This thesis contributes to the field of Gaussian Graphical Models by exploring either numerically or theoretically various topics of Bayesian Methods in Gaussian Graphical Models and by providing a number of interesting results, the further exploration of which would be promising, pointing to numerous future research directions. Gaussian Graphical Models are statistical methods for the investigation and representation of interdependencies between components of continuous random vectors. This thesis aims to investigate some issues related to the application of Bayesian methods for Gaussian Graphical Models. We adopt the popular $G$-Wishart conjugate prior $W_G(\delta,D)$ for the precision matrix. We propose an efficient sampling method for the $G$-Wishart distribution based on the Metropolis Hastings algorithm and show its validity through a number of numerical experiments. We show that this method can be easily used to estimate the Deviance Information Criterion, providing a computationally inexpensive approach for model selection. In addition, we look at the marginal likelihood of a graphical model given a set of data. This is proportional to the ratio of the posterior over the prior normalizing constant. We explore methods for the estimation of this ratio, focusing primarily on applying the Monte Carlo simulation method of path sampling. We also explore numerically the effect of the completion of the incomplete matrix $D^{\mathcal{V}}$, hyperparameter of the $G$-Wishart distribution, for the estimation of the normalizing constant. We also derive a series of exact and approximate expressions for the Bayes Factor between two graphs that differ by one edge. A new theoretical result regarding the limit of the normalizing constant multiplied by the hyperparameter $\delta$ is given and its implications to the validity of an improper prior and of the subsequent Bayes Factor are discussed.

在迴歸分析中，若變數間具有非線性的關係時，B-Spline線性迴歸是以無母數的方式建立模型。B-Spline函數為具有節點(knots)的分段多項式，選取合適節點的位置對B-Spline的估計有重要的影響，在近年來許多的文獻中已提出一些尋找節點位置的估計方法，而本文中我們提出了一種基於Bayesian information criterion(BIC)的節點估計方式。 我們想要深入了解在不同類型的迴歸函數間，各種選取節點方法的配適效果與模擬時間，並且加以比較，在使用B-Spline函數估計時，能夠使用合適的方法尋找節點。 / In regression analysis, when the relation between the response variable and the explanatory variable is nonlinear, one can use nonparametric methods to estimate the regression function. B-Spline regression is one of the popular nonparametric regression methods. B-Splines are piecewise polynomial joint at knots, and the choice of knot locations is crucial. Zhou and Shen (2001) proposed to use spatially adaptive regression splines (SARS), where the knots are estimated using a selection scheme. Dimatteo, Genovese, and Kass (2001) proposed to use Bayesian adaptive regression splines (BARS), where certain priors for knot locations are considered. In this thesis, a knot estimation method based on the Bayesian information criterion (BIC) is proposed, and simulation studies are carried out to compare BARS, SARS and the proposed BIC-based method.

[pt] Nesta tese é apresentada uma metodologia de seleção de modelos em experimentos mistura-processo e reunidas as técnicas estatísticas necessárias ao planejamento e análise de experimentos com mistura com ou sem variáveis de processo. Na pesquisa de seleção de modelos foi utilizado um experimento para determinar as proporções ótimas de um misto químico do mecanismo de retardo para ignição de um motor foguete. O misto químico consiste de uma mistura de três componentes. Além das proporções dos componentes da mistura, são consideradas duas variáveis de processo. O objetivo do estudo é investigar as proporções dos componentes da mistura e os níveis das variáveis de processo que colocam o valor esperado do tempo de retardo (resposta) o mais próximo possível do valor alvo e, ao mesmo tempo, minimizam o tamanho do intervalo de previsão de uma futura resposta. Foi ajustado um modelo de regressão linear com respostas normais. Com o modelo desenvolvido foram determinadas as proporções ótimas dos componentes da mistura e os níveis ótimos das variáveis de processo. Para a seleção do modelo foi utilizada uma metodologia de duas etapas, que provou ser eficiente no caso estudado. / [en] This thesis presents a methodology for model selection in mixture-process experiments and puts together the statistical techniques for the design and analysis of mixture experiments with or without process variables. An experiment of a three-component mixture of a delay mechanism to start a rocket engine was used in the research. Besides the mix components proportions, two process variables are considered. The aim of the study is to investigate the proportions of the mix components and the levels of the process variables that set the expected delay time (response) as close as possible to the target value and, at the same time, minimize the width of the prediction interval for the response. A linear regression model with normal responses was fitted. Through the developed model, the optimal proportions of the mix components and the levels of the process variables were determined. A two-stage methodology was used to select the model. This methodology for model selection proved to be efficient in the studied case.

