Contributions to the theory of maximum entropy estimation for ill-posed models

As técnicas estatísticas são fundamentais em ciência e a análise de regressão linear é, quiçá, uma das metodologias mais usadas. É bem conhecido da literatura que, sob determinadas condições, a regressão linear é uma ferramenta estatística poderosíssima. Infelizmente, na prática, algumas dessas condições raramente são satisfeitas e os modelos de regressão tornam-se mal-postos, inviabilizando, assim, a aplicação dos tradicionais métodos de estimação. Este trabalho apresenta algumas contribuições para a teoria de máxima entropia na estimação de modelos mal-postos, em particular na estimação de modelos de regressão linear com pequenas amostras, afetados por colinearidade e outliers. A investigação é desenvolvida em três vertentes, nomeadamente na estimação de eficiência técnica com fronteiras de produção condicionadas a estados contingentes, na estimação do parâmetro ridge em regressão ridge e, por último, em novos desenvolvimentos na estimação com máxima entropia. Na estimação de eficiência técnica com fronteiras de produção condicionadas a estados contingentes, o trabalho desenvolvido evidencia um melhor desempenho dos estimadores de máxima entropia em relação ao estimador de máxima verosimilhança. Este bom desempenho é notório em modelos com poucas observações por estado e em modelos com um grande número de estados, os quais são comummente afetados por colinearidade. Espera-se que a utilização de estimadores de máxima entropia contribua para o tão desejado aumento de trabalho empírico com estas fronteiras de produção. Em regressão ridge o maior desafio é a estimação do parâmetro ridge. Embora existam inúmeros procedimentos disponíveis na literatura, a verdade é que não existe nenhum que supere todos os outros. Neste trabalho é proposto um novo estimador do parâmetro ridge, que combina a análise do traço ridge e a estimação com máxima entropia. Os resultados obtidos nos estudos de simulação sugerem que este novo estimador é um dos melhores procedimentos existentes na literatura para a estimação do parâmetro ridge. O estimador de máxima entropia de Leuven é baseado no método dos mínimos quadrados, na entropia de Shannon e em conceitos da eletrodinâmica quântica. Este estimador suplanta a principal crítica apontada ao estimador de máxima entropia generalizada, uma vez que prescinde dos suportes para os parâmetros e erros do modelo de regressão. Neste trabalho são apresentadas novas contribuições para a teoria de máxima entropia na estimação de modelos mal-postos, tendo por base o estimador de máxima entropia de Leuven, a teoria da informação e a regressão robusta. Os estimadores desenvolvidos revelam um bom desempenho em modelos de regressão linear com pequenas amostras, afetados por colinearidade e outliers. Por último, são apresentados alguns códigos computacionais para estimação com máxima entropia, contribuindo, deste modo, para um aumento dos escassos recursos computacionais atualmente disponíveis.

Reflections of universal algebras into semilattices, their Galois theories, and related factorization systems

Estabelecemos uma condição suficiente para a preservação dos produtos finitos, pelo reflector de uma variedade de álgebras universais numa subvariedade, que é, também, condição necessária se a subvariedade for idempotente. Esta condição é estabelecida, seguidamente, num contexto mais geral e caracteriza reflexões para as quais a propriedade de ser semi-exacta à esquerda e a propriedade, mais forte, de ter unidades estáveis, coincidem. Prova-se que reflexões simples e semi-exactas à esquerda coincidem, no contexto das variedades de álgebras universais e caracterizam-se as classes do sistema de factorização derivado da reflexão. Estabelecem-se resultados que ajudam a caracterizar morfismos de cobertura e verticais-estáveis em álgebras universais e no contexto mais geral já referido. Caracterizam-se as classes de morfismos separáveis, puramente inseparáveis e normais. O estudo dos morfismos de descida de Galois conduz a condições suficientes para que o seu par kernel seja preservado pelo reflector.

Channel estimation and parameters acquisition systems employing cooperative diversity

This work investigates new channel estimation schemes for the forthcoming and future generation of cellular systems for which cooperative techniques are regarded. The studied cooperative systems are designed to re-transmit the received information to the user terminal via the relay nodes, in order to make use of benefits such as high throughput, fairness in access and extra coverage. The cooperative scenarios rely on OFDM-based systems employing classical and pilot-based channel estimators, which were originally designed to pointto-point links. The analytical studies consider two relaying protocols, namely, the Amplifyand-Forward and the Equalise-and-Forward, both for the downlink case. The relaying channels statistics show that such channels entail specific characteristics that comply to a proper filter and equalisation designs. Therefore, adjustments in the estimation process are needed in order to obtain the relay channel estimates, refine these initial estimates via iterative processing and obtain others system parameters that are required in the equalisation. The system performance is evaluated considering standardised specifications and the International Telecommunication Union multipath channel models.

