Mark-recapture methods use repeated captures of individually identifiable animals to provide estimates of properties of populations. Different models allow estimates to be obtained for population size and rates of processes governing population dynamics. State-space models consist of two linked processes evolving simultaneously over time. The state process models the evolution of the true, but unknown, states of the population. The observation process relates observations on the population to these true states. Mark-recapture models specified within a state-space framework allow population dynamics models to be embedded in inference ensuring that estimated changes in the population are consistent with assumptions regarding the biology of the modelled population. This overcomes a limitation of current mark-recapture methods. Two alternative approaches are considered. The "conditional" approach conditions on known numbers of animals possessing capture history patterns including capture in the current time period. An animal's capture history determines its state; consequently, capture parameters appear in the state process rather than the observation process. There is no observation error in the model. Uncertainty occurs only through the numbers of animals not captured in the current time period. An "unconditional" approach is considered in which the capture histories are regarded as observations. Consequently, capture histories do not influence an animal's state and capture probability parameters appear in the observation process. Capture histories are considered a random realization of the stochastic observation process. This is more consistent with traditional mark-recapture methods. Development and implementation of particle filtering techniques for fitting these models under each approach are discussed. Simulation studies show reasonable performance for the unconditional approach and highlight problems with the conditional approach. Strengths and limitations of each approach are outlined, with reference to Soay sheep data analysis, and suggestions are presented for future analyses.

<p>This thesis deals with the problem of detecting faults in an environment where the measurements are affected by additive noise. To do this, a residual sensitive to faults is derived and statistical methods are used to distinguish faults from noise. Standard methods for fault detection compare a batch of data with a model of the system using the generalized likelihood ratio. Careful treatment of the initial state of the model is quite important, in particular for short batch sizes. One method to handle this is the parity-space method which solves the problem by removing the influence of the initial state using a projection.</p><p>In this thesis, the case where prior knowledge about the initial state is available is treated. This can be obtained for example from a Kalman filter. Combining the prior estimate with a minimum variance estimate from the data batch results in a smoothed estimate. The influence of the estimated initial state is then removed. It is also shown that removing the influence of the initial state by an estimate from the data batch will result in the parity-space method. To model slowly changing faults, an efficient parameterization using Chebyshev polynomials is given.</p><p>The methods described above have been applied to an Inertial Measurement Unit, IMU. The IMU usually consists of accelerometers and gyroscopes, but has in this work been extended with a magnetometer. Traditionally, the IMU has been used to estimate position and orientation of airplanes, missiles etc. Recently, the size and cost has decreased making it possible to use IMU:s for applications such as augmented reality and body motion analysis. Since a magnetometer is very sensitive to disturbances from metal, such disturbances have to be detected. Detection of the disturbances makes compensation possible. Another topic covered is the fundamental question of observability for fault inputs. Given a fixed or linearly growing fault, conditions for observability are given.</p><p>The measurements from the IMU show that the noise distribution of the sensors can be well approximated with white Gaussian noise. This gives good correspondence between practical and theoretical results when the sensor is kept at rest. The disturbances for the IMU can be approximated using smooth functions with respect to time. Low rank parameterizations can therefore be used to describe the disturbances. The results show that the use of smoothing to obtain the initial state estimate and parameterization of the disturbances improves the detection performance drastically.</p>

