abstract: Behavior-driven obesity has become one of the most challenging global epidemics since the 1990s, and is presently associated with the leading causes of death in the U.S. and worldwide, including diabetes, cardiovascular disease, strokes, and some forms of cancer. The use of system identification and control engineering principles in the design of novel and perpetually adaptive behavioral health interventions for promoting physical activity and healthy eating has been the central theme in many recent contributions. However, the absence of experimental studies specifically designed with the purpose of developing control-oriented behavioral models has restricted prior efforts in this domain to the use of hypothetical simulations to demonstrate the potential viability of these interventions. In this dissertation, the use of first-of-a-kind, real-life experimental results to develop dynamic, participant-validated behavioral models essential for the design and evaluation of optimized and adaptive behavioral interventions is examined. Following an intergenerational approach, the first part of this work aims to develop a dynamical systems model of intrauterine fetal growth with the prime goal of predicting infant birth weight, which has been associated with subsequent childhood and adult-onset obesity. The use of longitudinal input-output data from the “Healthy Mom Zone” intervention study has enabled the estimation and validation of this fetoplacental model. The second part establishes a set of data-driven behavioral models founded on Social Cognitive Theory (SCT). The “Just Walk” intervention experiment, developed at Arizona State University using system identification principles, has lent a unique opportunity to estimate and validate both black-box and semiphysical SCT models for predicting physical activity behavior. Further, this dissertation addresses some of the model estimation challenges arising from the limitations of “Just Walk”, including the need for developing nontraditional modeling approaches for short datasets, as well as delivers a new theoretical and algorithmic framework for structured state-space model estimation that can be used in a broader set of application domains. Finally, adaptive closed-loop intervention simulations of participant-validated SCT models from “Just Walk” are presented using a Hybrid Model Predictive Control (HMPC) control law. A simple HMPC controller reconfiguration strategy for designing both single- and multi-phase intervention designs is proposed. / Dissertation/Thesis / Doctoral Dissertation Chemical Engineering 2021

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Stavové modely jsou neobyčejně užitečné v mnoha inženýrských a vědeckých oblastech. Jejich atraktivita vychází především z toho faktu, že poskytují obecný nástroj pro popis široké škály dynamických systémů reálného světa. Nicméně, z důvodu jejich obecnosti, přidružené úlohy inference parametrů a stavů jsou ve většině praktických situacích nepoddajné. Tato dizertační práce uvažuje dvě zvláště důležité třídy nelineárních a ne-Gaussovských stavových modelů: podmíněně konjugované stavové modely a Markovsky přepínající nelineární modely. Hlavní rys těchto modelů spočívá v tom, že---navzdory jejich nepoddajnosti---obsahují poddajnou podstrukturu. Nepoddajná část požaduje abychom využily aproximační techniky. Monte Carlo výpočetní metody představují teoreticky a prakticky dobře etablovaný nástroj pro řešení tohoto problému. Výhoda těchto modelů spočívá v tom, že poddajná část může být využita pro zvýšení efektivity Monte Carlo metod tím, že se uchýlíme k Rao-Blackwellizaci. Konkrétně, tato doktorská práce navrhuje dva Rao-Blackwellizované částicové filtry pro identifikaci buďto statických anebo časově proměnných parametrů v podmíněně konjugovaných stavových modelech. Kromě toho, tato práce adoptuje nedávnou particle Markov chain Monte Carlo metodologii pro návrh Rao-Blackwellizovaných částicových Gibbsových jader pro vyhlazování stavů v Markovsky přepínajících nelineárních modelech. Tyto jádra jsou posléze použity pro inferenci parametrů metodou maximální věrohodnosti v uvažovaných modelech. Výsledné experimenty demonstrují, že navržené algoritmy překonávají příbuzné techniky ve smyslu přesnosti odhadu a výpočetního času.

Network reconstruction is the process of recovering a unique structured representation of some dynamic system using input-output data and some additional knowledge about the structure of the system. Many network reconstruction algorithms have been proposed in recent years, most dealing with the reconstruction of strictly proper networks (i.e., networks that require delays in all dynamics between measured variables). However, no reconstruction technique presently exists capable of recovering both the structure and dynamics of networks where links are proper (delays in dynamics are not required) and not necessarily strictly proper.The ultimate objective of this dissertation is to develop algorithms capable of reconstructing proper networks, and this objective will be addressed in three parts. The first part lays the foundation for the theory of mathematical representations of proper networks, including an exposition on when such networks are well-posed (i.e., physically realizable). The second part studies the notions of abstractions of a network, which are other networks that preserve certain properties of the original network but contain less structural information. As such, abstractions require less a priori information to reconstruct from data than the original network, which allows previously-unsolvable problems to become solvable. The third part addresses our original objective and presents reconstruction algorithms to recover proper networks in both the time domain and in the frequency domain.

