Normalizing flows represent a class of generative models that exhibit a number of attractive properties, but do not always achieve state-of-the-art performance when it comes to perceived naturalness of generated samples. To improve the quality of generated samples, this thesis examines methods to enhance the expressivity of discrete-time normalizing flow models and thus their ability to capture different aspects of the data. In the first part of the thesis, we propose an invertible neural network architecture as an alternative to popular architectures like Glow that require an individual neural network per flow step. Although our proposal greatly reduces the number of parameters, it has not been done before, as such architectures are believed to not be powerful enough. For this reason, we define two optional extensions that could greatly increase the expressivity of the architecture. We use augmentation to add Gaussian noise variables to the input to achieve arbitrary hidden-layer widths that are no longer dictated by the dimensionality of the data. Moreover, we implement Piecewise Affine Activation Functions that represent a generalization of Leaky ReLU activations and allow for more powerful transformations in every individual step. The resulting three models are evaluated on two simple synthetic datasets – the two moons dataset and one generated from a mixture of eight Gaussians. Our findings indicate that the proposed architectures cannot adequately model these simple datasets and thus do not represent alternatives to current stateof-the-art models. The Piecewise Affine Activation Function significantly improved the expressivity of the invertible neural network, but could not make use of its full potential due to inappropriate assumptions about the function’s input distribution. Further research is needed to ensure that the input to this function is always standard normal distributed. We conducted further experiments with augmentation using the Glow model and could show minor improvements on the synthetic datasets when only few flow steps (two, three or four) were used. However, in a more realistic scenario, the model would encompass many more flow steps. Lastly, we generalized the transformation in the coupling layers of modern flow architectures from an elementwise affine transformation to a matrixbased affine transformation and studied the effect this had on MoGlow, a flow-based model of motion. We could show that McMoGlow, our modified version of MoGlow, consistently achieved a better training likelihood than the original MoGlow on human locomotion data. However, a subjective user study found no statistically significant difference in the perceived naturalness of the samples generated. As a possible reason for this, we hypothesize that the improvements are subtle and more visible in samples that exhibit slower movements or edge cases which may have been underrepresented in the user study. / Normalizing flows representerar en klass av generativa modeller som besitter ett antal eftertraktade egenskaper, men som inte alltid uppnår toppmodern prestanda när det gäller upplevd naturlighet hos genererade data. För att förbättra kvaliteten på dessa modellers utdata, undersöker detta examensarbete metoder för att förbättra uttrycksfullheten hos Normalizing flows-modeller i diskret tid, och därmed deras förmåga att fånga olika aspekter av datamaterialet. I den första delen av uppsatsen föreslår vi en arkitektur uppbyggt av ett inverterbart neuralt nätverk. Vårt förslag är ett alternativ till populära arkitekturer som Glow, vilka kräver individuella neuronnät för varje flödessteg. Även om vårt förslag kraftigt minskar antalet parametrar har detta inte gjorts tidigare, då sådana arkitekturer inte ansetts vara tillräckligt kraftfulla. Av den anledningen definierar vi två oberoende utökningar till arkitekturen som skulle kunna öka dess uttrycksfullhet avsevärt. Vi använder så kallad augmentation, som konkatenerar Gaussiska brusvariabler till observationsvektorerna för att uppnå godtyckliga bredder i de dolda lagren, så att deras bredd inte längre begränsas av datadimensionaliteten. Dessutom implementerar vi Piecewise Affine Activation-funktioner (PAAF), vilka generaliserar Leaky ReLU-aktiveringar genom att möjliggöra mer kraftfulla transformationer i varje enskilt steg. De resulterande tre modellerna utvärderas med hjälp av två enkla syntetiska datamängder - ”the two moons dataset” och ett som genererats genom att blanda av åtta