In this thesis we propose to use a penalized maximum conditional likelihood criterion to estimate the graph of a general discrete Markov random field. We prove the almost sure convergence of the estimator of the graph in the case of a finite or countable infinite set of variables. Our method requires minimal assumptions on the probability distribution and contrary to other approaches in the literature, the usual positivity condition is not needed. We present several examples with a finite set of vertices and study the performance of the estimator on simulated data from theses examples. We also introduce an empirical procedure based on k-fold cross validation to select the best value of the constant in the estimators definition and show the application of this method in two real datasets. / Nesta tese propomos um critério de máxima verossimilhança penalizada para estimar o grafo de dependência condicional de um campo aleatório Markoviano discreto. Provamos a convergência quase certa do estimador do grafo no caso de um conjunto finito ou infinito enumerável de variáveis. Nosso método requer condições mínimas na distribuição de probabilidade e contrariamente a outras abordagens da literatura, a condição usual de positividade não é necessária. Introduzimos alguns exemplos com um conjunto finito de vértices e estudamos o desempenho do estimador em dados simulados desses exemplos. Também propomos um procedimento empírico baseado no método de validação cruzada para selecionar o melhor valor da constante na definição do estimador, e mostramos a aplicação deste procedimento em dois conjuntos de dados reais.

Orientador: Simone Aparecida Vieira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Biologia / Made available in DSpace on 2018-08-27T10:19:45Z (GMT). No. of bitstreams: 1 Bakker_YvonneVanessa_M.pdf: 1853475 bytes, checksum: 2ff87ee7761a486f4b4ef47d5be567c8 (MD5) Previous issue date: 2015 / Resumo: A Mata Atlântica é um dos principais biomas do mundo sendo considerada um dos 25 hotspots de biodiversidade. Dentre os ecossistemas associados à Mata Atlântica, a Floresta de Restinga foi quase totalmente dizimada, restando apenas 0,5% de sua área original. A Restinga se caracteriza por ocorrer nos cordões arenosos ao longo da costa onde o solo é distrófico e sujeito a inundações sazonais. Entre as comunidades que ocorrem nas florestas de restinga, destacam-se as epífitas vasculares que, por não terem contato com o solo, possuem adaptações ecológicas que garantem a aquisição de nutrientes via deposição seca e úmida. Para avaliar o papel das epífitas vasculares no funcionamento das Florestas de Restinga realizou-se o levantamento quantitativo da biomassa das epífitas vasculares em uma área de um hectare de Floresta de Restinga, no Núcleo Picinguaba do Parque Estadual da Serra do Mar (PESM), no litoral norte paulista, município de Ubatuba. Para tanto, foi coletado todo o material epifítico presente em 23 forófitos com DAP entre 4,9 e 41,7 cm, previamente selecionados. Cada forófito foi dividido por zonas ecológicas (copa, galhos e tronco), buscando amostrar os indivíduos arbóreos com diferentes (a) arquitetura de copa (A, para palmeiras; B para copa pequena e C, para copa grande) e (b) índice de cobertura por epífitas (ICE) que classifica os indivíduos arbóreos de acordo com o porte e a biomassa das epífitas. Esse material foi então separado e determinado o peso seco por grupos de epífitas: Arácea (Araceae, Gesneriaceae e Piperaceae), Bromeliacea, Orchidaceae e Miscelânia (Cactaceae, Pteridófitas, raízes, e solo aéreo). A zona ecológica que apresentou maior biomassa epifítica foi o tronco, com 54% do total, seguida pelos galhos com 45% do total. A biomassa epifítica variou de 0,01 kg a 28,9 kg por forófito. A biomassa epifítica total de um hectare de floresta, foi estimada em 2,32 Mg ha-1 representando apenas 1,34% de toda biomassa viva acima do solo, no entanto sua contribuição é de 18% da biomassa fotossintetizante da floresta e de mais de 10 Mg ha-1 de biomassa fresca evidenciando a importante contribuição do componente para o funcionamento do ecossistema. A estimativa de biomassa através do modelo alométrico desenvolvido neste estudo, utilizando-se como variáveis preditoras o índice de cobertura por epífitas e o DAP do forófito, representa um importante avanço nos estudos que envolvem a quantificação da biomassa de epífitas vasculares, sendo de fácil utilização