Estimation of unemployment rates in small areas of Portugal: a best linear unbiased prediction approach versus a hierarchical Bayes approach

The high level of unemployment is one of the major problems in most European countries nowadays. Hence, the demand for small area labor market statistics has rapidly increased over the past few years. The Labour Force Survey (LFS) conducted by the Portuguese Statistical Office is the main source of official statistics on the labour market at the macro level (e.g. NUTS2 and national level). However, the LFS was not designed to produce reliable statistics at the micro level (e.g. NUTS3, municipalities or further disaggregate level) due to small sample sizes. Consequently, traditional design-based estimators are not appropriate. A solution to this problem is to consider model-based estimators that "borrow information" from related areas or past samples by using auxiliary information. This paper reviews, under the model-based approach, Best Linear Unbiased Predictors and an estimator based on the posterior predictive distribution of a Hierarchical Bayesian model. The goal of this paper is to analyze the possibility to produce accurate unemployment rate statistics at micro level from the Portuguese LFS using these kinds of stimators. This paper discusses the advantages of using each approach and the viability of its implementation.

Open source data sensing software for ultrasonic non-invasive temperature estimation

In this paper, an open source solution for measurement of temperature and ultrasonic signals (RF-lines) is proposed. This software is an alternative to the expensive commercial data acquisition software, enabling the user to tune applications to particular acquisition architectures. The collected ultrasonic and temperature signals were used for non-invasive temperature estimation using neural networks. The existence of precise temperature estimators is an essential point aiming at the secure and effective applica tion of thermal therapies in humans. If such estimators exist then effective controllers could be developed for the therapeutic instrumentation. In previous works the time-shift between RF-lines echoes were extracted, and used for creation of neural networks estimators. The obtained estimators successfully represent the temperature in the time-space domain, achieving a maximum absolute error inferior to the threshold value defined for hyperthermia/diathermia applications.

A soft-computing approach for non-invasive temperature estimation

The domain of thermal therapies applications can be improved with the development of accurate non-invasive timespatial temperature models. These models should represent the non-linear tissue thermal behaviour and be capable of tracking temperature at both time-instant and spatial position. If such estimators exist then efficient controllers for the therapeutic instrumentation could be developed, and the desired safety and effectiveness reached.

A time frequency approach to blind deconvolution in multipath underwater channels

Blind deconvolution is studied in the underwater acoustic channel context, by time-frequency (TF) processing. The acoustic propagation environment is modelled by ray tracing and mathematically described by a multipath propagation channel. Representation of the received signal by means of a signal-dependent TF distribution (radially Gaussian kernel distribution) allowed to visualize the resolved replicas of the emitted signal, while signi cantly attenuating the inherent interferences of classic quadratic TF distributions. The source signal instantaneous frequency estimation was the starting point for both source and channel estimation. Source signature estimation was performed by either TF inversion, based on the Wigner-Ville distribution of the received signal, or a subspace- -based method. The channel estimate was obtained either via a TF formulation of the conventional matched- lter, or via matched- - ltering with the previously obtained source estimate. A shallow water realistic scenario is considered, comprising a 135-m depth water column and an acoustic source located at 90-m depth and 5.6-km range from the receiver. For the corresponding noiseless simulated data, the quality of the best estimates was 0.856 for the source signal, and 0.9664 and 0.9996 for the amplitudes and time-delays of the impulse response, respectively. Application of the proposed deconvolution method to real data of the INTIMATE '96 sea trial conduced to source and channel estimates with the quality of 0.530 and 0.843, respectively. TF processing has proved to remove the typical ill-conditioning of single sensor deterministic deconvolution techniques.