Gaussfördelningar. Våra resultat visar att de föreslagna arkitekturerna inte kan modellera de enkla datamängderna på ett tillfredsställande sätt, och därmed inte utgör kompetitiva alternativ till nuvarande moderna modeller. Den styckvisa aktiveringsfunktionen förbättrade det inverterbara neurala nätverkets uttrycksfullhet avsevärt, men kunde inte utnyttja sin fulla potential på grund av felaktiga antaganden om funktionens indatafördelning. Ytterligare forskning behövs för att hantera detta problem. Vi genomförde ytterligare experiment med augmentation av Glow-modellen och kunde påvisa vissa förbättringar på de syntetiska dataseten när endast ett fåtal flödessteg (två, tre eller fyra) användes. Däremot omfattar modeller i mer realistiska scenarion många fler flödessteg. Slutligen generaliserade vi transformationen i kopplingslagren hos moderna flödesarkitekturer från en elementvis affin transformation till en matrisbaserad affin transformation, samt studerade vilken effekt detta hade på MoGlow, en flödesbaserad modell av 3D-rörelser. Vi kunde visa att McMoGlow, vår modifierade version av MoGlow, konsekvent uppnådde bättre likelihood i träningen än den ursprungliga MoGlow gjorde på mänskliga rörelsedata. En subjektiv användarstudie på exempelrörelser genererade från MoGlow och McMoGlow visade dock ingen statistiskt signifikant skillnad i användarnas uppfattning av hur naturliga rörelserna upplevdes. Som en möjlig orsak till detta antar vi att förbättringarna är subtila och mer synliga i situationer som uppvisar långsammare rörelser eller i olika gränsfall som kan ha varit underrepresenterade i användarstudien.

This project focuses on deep neural network (DNN)-based non-intrusive speech quality assessment, specifically addressing the challenge of predicting mean-opinion-score (MOS) with interpretable posterior distributions. The conventional approach of providing a single point estimate for MOS lacks interpretability and doesn't capture the uncertainty inherent in subjective assessments. This thesis introduces DeePMOS, a novel framework capable of producing MOS predictions in the form of posterior distributions, offering a more nuanced and understandable representation of speech quality. DeePMOS adopts a CNN-BLSTM architecture with multiple prediction heads to model Gaussian and Beta posterior distributions. For robust training, we use a combination of maximum-likelihood learning, stochastic gradient noise, and a student-teacher learning setup to handle limited and noisy training data. Results showcase DeePMOS's competitive performance, particularly with DeePMOS-B achieving state-of-the-art utterance-level performance. The significance lies in providing accurate predictions along with a measure of confidence, enhancing transparency and reliability. This opens avenues for application in domains such as telecommunications and audio-processing systems. Future work could explore additional posterior distributions, evaluate the model on high-quality datasets, and consider incorporating listener-dependent scores. / Detta projekt fokuserar på icke-intrusiv bedömning av tal-kvalitet med hjälp av djupa neurala nätverk (DNN), särskilt för att hantera utmaningen att förutsäga mean-opinion-score (MOS) med tolkningsbara posteriora fördelningar. Den konventionella metoden att ge en enda punktsuppskattning för MOS saknar tolkningsbarhet och fångar inte osäkerheten som är inneboende i subjektiva bedömningar. Denna avhandling introducerar DeePMOS, en ny ramverk kapabel att producera MOS-förutsägelser i form av posteriora fördelningar, vilket ger en mer nyanserad och förståelig representation av tal-kvalitet. DeePMOS antar en CNN-BLSTM-arkitektur med flera förutsägelsehuvuden för att modellera Gaussiska och Beta-posteriora fördelningar. För robust träning använder vi en kombination av maximum-likelihood learning, stokastisk gradientbrus och en student-lärare inlärningsuppsättning för att hantera begränsad och brusig träningsdata. Resultaten visar DeePMOS konkurrenskraftiga prestanda, särskilt DeePMOS-B som uppnår state-of-the-art prestanda på uttalnivå. Signifikansen ligger i att ge noggranna förutsägelser tillsammans med en mått på förtroende, vilket ökar transparensen och tillförlitligheten. Detta öppnar möjligheter för tillämpningar inom områden som telekommunikation och ljudbehandlingssystem. Framtida arbete kan utforska ytterligare posteriora fördelningar, utvärdera modellen på högkvalitativa dataset och överväga att inkludera lyssnarberoende poäng.