e passível de aplicação em diferentes fitofisionomias, permitindo a comparação entre estudos distintos / Abstract: The Atlantic Forest is one of the most important biomes of the world and is considered one of the 25 hotspots of biodiversity. Among the ecosystems associated with the Atlantic Forest, one of the more endangered is the Restinga Forest with only 0,5% of its original area preserved. Restinga is the seasonally flooded coastal forest that occurs in sandy ridges along the coast where the soil is extremely poor in nutrients, very acid and subject to seasonal flooding. Among the communities that occur in Restinga forest, we highlight the vascular epiphytes that by not depending on soil nutrients, may play an important role in nutrient dynamics in these systems. To evaluate the role of vascular epiphytes in Restinga Forests, this study proceeded a quantitative survey of the biomass of vascular epiphytes in an area of one hectare of Restinga forest, in Picinguaba at the Serra do Mar State Park (PESM), Ubatuba, north coast of São Paulo State. On 23 phorophytes with diameter at breast height (DBH) ? 4.8 cm, previously selected, was all the epiphytic material collected, divided by ecological zones (canopy, branches and trunk). The trees were sample trees with different (a) canopy architecture (A, to palm trees; B, to small crown; and C, for large crown) and (b) coverage ratio by epiphytes (ICE), which classifies individual trees according to the size and biomass of epiphytes. This material was separate and determined the dry weight per epiphytes groups: Arácea (Araceae, Gesneriaceae and Piperaceae), Bromeliacea, Orchidaceae and Miscellany (Cactaceae, Pteridophytes, roots, organic matter). The ecological zone with the highest biomass epiphytic was the trunk, with 54% of the total, followed by branches with 45%. An allometric model for the estimation of epiphytes biomass as a function of the host tree DBH, ICE and dry weight of epiphytes was develop based in the information collected. From this model, biomass of vascular epiphytes was estimate in 2,32 Mg ha-1 for 1ha of Restinga forest. The epiphytic biomass per host tree varied from 0.01 kg to 28.9 kg. The total epiphytic biomass represent only 1.34% of all living biomass above ground (AGB), but its contribution is 18% of the photosynthetic biomass of the forest and more than 10 Mg ha-1 of wet biomass, showing the importance of this component to the functioning of the ecosystem. The estimate of biomass through allometric model developed in this study, using as predictors the epiphyte coverage index and the DAP of the host tree, represents an important advance in studies involving the quantification of biomass of vascular epiphytes, being easy to use and applicable in different vegetation types, allowing comparison between different studies / Mestrado / Ecologia / Mestra em Ecologia

Several studies point out different causes of performance degradation in supervised machine learning. Problems such as class imbalance, overlapping, small-disjuncts, noisy labels, and sparseness limit accuracy in classification algorithms. Even though a number of approaches either in the form of a methodology or an algorithm try to minimize performance degradation, they have been isolated efforts with limited scope. This research consists of three main parts: In the first part, a novel probabilistic diagnostic model based on identifying signs and symptoms of each problem is presented. Secondly, the behavior and performance of several supervised algorithms are studied when training sets have such problems. Therefore, prediction of success for treatments can be estimated across classifiers. Finally, a probabilistic sampling technique based on training set diagnosis for avoiding classifier degradation is proposed<br>

In this paper, we examine the feasibility of extending the Akaike information criterion (AIC) for deterministic systems as a potential model selection criteria for stochastic models. We discuss the implementation method for three different classes of stochastic models: continuous time Markov chains (CTMC), stochastic differential equations (SDE), and random differential equations (RDE). The effectiveness and limitations of implementing the AIC for comparison of stochastic models is demonstrated using simulated data from the three types of models and then applied to experimental longitudinal growth data for algae.