Exponential smoothing algorithms are very attractive for the practical world such as in industry. When considering bivariate exponential smoothing methods, in addition to the properties of univariate methods, additional properties give insight to relationships between the two components of a process, and also to the overall structure of the model. It is important to study these properties, but even with the merits the bivariate exponential smoothing algorithms have, exponential smoothing algorithms are nonstatistical/nonstochastic and to study the properties within exponential smoothing may be worthless. As an alternative approach, the (bivariate) ARIMA and the structural models which are classes of statistical models, are shown to generalize the exponential smoothing algorithms. We study these properties within these classes as they will have implications on exponential smoothing algorithms. Forecast properties are studied using the state space model and the Kalman filter. Comparison of ARIMA and structural model completes the study. / Mathematical Sciences / M. Sc. (Statistics)

This thesis studies bubbles in the U.S. stock market and how they are influenced by monetary policy pursued by the FED. Using Kalman filtering, the log-real price of S&P 500 is decomposed into a market-fundamentals component and a bubble component. The market-fundamentals component depends on the expected future dividends and the required rate of return, while the bubble component is treated as an unobserved state vector in the state-space model. The results suggest that, mainly in recent decades, the bubble has accounted for a substantial portion of S&P 500 price dynamics and might have played a significant role during major bull and bear markets. The innovation of this thesis is that it goes one step further and investigates the effects of monetary policy on both estimated components of S&P 500. For this purpose, the block- restriction VAR model is employed. The findings indicate that the decreasing interest rates have a significant short-term positive effect on the market-fundamentals component but not on the bubble. On the other hand, quantitative easing seems to have a positive effect on the bubble but not on the market-fundamentals component. Finally, the results suggest that the FED has not been successful at distinguishing between stock price movements due to fundamentals or the price misalignment.

[pt] Esta Dissertação procura, sob um enfoque freqüentista, discutir tecnologias para que se imponham restrições no processo de estimação de componentes não observáveis associadas a um modelo em Espaço de Estado (EE) arbitrário. O escopo do texto abrange desde procedimentos propostos pioneiramente por Howard Doran para restrições de igualdade, lineares e/ou não lineares, invariantes ou variantes no tempo, em modelos em EE lineares, até a adoção e o ajuste de estruturas mais delicadas, como os modelos em EE não lineares. Entende-se que estes últimos se constituem em uma alternativa relevante, caso seja requerida, por exemplo, a imposição de restrições de desigualdade. Técnicas e estratégias de implementação são apresentadas, debatidas e comparadas, incluindo-se também o processo de estimação de parâmetros desconhecidos e a questão de diagnósticos. Ao final, são apresentados exercícios empíricos com base nas tecnologias discutidas. Os modelos propostos para esta ilustração visam à realização da análise dinâmica de estilo baseado no retorno para carteiras de investimento brasileiras (a versão estática desses modelos fora introduzida por William Sharpe, para carteiras norte-americanas), os quais devem, eventualmente, abranger dois tipos de restrições nas componentes de interesse, quais sejam, um de igualdade e outro de desigualdade. / [en] This Dissertation aims, in a frequentist way, to discuss technologies for imposing restrictions in non-observable components associated with an arbitrary State Space (SS) model. The text scope ranges from procedures proposed originally by Howard Doran for equality, linear or non- linear, time invariant or time varying restrictions in a linear SS model, to adoption and estimation of more complicated structures like non-linear SS models. It is understood that these last ones are a relevant alternative, in cases of, for instance, inequality restrictions requirement. Implementation techniques and strategies are given, debated and compared, also including unknown parameters estimation and diagnostics analysis. At the end, empirical exercises are presented based on discussed methodologies. The proposed models for this illustration aim at dynamic return based style analysis for Brazilian investment portfolios (the static version of these models had been introduced by William Sharpe, for American portfolios), which shall eventually satisfy two kinds of restrictions on components of interest, namely one of equality and other of inequality.

Nous considérions des modèles à espace d'état où les observations sont multicatégorielles et longitudinales, et l'état est décrit par des modèles du type CHARN. Nous estimons l'état au moyen des récursivités de Kalman généralisées. Celles-ci reposent sur l'application d'une variété de filtres particulaires et de l’algorithme EM. Nos résultats sont appliqués à l'estimation du trait latent en qualité de vie. Ce qui fournit une alternative et une généralisation des méthodes existantes dans la littérature. Ces résultats sont illustrés par des simulations numériques et une application aux données réelles sur la qualité de vie des femmes ayant subi une opération pour cause de cancer du sein / We consider state space models where the observations are multicategorical and longitudinal, and the state is described by CHARN models. We estimate the state by generalized Kalman recursions, which rely on a variety of particle filters and EM algorithm. Our results are applied to estimating the latent trait in quality of life, and this furnishes an alternative and a generalization of existing methods. These results are illustrated by numerical simulations and an application to real data in the quality of life of patients surged for breast cancer

The aim of this thesis is to model the dynamics of international term structure of interest rates taking into consideration several dependence channels.Thanks to a new international Treasury yield curve database, we observe that the explained variability decision criterion, suggested by the literature, is not able to select the best combination of factors characterizing the joint dynamics of yield curves. We propose a new methodology based on the maximisation of the likelihood function of a Gaussian state-space model with common and local factors. The associated identification problem is solved in an innovative way. By estimating several sets of countries, we select two global (and three local) factors which are also useful to forecast macroeconomic variables in each considered economy.In addition, our method allows us to detect hidden factors in the international bond returns. They are not visible through a classical principal component analysis of expected bond returns but they are helpful to forecast inflation and industrial production. Keywords: International treasury yield curves, common and local factors, state-space models, EM algorithm, International bond risk premia, principal components.

Diss. (sammanfattning) Stockholm : Handelshögskolan, 2008 Sammanfattning jämte 3 uppsatser