This thesis presents an empirical analysis of the unemployment hysteresis in the Czech Republic on quarterly data from 1999 to 2015. The hysteresis is modelled by allowing for: (i) impact of the cyclical unemployment on the NAIRU; (ii) impact of the long-term un- employment on the NAIRU. Models are written in state space form and estimated using Bayesian approach. The main contributions of this thesis are as follows. The results pro- vide robust evidence in favour of the hysteresis in the Czech Republic, but precise size of the hysteresis effect is surrounded by relatively large uncertainty. Posterior mean estimates of key parameters indicate that in response to increase in the cyclical unemployment of 1 percentage point, the NAIRU increases by 0.15 percentage points. The first specification of the hysteresis implies that the hysteresis induced changes in the Czech Republic's NAIRU of at most 1 percentage point. The hysteresis specified as impact of the long-term unemploy- ment on the NAIRU then implies even weaker effect, inducing changes in the NAIRU of at most 0.6 percentage points. The models are estimated jointly with the hybrid Phillips curve identified using survey forecasts as proxies for the expectations. Estimate of the expecta- tions' parameter 0.65 indicates the forward-looking nature of the Czech...

<p>Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, the spectral mixture (SM) kernel was proposed to model the spectral density of a single task in a Gaussian process framework. This work develops a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. The expressive capabilities of the CSM kernel are demonstrated through implementation of 1) a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel, and 2) a Gaussian process factor analysis model, where factor scores represent the utilization of cross-spectral neural circuits. Results are presented for measured multi-region electrophysiological data.</p> / Dissertation

With the technical advances in neuroscience experiments in the past few decades, we have seen a massive expansion in our ability to record neural activity. These advances enable neuroscientists to analyze more complex neural coding and communication properties, and at the same time, raise new challenges for analyzing neural spiking data, which keeps growing in scale, dimension, and complexity. This thesis proposes several new statistical methods that advance statistical analysis approaches for neural spiking data, including sequential Monte Carlo (SMC) methods for efficient estimation of neural dynamics from membrane potential threshold crossings, state-space models using multimodal observation processes, and goodness-of-fit analysis methods for neural marked point process models. In a first project, we derive a set of iterative formulas that enable us to simulate trajectories from stochastic, dynamic neural spiking models that are consistent with a set of spike time observations. We develop a SMC method to simultaneously estimate the parameters of the model and the unobserved dynamic variables from spike train data. We investigate the performance of this approach on a leaky integrate-and-fire model. In another project, we define a semi-latent state-space model to estimate information related to the phenomenon of hippocampal replay. Replay is a recently discovered phenomenon where patterns of hippocampal spiking activity that typically occur during exploration of an environment are reactivated when an animal is at rest. This reactivation is accompanied by high frequency oscillations in hippocampal local field potentials. However, methods to define replay mathematically remain undeveloped. In this project, we construct a novel state-space model that enables us to identify whether replay is occurring, and if so to estimate the movement trajectories consistent with the observed neural activity, and to categorize the content of each event. The state-space model integrates information from the spiking activity from the hippocampal population, the rhythms in the local field potential, and the rat's movement behavior. Finally, we develop a new, general time-rescaling theorem for marked point processes, and use this to develop a general goodness-of-fit framework for neural population spiking models. We investigate this approach through simulation and a real data application.

In this thesis, we study the queueing systems with heterogeneous servers and service rate uncertainty under the Halfin-Whitt heavy traffic regime. First, we analyse many server queues with abandonments when service rates are i.i.d. random variables. We derive a diffusion approximation using a novel method. The diffusion has a random drift, and hence depending on the realisations of service rates, the system can be in Quality Driven (QD), Efficiency Driven (ED) or Quality-Efficiency-Driven (QED) regime. When the system is under QD or QED regime, the abandonments are negligible in the fluid limit, but when it is under ED regime, the probability of abandonment will converge to a non-zero value. We then analyse the optimal staffing levels to balance holding costs with staffing costs combining these three regimes. We also analyse how the variance of service rates influence abandonment rate. Next, we focus on the state space collapse (SSC) phenomenon. We prove that under some assumptions, the system process will collapse to a lower dimensional process without losing essential information. We first formulate a general method to prove SSC results inside pools for heavy traffic systems using the hydrodynamic limit idea. Then we work on the SSC in multi-class queueing networks under the Halfin-Whitt heavy traffic when service rates are i.i.d. random variables within pools. For such systems, exact analysis provides limited insight on the general properties. Alternatively, asymptotic analysis by diffusion approximation proves to be effective. Further, limit theorems, which state the diffusively scaled system process weakly converges to a diffusion process, are usually the central part in such asymptotic analysis. The SSC result is key to proving such a limit. We conclude by giving examples on how SSC is applied to the analysis of systems.