International Telemetering Conference Proceedings / October 21, 2002 / Town & Country Hotel and Conference Center, San Diego, California / This paper presents noncoherent limiter-discriminator detection and differential detection of FQPSK (Feher quadrature phase-shift-keying) with maximum-likelihood sequence estimation (MLSE) techniques. Noncoherent FQPSK systems are suitable for fast fading and cochannel interference channels and channels with strong phase noise, and they can offer faster synchronization and reduce outage events compared with conventional coherent systems. In this paper, both differential detection and limiter-discriminator detection of FQPSK are discussed. We use MLSE with lookup tables to exploit the memory in noncoherently detected FQPSK signals and thus significantly improve the bit error rate (BER) performance in an additive white Gaussian noise (AWGN) channel.

Multicarrier (MC) Modulation attracts a lot of attention for high speed wireless transmissions because of its capability to cope with frequency selective fading channels turning the wideband transmission link into several narrowband subchannels whose equalization, in some situations, can be performed independently and in a simple manner. Nowadays, orthogonal frequency division multiplexing (OFDM) with the cyclic prefix (CP) insertion is the most widespread modulation among all MC modulations, and this thanks to its simplicity and its robustness against multipath fading using the cyclic prefix. Systems or standards such as ADSL or IEEE802.11a have already implemented the CP-OFDM modulation. Other standards like IEEE802.11n combine CP-OFDM and multiple-input multiple-output (MIMO) in order to increase the bit rate and to provide a better use of the channel spatial diversity. Nevertheless, CP-OFDM technique causes a loss of spectral efficiency due to the CP as it contains redundant information. Moreover, the rectangular prototype filter used in CP-OFDM has a poor frequency localization. This poor frequency localization makes it difficult for CP-OFDM systems to respect stringent specifications of spectrum masks.To overcome these drawbacks, filter-bank multicarrier (FBMC) was proposed as an alternative approach to CP-OFDM. Indeed, FBMC does not need any CP, and it furthermore offers the possibility to use different time-frequency well-localized prototype filters which allow much better control of the out-of-band emission. In the literature we find several FBMC systems based on different structures. In this thesis, we focus on the Saltzberg's scheme called OFDM/OQAM (or FBMC/OQAM). The orthogonality constraint for FBMC/OQAM is relaxed being limited only to the real field while for OFDM it has to be satisfied in the complex field. Consequently, one of the characteristics of FBMC/OQAM is that the demodulated transmitted symbols are accompanied by interference terms caused by the neighboring transmitted data in time-frequency domain. The presence of this interference is an issue for some MIMO schemes and until today their combination with FBMC remains an open problem.The aim of this thesis is to study the combination between FBMC and MIMO techniques, namely spatial multiplexing with ML detection. In the first part, we propose to analyze different intersymbol interference (ISI) cancellation techniques that we adapt to the FBMC/OQAM with MIMO context. We show that, in some cases, we can cope with the presence of the inherent FBMC interference and overcome the difficulties of performing ML detection in spatial multiplexing with FBMC/OQAM. After that, we propose a modification in the conventional FBMC/OQAM modulation by transmitting complex QAM symbols instead of OQAM ones. This proposal allows to reduce considerably the inherent interference but at the expense of the orthogonality condition. Indeed, in the proposed FBMC/QAM,the data symbol and the inherent interference term are both complex. Finally, we introduce a novel FBMC scheme and a transmission strategy in order to avoid the inherent interference terms. This proposed scheme (that we call FFT-FBMC) transforms the FBMC system into an equivalent system formulated as OFDM regardless of some residual interference. Thus, any OFDM transmission technique can be performed straightforwardly to the proposed FBMC scheme with a corresponding complexity growth. We develop the FFT-FBMC in the case of single-input single-output (SISO) configuration. Then, we extend its application to SM-MIMO configuration with ML detection and Alamouti coding scheme.