This thesis deals with the problem of detecting faults in an environment where the measurements are affected by additive noise. To do this, a residual sensitive to faults is derived and statistical methods are used to distinguish faults from noise. Standard methods for fault detection compare a batch of data with a model of the system using the generalized likelihood ratio. Careful treatment of the initial state of the model is quite important, in particular for short batch sizes. One method to handle this is the parity-space method which solves the problem by removing the influence of the initial state using a projection. In this thesis, the case where prior knowledge about the initial state is available is treated. This can be obtained for example from a Kalman filter. Combining the prior estimate with a minimum variance estimate from the data batch results in a smoothed estimate. The influence of the estimated initial state is then removed. It is also shown that removing the influence of the initial state by an estimate from the data batch will result in the parity-space method. To model slowly changing faults, an efficient parameterization using Chebyshev polynomials is given. The methods described above have been applied to an Inertial Measurement Unit, IMU. The IMU usually consists of accelerometers and gyroscopes, but has in this work been extended with a magnetometer. Traditionally, the IMU has been used to estimate position and orientation of airplanes, missiles etc. Recently, the size and cost has decreased making it possible to use IMU:s for applications such as augmented reality and body motion analysis. Since a magnetometer is very sensitive to disturbances from metal, such disturbances have to be detected. Detection of the disturbances makes compensation possible. Another topic covered is the fundamental question of observability for fault inputs. Given a fixed or linearly growing fault, conditions for observability are given. The measurements from the IMU show that the noise distribution of the sensors can be well approximated with white Gaussian noise. This gives good correspondence between practical and theoretical results when the sensor is kept at rest. The disturbances for the IMU can be approximated using smooth functions with respect to time. Low rank parameterizations can therefore be used to describe the disturbances. The results show that the use of smoothing to obtain the initial state estimate and parameterization of the disturbances improves the detection performance drastically.

Model diagnostics for normal and non-normal state space models is based on recursive residuals which are defined from the one-step ahead predictive distribution. Routine calculation of these residuals is discussed in detail. Various tools of diagnostics are suggested to check e.g. for wrong observation distributions and for autocorrelation. The paper also covers such topics as model diagnostics for discrete time series, model diagnostics for generalized linear models, and model discrimination via Bayes factors. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

In this study, neutral real interest rate gap and output gap are estimated jointly under two different multivariate unobserved components models with the motivation to provide empirical measures that can be used to analyze the amount of stimulus that monetary policy is passing on to the economy, and to understand historical macroeconomic developments. In the analyses, Kalman filter technique is applied to a small-scale macroeconomic model of the Turkish economy to estimate the unobserved variables for the period 1989-2005. In addition, two alternative specifications for neutral real interest rate are used in the analyses. The first model uses a random walk model for the neutral real interest rate, whereas the second one employs more structural specification, which specifically links the neutral real rate with the trend growth rate and the long-term course of the risk premium. Comparison of the models developed by using various performance criteria clearly indicates the use of more structural specification against random walk specification. Results suggest that though there is relatively high uncertainty surrounding the neutral real interest rate estimates to use them directly in the policy-making process, estimates appear to be very useful for ex-post monetary policy evaluations.

In recent years, trade activity in stock markets has increased substantially. This is mainly attributed to the development of powerful computers and intranets connecting traders to markets across the globe. The trades have to be carried out almost instantaneously and the systems in place that handle trades are burdened with millions of transactions a day, several thousand a minute. With increasing transactions the time to execute a single trade increases, and this can be seen as an impact on the performance. There is a need to model the performance of these systems and provide forecasts to give a heads up on when a system is expected to be overwhelmed by transactions. This was done in this study, in cooperation with Cinnober Financial Technologies, a firm which provides trading solutions to stock markets. To ensure that the models developed weren‟t biased, the dataset was cleansed, i.e. operational and other transactions were removed, and only valid trade transactions remained. For this purpose, a descriptive analysis of time series along with change point detection and LOESS regression were used. State space model with Kalman Filtering was further used to develop a time varying coefficient model for the performance, and this model was applied to make forecasts. Wavelets were also used to produce forecasts, and besides this high pass filters were used to identify low performance regions. The State space model performed very well to capture the overall trend in performance and produced reliable forecasts. This can be ascribed to the property of Kalman Filter to handle noisy data well. Wavelets on the other hand didn‟t produce reliable forecasts but were more efficient in detecting regions of low performance.