The control theory of nonlinear systems has been receiving increasing attention in recent years, both for its technical importance as well as for its impact in various fields of application. In several key areas, such as aerospace, chemical and petrochemical industries, bioengineering, and robotics, a new practical application for this tool appears every day. System nonlinearity is characterized when at least one component or subsystem is nonlinear. Classical methods used in the study of linear systems, particularly superposition, are not usually applied to the nonlinear systems. It is necessary to use other methods to study the control of these systems. For a wide class of nonlinear systems, a rather important structural feature comes from the strong nonlinearity appearing as coupling between spectrally decoupled parts of the system. Even in the case of low frequencies, where lumped models can still be employed the nonlinear coupling between parts of the system requires specific treatment, using advanced mathematical tools. In this context, an alternative, frequency domain approach is pursued here. In the rest of this work, a specific system form of linearly decoupled but nonlinearly coupled subsystems is examined. The mathematical toolbox of the Hilbert transform is appropriately introduced for obtaining two low-pass subsystems that form an equivalent description of the essential overall system dynamics. The nonlinear coupled dynamics is investigated systematically by partitioning the coupled system state vector in such a way as to fully exploit the low-pass and the band-pass intrinsic features of free dynamics. In particular, by employing the Hilbert Transform, a low-pass equivalent system is derived. Then, a typical case is investigated thoroughly by means of numerical simulation of the original coupled low and band-pass, real-state-variable system and the low-pass-equivalent, complex-state-variable derived one. The nonlinear model equations considered here pave the way for a systematic investigation of nonlinear feedback control options designed to operate mechatronic transducers in energy harvesting, sensing or actuation modes.

This study applied a contemporary dynamic systems methodology (state space grids) to examine how the structure of parent-child coping interactions, above and beyond the content of such interactions, influences adjustment (i.e., internalizing problems, externalizing problems, and coping efficacy) over time in middle childhood. A community sample of children (N = 65) completed a stressful laboratory task with a parent present, during which parent and child behavior were observed. Parent behavior during the task was coded using a socialization of coping framework. Parents' verbal suggestions to their child about how to cope with the stressful task were coded as primary control engagement suggestions (i.e., suggestions encouraging the child to directly address and attempt to change the stressor or the child's associated emotions), secondary control engagement suggestions (i.e., suggestions encouraging the child to change their own reaction to their stressor), or disengagement suggestions (i.e., suggestions encouraging the child to take their attention away from the stressor). Child coping verbalizations and behavior during the task was coded as either engaging with the stressor or disengaging from the stressor. The structure of the parent-child coping interaction was measured in two ways: (a) dyadic flexibility, defined as the dispersion of parent and child behavior across all possible behaviors and the number of transitions between different parent or child behaviors during the task, and (b) attractor (i.e., parent-focused, child-focused, or dyad-focused interaction pattern) strength, defined as the number of visits, duration per visit, and return time to that interaction pattern. Child adjustment outcomes were measured using parent-report (internalizing and externalizing problems) and child-report (coping efficacy) at baseline and a 6-month follow-up. Linear regression analyses were conducted examining dyadic flexibility and the proposed attractors as predictors of child adjustment, while accounting for demographic variables, attractor content, and adjustment at baseline. Findings suggested that dyadic flexibility in the parent-child coping interaction was largely adaptive for child adjustment, whereas attractor strength demonstrated a more complex relationship with child adjustment outcomes. This study demonstrates the utility of applying state-space grids to examine the structure of parent-child coping interactions, in addition to content, as predictors of child adjustment. Furthermore, this study offers novel, detailed information about coping interactions in families with children in middle childhood. Clinical implications, limitations, and future directions are discussed.

<p>This report presents work done in the field of output error identification, with application to spark ignition (SI) engine identification for the purpose of air to fuel ratio control. The generic parts of the project consist mainly in setting out the basis for the design of output error identification software. Efficiency issues related to linear state space models have also been explored, and although the software design is not made explicit in this report, many of the important concepts have been implemented in order to provide powerful abstractions for the application to SI engine identification. </p><p>The SI engine identification data was obtained under normal operating conditions. The goal is to re- estimate models without utilizing a virtual measurement which has been used successfully to estimate models in the past. This turns out to be a difficult problem much related to the lack of excitation in the system input, shortcomings of the fuel dynamics model and the unknown and hard to estimate exhaust sensor characteristics. Indeed, the larger of the previously estimated models are found not to be identifiable in the present situation. However, trivial restrictions of the models (not meaning restriction to trivial models) avoid that problem.</p>

<p>By using AR/ARX-models on data generated by a nonlinear differential equation system representing a model for the cell-cycle control system in budding yeast, the interactions among proteins and thereby also to some extent the genes, are sought. A method consisting of graphical analysis of differences between estimates from two local linear models seems to make it possible to separate a set of linear equations from the nonlinear system. By comparing the properties of the estimations in the linear equations a set of approximate equations corresponding well to the real ones are found. </p><p>A NARX model is tested on the same system to see whether it is possible to find the dependencies in one of the nonlinear differential equations. This approach did, for the choice of model, not work.</p>

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 215-219).

Inflation is one of the most important macroeconomic variables. It is vital that policy makers receive accurate forecasts of inflation so that they can adjust their monetary policy to attain stability in the economy which has been shown to lead to economic growth. The purpose of this study is to model inflation and evaluate if applying the Kalman filter to SARIMA models lead to higher forecast accuracy compared to just using the SARIMA model. The Box-Jenkins approach to SARIMA modelling is used to obtain well-fitted SARIMA models and then to use a subset of observations to estimate a SARIMA model on which the Kalman filter is applied for the rest of the observations. These models are identified and then estimated with the use of monthly inflation for Luxembourg, Mexico, Portugal and Switzerland with the target to use them for forecasting. The accuracy of the forecasts are then evaluated with the error measures mean squared error (MSE), mean average deviation (MAD), mean average percentage error (MAPE) and the statistic Theil's U. For all countries these measures indicate that the Kalman filtered model yield more accurate forecasts. The significance of these differences are then evaluated with the Diebold-Mariano test for which only the difference in forecast accuracy of Swiss inflation is proven significant. Thus, applying the Kalman filter to SARIMA models with the target to obtain forecasts of monthly inflation seem to lead to higher or at least not lower predictive accuracy for the monthly inflation of these countries.