This thesis consists of four papers concerning modelling of count data and tourism demand. For three of the papers the focus is on the integer-valued autoregressive moving average model class (INARMA), and especially on the ENAR(l) model. The fourth paper studies the interaction between households' choice of number of leisure trips and number of overnight stays within a bivariate count data modelling framework. Paper [I] extends the basic INAR(1) model to enable more flexible and realistic empirical economic applications. The model is generalized by relaxing some of the model's basic independence assumptions. Results are given in terms of first and second conditional and unconditional order moments. Extensions to general INAR(p), time-varying, multivariate and threshold models are also considered. Estimation by conditional least squares and generalized method of moments techniques is feasible. Monte Carlo simulations for two of the extended models indicate reasonable estimation and testing properties. An illustration based on the number of Swedish mechanical paper and pulp mills is considered. Paper[II] considers the robustness of a conventional Dickey-Fuller (DF) test for the testing of a unit root in the INAR(1) model. Finite sample distributions for a model with Poisson distributed disturbance terms are obtained by Monte Carlo simulation. These distributions are wider than those of AR(1) models with normal distributed error terms. As the drift and sample size, respectively, increase the distributions appear to tend to T-2) and standard normal distributions. The main results are summarized by an approximating equation that also enables calculation of critical values for any sample and drift size. Paper[III] utilizes the INAR(l) model to model the day-to-day movements in the number of guest nights in hotels. By cross-sectional and temporal aggregation an INARMA(1,1) model for monthly data is obtained. The approach enables easy interpretation and econometric modelling of the parameters, in terms of daily mean check-in and check-out probability. Empirically approaches accounting for seasonality by dummies and using differenced series, as well as forecasting, are studied for a series of Norwegian guest nights in Swedish hotels. In a forecast evaluation the improvements by introducing economic variables is minute. Paper[IV] empirically studies household's joint choice of the number of leisure trips and the total night to stay on these trips. The paper introduces a bivariate count hurdle model to account for the relative high frequencies of zeros. A truncated bivariate mixed Poisson lognormal distribution, allowing for both positive as well as negative correlation between the count variables, is utilized. Inflation techniques are used to account for clustering of leisure time to weekends. Simulated maximum likelihood is used as estimation method. A small policy study indicates that households substitute trips for nights as the travel costs increase. / <p>Härtill 4 uppsatser.</p> / digitalisering@umu

Thesis (PhD)--Stellenbosch University, 2008. / ENGLISH ABSTRACT: The growing need to improve accounting accuracy, precision and to standardise generally accepted measurement methods in the mining and processing industries has led to the joining of a number of organisations under the AMIRA International umbrella, with the purpose of fulfilling these objectives. As part of this venture, Anglo Platinum undertook a project on the material balancing around its largest smelter, the Waterval Smelter. The primary objective of the project was to perform a statistical material balance around the Waterval Smelter using the Maximum Likelihood method with respect to platinum, rhodium, nickel, sulphur and chrome (III) oxide. Pt, Rh and Ni were selected for their significant contribution to the company’s profit margin, whilst S was included because of its environmental importance. Cr2O3 was included for its importance in as far as the difficulties its presence poses in smelting of PGMs. The objective was achieved by performing a series of statistical computations. These include; quantification of total and analytical uncertainties, detection of outliers, estimation and modelling of daily and monthly measurement uncertainties, parameter estimation and data reconciliation. Comparisons