No description available.

Vehicle communication using sensors and wireless channels plays an important role to allow exchanging information. Adding more components to allow exchanging more information with infrastructure enhanced the capabilities of vehicles and enabled the rise of Cooperative Intelligent Transport Systems (C-ITS). Leveraging such capabilities, more applications such as Cooperative Adaptive Cruise Control (CACC) and platooning were introduced. CACC is an enhancement of Adaptive Cruise Control (ACC). It enables longitudinal automated vehicle control and follows the Constant Time Gap (CTG) strategy where, distance between vehicles is proportional to the speed. Platooning is different in terms of addressing both longitudinal and lateral control. In addition, it adopts the Constant Distance Gap (CDG) control strategy, with separation between vehicles unchanged with speed. Platooning requires close coupling and accordingly achieves goals of increased lane throughput and reduced energy consumption. When a longitudinal controller only is used, platooning operates in car-following mode and no Platoon Management Protocol (PMP) is used. On the other hand, when both longitudinal and lateral controllers are used, platooning operates in maneuver mode and coordination between vehicles is needed to perform maneuvers. Exchanging information allows the platoon to make real time maneuvering decisions. However, all the aforementioned benefits of platooning cannot be achieved if the system is vulnerable to misbehavior (i.e., the platoon is behaving incorrectly). Most of work in the literature attributes this misbehavior to malicious actors where an attacker injects malicious messages. Standards made efforts to develop security services to authenticate and authorize the sender. However, authenticated users equipped with cryptographic primitives can mount attacks (i.e., falsification attacks) and accordingly they cannot be detected by standard services such as cryptographic signatures. Misbehavior can disturb platoon behavior or even cause collision. Many Misbehavior Detection Schemes (MDSs) are proposed in the literature in the context of Vehicular ad hoc network (VANET) and CACC. These MDSs apply algorithms or rules to detect sudden or gradual changes of kinematic information disseminated by other vehicles. Reusing these MDSs directly during maneuvers can lead to false positives when they treat changes in kinematic information during the maneuver as an attack. This thesis addresses this gap by designing a new modular framework that has the capability to discern maneuvering process from misbehavior by leveraging platoon behavior recognition, that is, the platoon mode of operation (e.g., car-following mode or maneuver mode). In addition, it has the ability to recognize the undergoing maneuver (e.g., middle join or exit). Based on the platoon behavior recognition module, the anomaly detection module detects deviations from expected behavior. Unsupervised machine learning, notably Hidden Markov Model with Gaussian Mixture Model emission (GMMHMM), is used to learn the nominal behavior of the platoon during different modes and maneuvers. This is used later by the platoon behavior recognition and anomaly detection modules. GMMHMM is trained with nominal behavior of platoon using multivariate time series representing kinematic characteristics of the vehicles. Different models are used to detect attacks in different scenarios (e.g., different speeds). Two approaches for anomaly detection are investigated, Viterbi algorithm based anomaly detection and Forward algorithm based anomaly detection. The proposed framework managed to detect misbehavior whether the compromised vehicle is a platoon leader or follower. Empirical results show very high performance, with the platoon behavior recognition module reaching 100% in terms of accuracy. In addition, it can predict ongoing platoon behavior at early stages and accordingly, use the correct model representing the nominal behavior. Forward algorithm based anomaly detection, which rely on computing likelihood, showed better performance reaching 98% with slight