention and direct their gaze toward the ads, and distract the reading process. Compared to a reading-for-comprehension task, online ads are attended to more in a free browsing task. Moreover, in both tasks abrupt ad onsets result in rather immediate fixations toward the ads. This effect is enhanced when the ad is presented in the proximity of the text being read. In addition, the reading processes vary when Web users proceed in online information search tasks, for example when they are searching for a specific keyword, looking for an answer to a question, or trying to find a subjectively most interesting topic. A scanning type of behavior is typical at the beginning of the tasks, after which participants tend to switch to a more careful reading state before finishing the tasks in the states referred to as decision states. Furthermore, the results also provided evidence that left-to-right readers extract more parafoveal information to the right of the fixated word than to the left, suggesting that learning biases attentional orienting towards the reading direction.