were made between the Maximum Likelihood and Least Squares methods. Total uncertainties associated with the daily grades were determined by use of variographic studies. The estimated Pt standard deviations were within 10% relative to the respective average grades with a few exceptions. The total uncertainties were split into their respective components by determining analytical variances from analytical replicates. The results indicated that the sampling components of the total uncertainty were generally larger as compared to their analytical counterparts. WCM, the platinum rich Waterval smelter product, has an uncertainty that is worth ~R2 103 000 in its daily Pt grade. This estimated figure shows that the quality of measurements do not only affect the accuracy of metal accounting, but can have considerable implications if not quantified and managed. The daily uncertainties were estimated using Kriging and bootstrapped to obtain estimates for the monthly uncertainties. Distributions were fitted using MLE on the distribution fitting tool of the JMP6.0 programme and goodness of fit tests were performed. The data were fitted with normal and beta distributions, and there was a notable decrease in the skewness from the daily to the monthly data. The reconciliation of the data was performed using the Maximum Likelihood and comparing that with the widely used Least Squares. The Maximum Likelihood and Least Squares adjustments were performed on simulated data in order to conduct a test of accuracy and to determine the extent of error reduction after the reconciliation exercise. The test showed that the two methods had comparable accuracies and error reduction capabilities. However, it was shown that modelling of uncertainties with the unbounded normal distribution does lead to the estimation of adjustments so large that negative adjusted values are the result. The benefit of modelling the uncertainties with a bounded distribution, which is the beta distribution in this case, is that the possibility of obtaining negative adjusted values is annihilated. ML-adjusted values (beta) will always be non-negative, therefore feasible. In a further comparison of the ML(bounded model) and the LS methods in the material balancing of the Waterval smelter complex, it was found that for all those streams whose uncertainties were modelled with a beta distribution, i.e. those whose distribution possessed some degree of skewness, the ML adjustments were significantly smaller than the LS counterparts It is therefore concluded that the Maximum Likelihood (bounded models) is a rigorous alternative method of data reconciliation to the LS method with the benefits of; -- Better estimates due to the fact that the nature of the data (distribution) is not assumed, but determined through distribution fitting and parameter estimation -- Adjusted values can never be negative due to the bounded nature of the distribution The novel contributions made in this thesis are as follows; -- The Maximum Likelihood method was for the first time employed in the material balancing of non-normally distributed data and compared with the well-known Least Squares method -- This was an original integration of geostatistical methods with data reconciliation to quantify and predict measurement uncertainties. -- For the first time, measurement uncertainties were modeled with a distribution that was non-normal and bounded in nature, leading to smaller adjustments / AFRIKAANSE OPSOMMING: Die groeiende behoefte aan rekeningkundige akkuraatheid, en om presisie te verbeter, en te standardiseer op algemeen aanvaarde meetmetodes in die mynbou en prosesseringsnywerhede, het gelei tot die samwewerking van 'n aantal van organisasies onder die AMIRA International sambreel, met die doel om bogenoemde behoeftes aan te spreek. As deel van hierdie onderneming, het Anglo Platinum onderneem om 'n projek op die materiaal balansering rondom sy grootste smelter, die Waterval smelter. Die primêre doel van die projek was om 'n statistiese materiaal balans rondom die Waterval smelter uit te voer deur gebruik te maak van die sogenaamde maksimum waarskynlikheid metode met betrekking tot platinum, rodium, nikkel, swawel en chroom (iii) oxied. Pt, Rh en Ni was gekies vir hul beduidende bydrae tot die maatskappy se winsmarge, terwyl