variations in terms of accuracy, precision, recall and F1 score. Different platooning controllers can be resilient to some attacks and accordingly, the attack can result in slight deviation from nominal behavior. However, The anomaly detection module was able to detect this deviation. / Kommunikation mellan fordon som använder sensorer och radiokommunikation spelar en viktig roll för att kunna möjliggöra informationsutbyte. Genom att lägga till er komponenter för infrastrukturkommunikation förbättras fordonens generella kommunikationskapacitet och möjliggör C-ITS. Det möjliggör också för att introducera ytterligare applikationer, exempelvis CACC samt plutonering. CACC är en förbättring av ACC -konceptet. Denna teknik möjliggör longitudinell automatiserad fordonskontroll och följer en CTG -strategi där avståndet mellan fordon är proportionellt mot hastigheten. Plutonering är annorlunda med avseende på att hantera longitudinell och lateral kontroll. Dessutom antar den en kontrollstrategi för CDG där avståndet mellan fordon förblir oförändrat med hastighet. Plutonering kräver en nära koppling mellan fordon för att uppnå målet med ökad filgenomströmning och reducerad energikonsumtion. När enbart longitudinell kontroll är aktiverad, fungerar plutonering i bilföljande läge och funktionen PMP används inte. När både longitudinella och laterala kontroller används, arbetar plutonen istället i manöverläge och samordning mellan fordon behövs för att utföra olika manövrar. Informationsutbytet möjliggör att plutonen kan man manövrera i realtid. Alla ovan nämnda fördelar med plutonering kan emellertid inte uppnås om systemet är sårbart för felbeteende, det vill säga att plutonen beter sig fel. I litteraturen kopplas detta missförhållande till skadliga aktörer där en angripare injicerar skadliga meddelanden. I standardiseringsarbeten har man försökt utveckla säkerhetstjänster för att autentisera och auktorisera avsändaren. Trots detta kan autentiserade användare utrustade med kryptografiska primitiv upprätta förfalskningsattacker som inte detekteras av standardtjänster som kryptografiska signaturer. Felaktigt handhavande kan orsaka störningar i plutonens beteende eller till och med orsaka kollisioner och följaktligen påverka tillförlitligheten. Det finns manga MDSs beskrivna i litteraturen i relation till VANET och CACC. MDSs använder algoritmer eller regler för att detektera snabba eller långsamma förändringar kinematisk information som sprids av andra fordon. Direkt användning av MDSs under manövrar kan leda till falska positiva resultat eftersom de kommer att behandla förändringar i kinematisk information under manövern som en attack. Denna avhandling adresserar detta gap genom utformningen av ett modulärt ramverk som kan urskilja manöverprocessen från misskötsamhet genom att utnyttja plutonens beteendeigenkänningsmodul för att intelligent känna igen plutonläget (t.ex. bilföljande läge eller manöverläge). Ramverket har vidare egenskapen att känna igen pågående manövrar (frikoppling eller växelbyte) och avvikelser från förväntat beteende. Modulen använder en oövervakad maskininlärningssmodell, GMMHMM, för att lära en plutons normala beteende under olika lägen och manövrar som sedan används för plutonbeteendeigenkänning och avvikelsedetektion. GMMHMM tränas på data från plutoneringens normalbeteende i form av multivariata tidsserier som representerar fordonets kinematiska karakteristik. Olika modeller används för att upptäcka attacker i olika scenarier (t.ex. olika hastigheter). Två tillvägagångssätt för avvikelsedetektion undersöks, Viterbi-algoritmen samt Forward-algoritmen. Det föreslagna systemet lyckas upptäcka det felaktiga beteendet oavsett om det komprometterade fordonet är en plutonledare eller följare. Empiriska resultat visar mycket hög prestanda för beteendeigenkänningsmodulen som när 100%. Dessutom kan den känna igen plutonens beteende i ett tidigt skede. Resultat med Forward- algoritmen för avvikelsedetektion visar på en prestanda på 98% med små variationer med avseende på måtten accuracy, precision, recall och F1-score. Avvikelsedetektionsmodulen kan även upptäcka små avvikelser i beteende.

