During the last few years nonlinear models have been a very active area of econometric research: new models have been introduced and existing ones generalized. To a large extent, these developments have concerned models in which the conditional moments are regime-dependent. In such models, the different regimes are usually linear and the change between them is governed by an observable or unobservable variable. These specifications can be useful in situations in which it is suspected that the behaviour of the dependent variable may vary between regimes. A classical example can be found the business cycle literature where it is argued that contractions in the economy are not only more violent but also short-lived than expansions. Unemployment, which tends to rise faster during recessions than decline during booms, constitutes another example. Two of the most popular regime-dependent models are the smooth transition and the threshold model. In both models cases the transition variable is observable but the specification of the way in which the model changes from one regime to the other is different. Particularly, in the smooth transition model the change is a continuous whereas in the threshold model it is abrupt. One of the factors that has influenced the development of nonlinear models are improvements in computer technology. They have not only permitted an introduction of more complex models but have also allowed the use of computer-intensive methods in hypothesis testing. This is particularly important in nonlinear models because there these methods have proved to be practical in testing statistical hypothesis such as linearity and parameter constancy. In general, these testing situation are not trivial and their solution often requires computer-intensive methods. In particular, bootstrapping and Monte Carlo testing are now commonly used. In this thesis the smooth transition model is used in different ways. In the first chapter, a vector smooth transition model is used as a device for deriving a test for parameter constancy in stationary vector autoregressive models. In the second chapter we introduce a panel model whose parameters can change in a smooth fashion between regimes as a function of an exogenous variable. The method is used to investigate whether financial constraints affect firms' \ investment decisions. The third chapter is concern with linearity testing in smooth transition models. New tests are introduced and Monte Carlo testing techniques are shown to be useful in achieving control over the size of the test. Finally, the last chapter is devoted to the Smooth Permanent Surge model. This is a nonlinear moving average model in which a shock can have transitory or permanent effects depending on its sign and magnitude. Test for linearity and random walk hypothesis are introduced. / Diss. Stockholm : Handelshögsk., 2004

Master of Science / Department of Statistics / Wei-Wen Hsu / BACKGROUND AND PURPOSE: Alzheimer's disease is currently a neurodegenerative diseases without any effective treatments to slow or reverse the progression. To develop any potential treatments, the need of a good statistical model to assess the progression of Alzheimer's disease is becoming increasingly urgent. This study proposed a latent transition model to monitor the progression of Alzheimer's disease which can help the development of a given proposed treatment. METHOD: A latent transition model was used to assess the progression of Alzheimer's disease. The volume of Hippocampus and fluorodeoxyglucose-PET (FDG) were employed as biomarkers in this model. These two biomarkers are very sensitive to the pathological signs of the Alzheimer's disease. The proposed latent transition model was performed with real data from Alzheimer's Disease Neuroimaging Initiative (ADNI), which contain 2,126 participants from 2005 to 2014. RESULTS/FINDINGS: The latent transition model suggested six states of disease progression and two different pathological profiles. One progression profile was mainly determined by the biomarker of FDG and the other by the volume of Hippocampus. CONCLUSION: The results revealed the existence of various progression profiles of Alzheimer's disease, suggesting a new way to evaluate the disease progression.

Anthropogenic utilization of forest and woodland ecosystems can cause declines in flora and fauna species. It is imperative to restore these ecosystems to mitigate further declines. In this thesis, I focused on a highly degraded region, the Box-Ironbark forests and woodlands of Victoria, Australia. Rather than mature stands with large trees, stands are currently dominated by high densities of small stems. This change has resulted in reduced populations of many flora and fauna species dependent on older-growth forests and woodlands. Managers are interested in restoring mature Box-Ironbark forests and woodlands through three alternative management strategies: allocating land to National Parks and allowing stands to develop naturally without harvesting, modifying timber harvesting regimes to retain more medium and large trees, or a new ecological thinning technique that retains target habitat trees and removes competing trees to encourage growth of retained stems. / The effects of each management strategy are not easy to predict due to complex interactions between intervention and stochastic natural processes. Forest simulation models are often employed to overcome this problem. I constructed state-and-transition simulation models (STSMs) to predict the effects of alternative management actions and natural disturbances on vegetation structure. Due to a lack of empirical data, I relied on the knowledge of experts in Box-Ironbark ecology and management to construct STSMs. Models predicted that the development of mature woodlands under all strategies was minimal over the next 150 years, and neither current harvesting nor ecological thinning is likely to expedite the development of mature stands relative to growth and natural disturbances. However, differences in experts’ opinions led to widely diverging model predictions. / Uncertainty must be acknowledged in model construction because it can affect model predictions. I quantified uncertainty due to four sources – between-expert variation, imperfect expert knowledge, natural stochasticity, and model parameterization – to determine which source caused the most variance in model predictions. I found that models were very uncertain and between-expert uncertainty contributed the majority of variance in model predictions. This brings into question the use of consensus methods in forest management where differences between experts are ignored. / Using uncertain model predictions to make management decisions is problematic because any given action can have many plausible outcomes. I applied several decision criteria to uncertain STSM predictions using a formal decision-making framework to determine the optimal management action in Box-Ironbark forests and woodlands. I found that natural development is the most risk-averse option, while ecological thinning is the most risky option because there is a small likelihood that it will greatly expedite the development of mature woodlands. Rather than selecting one option, managers could rely on a risk-spreading approach where the majority of land is allocated to no-cutting National Parks and a small amount of land is allocated to the other two harvesting strategies. This would allow managers to collect monitoring data for all management strategies in order to learn about effects of harvesting and update model predictions through time using adaptive management.