Numerical techniques for modeling Doppler ultrasound spectra systems

Evaluation of blood-flow Doppler ultrasound spectral content is currently performed on clinical diagnosis. Since mean frequency and bandwidth spectral parameters are determinants on the quantification of stenotic degree, more precise estimators than the conventional Fourier transform should be seek. This paper summarizes studies led by the author in this field, as well as the strategies used to implement the methods in real-time. Regarding stationary and nonstationary characteristics of the blood-flow signal, different models were assessed. When autoregressive and autoregressive moving average models were compared with the traditional Fourier based methods in terms of their statistical performance while estimating both spectral parameters, the Modified Covariance model was identified by the cost/benefit criterion as the estimator presenting better performance. The performance of three time-frequency distributions and the Short Time Fourier Transform was also compared. The Choi-Williams distribution proved to be more accurate than the other methods. The identified spectral estimators were developed and optimized using high performance techniques. Homogeneous and heterogeneous architectures supporting multiple instruction multiple data parallel processing were essayed. Results obtained proved that real-time implementation of the blood-flow estimators is feasible, enhancing the usage of more complex spectral models on other ultrasonic systems.

Essays on Applications of the Factor Model

Thesis (Ph.D.)--University of Washington, 2013

New methods for meta-analysis under a fixed effects framework, with frequentist and Bayesian estimation.

Thesis (Ph.D.)--University of Washington, 2015

Automatic Video Analysis for Fisheries Survey Systems

Thesis (Ph.D.)--University of Washington, 2015

Respiratory and non-respiratory sinus arrhythmia: implications for heart rate variability

The quantity of blood arriving at the left side of the heart oscillates throughout the breathing cycle due to the mechanics of breathing. Neurally regulated fluctuations in the length of the heart period act to dampen oscillations of the left ventricular stroke volume entering the aorta. We have reported that stroke volume oscillations but not spectral frequency variability stroke volume measures can be used to estimate the breathing frequency. This study investigated with the same recordings whether heart period oscillations or spectral heart rate variability measures could function as estimators of breathing frequency. Continuous 270 s cardiovascular recordings were obtained from 22 healthy adult volunteers in the supine and upright postures. Breathing was recorded simultaneously. Breathing frequency and heart period oscillation frequency were calculated manually, while heart rate variability spectral maximums were obtained using heart rate variability software. These estimates were compared to the breathing frequency using the Bland–Altman agreement procedure. Estimates were required to be \±10% (95% levels of agreement). The 95% levels of agreement measures for the heart period oscillation frequency (supine: -27.7 to 52.0%, upright: -37.8 to 45.9%) and the heart rate variability spectral maximum estimates (supine: -48.7 to 26.5% and -56.4 to 62.7%, upright: -37.8 to 39.3%) exceeded 10%. Multiple heart period oscillations were observed to occur during breathing cycles. Both respiratory and non-respiratory sinus arrhythmia was observed amongst healthy adults. This observation at least partly explains why heart period parameters and heart rate variability parameters are not reliable estimators of breathing frequency. In determining the validity of spectral heart rate variability measurements we suggest that it is the position of the spectral peaks and not the breathing

Advanced side information creation techniques and framework for Wyner-Ziv video coding

Recently, several distributed video coding (DVC) solutions based on the distributed source coding (DSC) paradigm have appeared in the literature. Wyner-Ziv (WZ) video coding, a particular case of DVC where side information is made available at the decoder, enable to achieve a flexible distribution of the computational complexity between the encoder and decoder, promising to fulfill novel requirements from applications such as video surveillance, sensor networks and mobile camera phones. The quality of the side information at the decoder has a critical role in determining the WZ video coding rate-distortion (RD) performance, notably to raise it to a level as close as possible to the RD performance of standard predictive video coding schemes. Towards this target, efficient motion search algorithms for powerful frame interpolation are much needed at the decoder. In this paper, the RD performance of a Wyner-Ziv video codec is improved by using novel, advanced motion compensated frame interpolation techniques to generate the side information. The development of these type of side information estimators is a difficult problem in WZ video coding, especially because the decoder only has available some reference, decoded frames. Based on the regularization of the motion field, novel side information creation techniques are proposed in this paper along with a new frame interpolation framework able to generate higher quality side information at the decoder. To illustrate the RD performance improvements, this novel side information creation framework has been integrated in a transform domain turbo coding based Wyner-Ziv video codec. Experimental results show that the novel side information creation solution leads to better RD performance than available state-of-the-art side information estimators, with improvements up to 2 dB: moreover, it allows outperforming H.264/AVC Intra by up to 3 dB with a lower encoding complexity.

Modelo de data mining para deteção de embolias pulmonares

Trabalho de Projeto para obtenção do grau de Mestre em Engenharia Informática e de Computadores

Sistema de multiprocessamento para simulação de N-corpos em FPGA

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia de Electrónica e Telecomunicações