Multiple studies have documented declines of forest breeding birds in the eastern United States, but the temporal and spatial scales of most studies limit inference regarding large scale bird-habitat trends. A potential solution to this challenge is integrating existing long-term datasets such as the U.S. Forest Service Forest Inventory and Analysis (FIA) program and U.S. Geological Survey Breeding Bird Survey (BBS) that span large geographic regions. The purposes of this study were to determine if FIA metrics can be related to BBS population indices at multiple spatial and temporal scales and to develop predictive models from these relationships that identify forest conditions favorable to forest songbirds. I accumulated annual route-level BBS data for 4 species guilds (canopy nesting, ground and shrub nesting, cavity nesting, early successional), each containing a minimum of five bird species, from 1966-2004. I developed 41 forest variables describing forest structure at the county level using FIA data from for the 2000 inventory cycle within 5 physiographic regions in 14 states (AL, GA, IL, IN, KY, MD, NC, NY, OH, PA, SC, TN, VA, and WV). I examine spatial relationships between the BBS and FIA data at 3 hierarchical scales: 1) individual BBS routes, 2) FIA units, and 3) and physiographic sections. At the BBS route scale, I buffered each BBS route with a 100m, 1km, and 10km buffer, intersected these buffers with the county boundaries, and developed a weighted average for each forest variable within each buffer, with the weight being a function of the percent of area each county had within a given buffer. I calculated 28 variables describing landscape structure from 1992 NLCD imagery using Fragstats within each buffer size. I developed predictive models relating spatial variations in bird occupancy and abundance to changes in forest and landscape structure using logistic regression and classification and regression trees (CART). Models were developed for each of the 3 buffer sizes, and I pooled the variables selected for the individual models and used them to develop multiscale models with the BBS route still serving as the sample unit. At the FIA unit and physiographic section scales I calculated average abundance/route for each bird species within each FIA unit and physiographic section and extrapolated the plot-level FIA variables to the FIA unit and physiographic section levels. Landscape variables were recalculated within each unit and section using NCLD imagery resampled to a 400 m pixel size. I used regression trees (FIA unit scale) and general linear models (GLM, physiographic section scale) to relate spatial variations in bird abundance to the forest and landscape variables. I examined temporal relationships between the BBS and FIA data between 1966 and 2000. I developed 13 forest variables from statistical summary reports for 4 FIA inventory cycles (1965, 1975, 1989, and 2000) within NY, PA, MD, and WV. I used linear interpolation to estimate annual values of each FIA variable between successive inventory cycles and GLMs to relate annual variations in bird abundance to the forest variables. At the BBS route scale, the CART models accounted for > 50% of the variation in bird presence-absence and abundance. The logistic regression models had sensitivity and specificity rates > 0.50. By incorporating the variables selected for the models developed within each buffer (100m, 1km, and 10km) around the BBS routes into a multiscale model, I was able to further improve the performance of many of the models and gain additional insight regarding the contribution of multiscale influences on bird-habitat relationships. The majority of the best CART models tended to be the multiscale models, and many of the multiscale logistic models had greater sensitivity and specificity than their single-scale counter parts. The relatively fine resolution and extensive coverage of the BBS, FIA, and NLCD datasets coupled with the overlapping multiscale approach of these analyses allowed me to incorporate levels of variation in both habitat and bird occurrence and abundance into my models that likely represented a more comprehensive range of ecological variability in the bird-habitat relationships relative to studies conducted at smaller scales and/or using data at coarser resolutions. At the FIA unit and physiographic section scales, the regression trees accounted for an average of 54.1% of the variability in bird abundance among FIA units, and the GLMs accounted for an average of 66.3% of the variability among physiographic sections. However, increasing the observational and analytical scale to the FIA unit and physiographic section decreased the measurement resolution of the bird abundance and landscape variables. This limits the applicability and interpretive strength of the models developed at these scales, but they may serve as indices to those habitat components exerting the greatest influences on bird abundance at these broader scales. The GLMs relating average annual bird abundance to annual estimates of forest variables developed using statistical report data from the 1965, 1975, 1989, and 2000 FIA inventories explained an average of 62.0% of the variability in annual bird abundance estimates. However, these relationships were a function of both the general habitat characteristics and the trends in bird abundance specific to the 4-state region (MD, NY, PA, and WV) used for these analyses and may not be applicable to other states or regions. The small suite of variables available from the FIA statistical reports and multicollinearity among all forest variables further limited the applicability of these models. As with those developed at the FIA unit and physiographic sections scales, these models may serve as general indices to the habitat components exerting the greatest influences on bird abundance trends through time at regional scales. These results demonstrate that forest variables developed from the FIA, in conjunction with landscape variables, can explain variations in occupancy and abundance estimated from BBS data for forest bird species with a variety of habitat requirements across spatial and temporal scales. / Ph. D.