This portfolio of compositions investigates the adaptation of state-space models, frequently used in engineering control theory, to the electroacoustic composition context. These models are mathematical descriptions of physical systems that provide several variables representing the system’s behaviours. The composer adapts a set of state-space models of either abstract, mechanical or electrical systems to a music creation environment. She uses them in eight compositions: five mixed media multi-channel pieces and three mixed media pieces. In the portfolio, the composer investigates multiple ways of meaningfully mapping these system’s behaviours into music parameters. This is done either by exploring and creating timbre in synthetic sound, or by transforming existing sounds. The research also involves the process of incorporating state-space models as a real-time software tool using Max and SuperCollider. As real-time models offer several variables of continuous evolutions, the composer mapped them to different dimensions of sound simultaneously. The composer represented the model’s evolutions with either short/interrupted, long or indefinitely evolving sounds. The evolution implies changes in timbre, length and dynamic range. The composer creates gestures, textures and spaces based on the model’s behaviours. The composer explores how the model’s nature influences the musical language and the integration of these with other music sources such as recordings or musical instruments. As the models represent physical processes, the composer observes that the resulting sounds evolve in organic ways. Moreover, the composer not only sonifies the real-time models, but actually excites them to cause changes. The composer develops a compositional methodology which involves interacting with the models while observing/designing changes in sound. In that sense, the composer regards real-time state-space models as her own instruments to create music. The models are regarded as additional forces and as sound transforming agents in mixed media pieces. In fixed media pieces, the composer additionally exploits their linearity to create space through sound de-correlation.

[pt] Esta dissertação tem como objetivo principal a apresentação, discussão e implementação de um modelo de espaço de estado, derivado do modelo desenvolvido por De Jong & Zenhwirth, no cenário de estimação de reservas IBNR. O modelo visa obter uma distribuição para as reservas e seu desvio padrão, que permite obter um intervalo de confiança para a estimativa. Também são propostas extensões para o modelo. / [en] The main purpose of this master thesis is the presentation, discussion and implementation of a state space model, derived from the De Jong & Zehnwirth model, on the IBNR Reserve estimation scenario. The model tries to obtain a distribution for the reserves and its standard deviation as well, allowing the cofidence interval estimation. Extensions for the model are also discussed.

Prediction of energy load profiles is an important topic in Smart Grid technologies. Accurate forecasts can lead to reduced costs and decreased dependency on commercial power suppliers by adapting to prices on energy market, efficient utilisation of solar and wind energy and sophisticated load scheduling. This thesis compares various statistical and machine learning models and their ability to forecast load profile for an entire day divided into 48 half-hour intervals. Additionally, we examine various preprocessing methods and their influence on the accuracy of the models. We also compare a variety of imputation methods that are designed to reconstruct missing observation commonly present in energy consumption data.

Bird migration is a poorly-known yet important phenomenon, as understanding movement patterns of birds can inform conservation strategies and public health policy for animal-borne diseases. Recent advances in wildlife tracking technology, in particular the Motus system, have allowed researchers to track even small flying birds and insects with radio transmitters that weigh fractions of a gram. This system relies on a community-based distributed sensor network that detects tagged animals as they move through the detection nodes on journeys that range from small local movements to intercontinental migrations. The quantity of data generated by the Motus system is unprecedented, is on its way to surpass the size of all other centralized databases of animal detection and requires novel statistical methods. Building from the bsam package in R, I propose two new biologically informed Bayesian state-space models for animal movement in JAGS that include informed assumptions about songbird behavior. I evaluate the models using a simulation study in realistic conditions of data missingness. One of these models is generalized to a hierarchical version that fits population-level movement through joint estimation of movement parameters over multiple animal tracks. To apply the models, I then employ a localization routine on a Motus data set from migrating songbirds (Red-eyed Vireos - Vireo olivaceus) from the Eastern coast of North America. This allows me to apply the new hierarchical model and its predecessor to estimate unobserved locations and behaviors. Migratory flights were observed to occur mostly in the evenings along the coast and directed migratory flights were detected over water over e.g. the Bay of Fundy, the Long Island Sound and the New York Bight. Area-restricted searches were confined to coastal areas, in particular the Gulf of Maine, Long Island and Cape May.