S ingesluit was weens sy belangrike omgewingsimpak. Cr2O3 was ingesluit weens sy impak op die smelting van Platinum groep minerale. Die doelstelling was bereik deur die uitvoering van 'n reeks van statistiese berekeninge. Hierdie sluit in: die kwantifisering van die totale en analitiese variansies, opsporing van uitskieters, beraming en modellering van daaglikse en maandelikse metingsvariansies, parameter beraming en data rekonsiliasie. Vergelykings was getref tussen die maksimum waarskynlikheid en kleinste kwadrate metodes. Totale onsekerhede of variansies geassosieer met die daaglikse grade was bepaal deur ’n Variografiese studie. Die beraamde Pt standaard afwykings was binne 10% relatief tot die onderskeie gemiddelde grade met sommige uitsonderings. Die totale onsekerhede was onderverdeel in hul onderskeie komponente deur bepaling van die ontledingsvariansies van duplikate. Die uitslae toon dat die monsternemings komponente van die totale onsekerheid oor die algemeen groter was as hul bypassende analitiese variansies. WCM, ‘n platinum-ryke Waterval Smelter produk, het 'n onsekerheid in die orde van ~twee miljoen rand in sy daagliks Pt graad. Hierdie beraamde waarde toon dat die kwaliteit van metings nie alleen die akkuraatheid van metaal rekeningkunde affekteer nie, maar aansienlike finansiële implikasies het indien nie die nie gekwantifiseer en bestuur word nie. Die daagliks onsekerhede was beraam deur gebruik te maak van “Kriging” en “Bootstrap” metodes om die maandelikse onsekerhede te beraam. Verspreidings was gepas deur gebruik te maak van hoogste waarskynlikheid beraming passings en goedheid–van-pas toetse was uitgevoer. Die data was gepas met Normaal en Beta verspreidings, en daar was 'n opmerklike vermindering in die skeefheid van die daaglikse tot die maandeliks data. Die rekonsiliasies van die massabalans data was uitgevoer deur die gebruik die maksimum waarskynlikheid metodes en vergelyk daardie met die algemeen gebruikde kleinste kwadrate metode. Die maksimum waarskynlikheid (ML) en kleinste kwadrate (LS) aanpassings was uitgevoer op gesimuleerde data ten einde die akkuraatheid te toets en om die mate van fout vermindering na die rekonsiliasie te bepaal. Die toets getoon dat die twee metodes het vergelykbare akkuraathede en foutverminderingsvermoëns. Dit was egter getoon dat modellering van die onsekerhede met die onbegrensde Normaal verdeling lei tot die beraming van aanpassings wat so groot is dat negatiewe verstelde waardes kan onstaan na rekosniliasie. Die voordeel om onsekerhede met 'n begrensde distribusie te modelleer, soos die beta distribusie in hierdie geval, is dat die moontlikheid om negatiewe verstelde waardes te verkry uitgelsuit word. ML-verstelde waardes (met die Beta distribusie funksie) sal altyd nie-negatief wees, en om hierdie rede uitvoerbaar. In 'n verdere vergelyking van die ML (begrensd) en die LS metodes in die materiaal balansering van die waterval smelter kompleks, is dit gevind dat vir almal daardie strome waarvan die onserkerhede gesimuleer was met 'n Beta distribusie, dus daardie strome waarvan die onsekerheidsdistribusie ‘n mate van skeefheid toon, die ML verstellings altyd beduidend kleiner was as die ooreenkomstige LS verstellings. Vervolgens word die Maksimum Waarskynlikheid metode (met begrensde modelle) gesien as 'n beter alternatiewe metode van data rekosiliasie in vergelyking met die kleinste kwadrate metode met die voordele van: • Beter beramings te danke aan die feit dat die aard van die onsekerheidsdistribusie nie aangeneem word nie, maar bepaal is deur die distribusie te pas en deur van parameter beraming gebruik te maak. • Die aangepaste waardes kan nooit negatief wees te danke aan die begrensde aard van die verdeling. Die volgende oorspronklike bydraes is gelewer in hierdie verhandeling: • Die Maksimum Waarskynlikheid metode was vir die eerste keer geëvalueer vir massa balans rekonsiliasie van nie-Normaal verspreide data en vergelyk met die bekendde kleinste kwadrate metode. • Dit is die eerste keer geostatistiese metodes geïntegreer is met data rekonsiliasie om onsekerhede te beraam waarbinne verstellings gemaak word. • Vir die eerste keer, is meetonsekerhede gemoddelleer met 'n distribusie wat nie- Normaal en begrensd van aard is, wat lei tot kleiner en meer realistiese verstellings.

En écologie comme dans bien d’autres domaines, les échantillons de données de comptage comprennent souvent de nombreux zéros et quelques abondances fortes. Leur distribution est particulièrement surdispersée et asymétrique. Les méthodes les plus classiques d’inférence sont souvent mal adaptées à ces distributions, à moins de disposer d’échantillons de très grande taille. Il est donc nécessaire de s’interroger sur la validité des méthodes d’inférence, et de quantifier les erreurs d’estimation pour de telles données. Ce travail de thèse a ainsi été motivé par un jeu de données d’abondance de poissons, correspondant à un échantillonnage ponctuel par pêche électrique. Ce jeu de données comprend plus de 2000 échantillons, dont chacun correspond aux abondances ponctuelles (considérées indépendantes et identiquement distribuées) d’une espèce pour une campagne de pêche donnée. Ces échantillons sont de petite taille (en général, 20 _ n _ 50) et comprennent de nombreux zéros (en tout, 80% de zéros). Les ajustements de plusieurs modèles de distribution classiques pour les données de comptage ont été comparés sur ces échantillons, et la distribution binomiale négative a été sélectionnée. Nous nous sommes donc intéressés à l’estimation des deux paramètres de cette distribution : le paramètre de moyenne m, et le paramètre de dispersion, q. Dans un premier temps, nous avons étudié les problèmes d’estimation de la dispersion. L’erreur d’estimation est d’autant plus importante que le nombre d’individus observés est faible, et l’on peut, pour une population donnée, quantifier le gain en précision résultant de l’exclusion d’échantillons comprenant très peu d’individus. Nous avons ensuite comparé plusieurs méthodes de calcul d’intervalles de confiance pour la moyenne. Les intervalles de confiance basés sur la vraisemblance du modèle binomial négatif sont, de loin, préférables à des méthodes plus classiques comme la méthode de Student. Par ailleurs, ces deux études ont révélé que certains problèmes d’estimation étaient prévisibles, à travers l’observation de statistiques simples des échantillons comme le nombre total d’individus, ou le nombre de comptages non-nuls. En conséquence, nous avons comparé la méthode d’échantillonnage à taille fixe, à une méthode séquentielle, où l’on échantillonne jusqu’à observer un nombre minimum d’individus ou un nombre minimum de comptages non-nuls. Nous avons ainsi montré que l’échantillonnage séquentiel améliore l’estimation du paramètre de dispersion mais induit un biais dans l’estimation de la moyenne ; néanmoins, il représente une amélioration des intervalles de confiance estimés pour la moyenne. Ainsi, ce travail quantifie les erreurs d’estimation de la moyenne et de la dispersion dans le cas de données de comptage surdispersées, compare certaines méthodes d’estimations, et aboutit à des recommandations pratiques en termes de méthodes d’échantillonnage et d’estimation. / In ecology as well as in other scientific areas, count samples often comprise many zeros, and few high abundances. Their distribution is particularly overdispersed, and skewed. The most classical methods of inference are often ill-adapted to these distributions, unless sample size is really large. It is thus necessary to question the validity of inference methods, and to quantify estimation errors for such data. This work has been motivated by a fish abundance dataset, corresponding to punctual sampling by electrofishing. This dataset comprises more than 2000 samples : each sample corresponds to punctual abundances (considered to be independent and identically distributed) for one species and one fishing campaign. These samples are small-sized (generally, 20 _ n _ 50) and comprise many zeros (overall, 80% of counts are zeros). The fits of various classical distribution models were compared on these samples, and the negative binomial distribution was selected. Consequently, we dealt with the estimation of the parameters of this distribution : the parameter of mean m and parameter of dispersion q. First, we studied estimation problems for the dispersion. The estimation error is higher when few individuals are observed, and the gain in precision for a population, resulting from the exclusion of samples comprising very few individuals, can be quantified. We then compared several methods of interval estimation for the mean. Confidence intervals based on negative binomial likelihood are, by far, preferable to more classical ones such as Student’s method. Besides, both studies showed that some estimation problems are predictable through simple statistics such as total number of individuals or number of non-null counts. Accordingly, we compared the fixed sample size sampling method, to a sequential method, where sampling goes on until a minimum number of individuals or positive counts have been observed. We showed that sequential sampling improves the estimation of dispersion but causes the estimation of mean to be biased ; still, it improves the estimation of confidence intervals for the mean. Hence, this work quantifies errors in the estimation of mean and dispersion in the case of overdispersed count data, compares various estimation methods, and leads to practical recommendations as for sampling and estimation methods.

Recursive partitioning algorithms separate a feature space into a set of disjoint rectangles. Then, usually, a constant in every partition is fitted. While this is a simple and intuitive approach, it may still lack interpretability as to how a specific relationship between dependent and independent variables may look. Or it may be that a certain model is assumed or of interest and there is a number of candidate variables that may non-linearly give rise to different model parameter values. We present an approach that combines generalized linear models with recursive partitioning that offers enhanced interpretability of classical trees as well as providing an explorative way to assess a candidate variable's in uence on a parametric model. This method conducts recursive partitioning of a generalized linear model by (1) fitting the model to the data set, (2) testing for parameter instability over a set of partitioning variables, (3) splitting the data set with respect to the variable associated with the highest instability. The outcome is a tree where each terminal node is associated with a generalized linear model. We will show the method's versatility and suitability to gain additional insight into the relationship of dependent and independent variables by two examples, modelling voting behaviour and a failure model for debt amortization, and compare it to alternative approaches.

Doctor of Philosophy / Department of Statistics / Weixin Yao / This dissertation contains two projects that are related to varying coefficient models. The traditional least squares based kernel estimates of the varying coefficient model will lose some efficiency when the error distribution is not normal. In the first project, we propose a novel adaptive estimation method that can adapt to different error distributions and provide an efficient EM algorithm to implement the proposed estimation. The asymptotic properties of the resulting estimator is established. Both simulation studies and real data examples are used to illustrate the finite sample performance of the new estimation procedure. The numerical results show that the gain of the adaptive procedure over the least squares estimation can be quite substantial for non-Gaussian errors. In the second project, we propose a unified inference for sparse and dense longitudinal data in time-varying coefficient models. The time-varying coefficient model is a special case of the varying coefficient model and is very useful in longitudinal/panel data analysis. A mixed-effects time-varying coefficient model is considered to account for the within subject correlation for longitudinal data. We show that when the kernel smoothing method is used to estimate the smooth functions in the time-varying coefficient model for sparse or dense longitudinal data, the asymptotic results of these two situations are essentially different. Therefore, a subjective choice between the sparse and dense cases may lead to wrong conclusions for statistical inference. In order to solve this problem, we establish a unified self-normalized central limit theorem, based on which a unified inference is proposed without deciding whether the data are sparse or dense. The effectiveness of the proposed unified inference is demonstrated through a simulation study and a real data application.

We apply the data cloning method developed by Lele et al. (2007) to estimate the model of Smets and Wouters (2007). The data cloning algorithm is a numerical method that employs replicas of the original sample to approximate the maximum likelihood estimator as the limit of Bayesian simulation-based estimators. We also analyze the identification properties of the model. We measure the individual identification strength of each parameter by observing the posterior volatility of data cloning estimates, and access the identification problem globally through the maximum eigenvalue of the posterior data cloning covariance matrix. Our results indicate that the model is only poorly identified. The system displays bad global identification properties, and most of its parameters seem locally ill-identified. / Neste trabalho aplicamos o método data cloning de Lele et al. (2007) para estimar o modelo de Smets e Wouters (2007). O algoritmo data cloning é um método numérico que utiliza réplicas da amostra original para aproximar o estimador de máxima verossimilhança como limite de estimadores Bayesianos obtidos por simulação. Nós também analisamos a identificação dos parâmetros do modelo. Medimos a identificação de cada parâmetro individualmente ao observar a volatilidade a posteriori dos estimadores de data cloning. O maior autovalor da matriz de covariância a posteriori proporciona uma medida global de identificação do modelo. Nossos resultados indicam que o modelo de Smets e Wouters (2007) não é bem identificado. O modelo não apresenta boas propriedades globais de identificação, e muitos de seus parâmetros são localmente mal identificados.