The thesis contains the four chapters: Testing parameter constancy in unit root autoregressive models against continuous change; Dickey-Fuller type of tests against nonlinear dynamic models; Inference for unit roots in a panel smooth transition autoregressive model where the time dimension is fixed; Testing unit roots in nonlinear dynamic heterogeneous panels. In Chapter  1 we derive tests for parameter constancy when the data generating process is non-stationary against the hypothesis that the parameters of the model change smoothly over time. To obtain the asymptotic distributions of the tests we generalize many theoretical results, as well as new are introduced, in the area of unit roots . The results are derived under the assumption that the error term is a strong mixing. Small sample properties of the tests are investigated, and in particular, the power performances are satisfactory. In Chapter 2 we introduce several test statistics of testing the null hypotheses of a random walk (with or without drift) against models that accommodate a smooth nonlinear shift in the level, the dynamic structure, and the trend. We derive analytical limiting distributions for all tests. Finite sample properties are examined. The performance of the tests is compared to that of the classical unit root tests by Dickey-Fuller and Phillips and Perron, and is found to be superior in terms of power. In Chapter 3 we derive a unit root test against a Panel Logistic Smooth Transition Autoregressive (PLSTAR). The analysis is concentrated on the case where the time dimension is fixed and the cross section dimension tends to infinity. Under the null hypothesis of a unit root, we show that the LSDV estimator of the autoregressive parameter in the linear component of the model is inconsistent due to the inclusion of fixed effects. The test statistic, adjusted for the inconsistency, has an asymptotic normal distribution whose first two moments are calculated analytically. To complete the analysis, finite sample properties of the test are examined. We highlight scenarios under which the traditional panel unit root tests by Harris and Tzavalis have inferior or reasonable power compared to our test. In Chapter 4 we present a unit root test against a non-linear dynamic heterogeneous panel with each country modelled as an LSTAR model. All parameters are viewed as country specific. We allow for serially correlated residuals over time and heterogeneous variance among countries. The test is derived under three special cases: (i) the number of countries and observations over time are fixed, (ii) observations over time are fixed and the number of countries tend to infinity, and (iii) first letting the number of observations over time tend to infinity and thereafter the number of countries. Small sample properties of the test  show modest size distortions and satisfactory power being superior to the Im, Pesaran and Shin t-type of test. We also show clear improvements in power compared to a univariate unit root test allowing for non-linearities under the alternative hypothesis. / Diss. Stockholm : Handelshögskolan, 2004

Broad-scale forest die-off associated with drought and heat has now been reported from every forested continent, posing a global-scale challenge to forest management. Climate-driven die-off is frequently compounded with other drivers of tree mortality, such as altered land use, wildfire, and invasive species, making forest management increasingly complex. Facing similar challenges, rangeland managers have widely adopted the approach of developing conceptual models that identify key ecosystem states and major types of transitions between those states, known as "state-and-transition models" (S&T models). Using expert opinion and available research, the development of such conceptual S&T models has proven useful in anticipating ecosystem changes and identifying management actions to undertake or to avoid. In cases where detailed data are available, S&T models can be developed into probabilistic predictions, but even where data are insufficient to predict transition probabilities, conceptual S&T models can provide valuable insights for managing a given ecosystem and for comparing and contrasting different ecosystem dynamics. We assembled a synthesis of 14 forest die-off case studies from around the globe, each with sufficient information to infer impacts on forest dynamics and to inform management options following a forest die-off event. For each, we developed a conceptual S&T model to identify alternative ecosystem states, pathways of ecosystem change, and points where management interventions have been, or may be, successful in arresting or reversing undesirable changes. We found that our diverse set of mortality case studies fit into three broad classes of ecosystem trajectories: (1) single-state transition shifts, (2) ecological cascading responses and feedbacks, and (3) complex dynamics where multiple interactions, mortality drivers, and impacts create a range of possible state transition responses. We integrate monitoring and management goals in a framework aimed to facilitate development of conceptual S&T models for other forest die-off events. Our results highlight that although forest die-off events across the globe encompass many different underlying drivers and pathways of ecosystem change, there are commonalities in opportunities for successful management intervention.

Esta tese apresenta o desenvolvimento e aplicação de modelos de turbulência, transição laminar-turbulenta e de interações fluido-estrutura ao escoamento externo em cilindro rígido estacionário e em vibrações induzidas por vórtices. Tais desenvolvimentos foram realizados no código ReFRESCO, baseado em técnicas de dinâmica de fluidos computacional (CFD). Realizou-se um estudo quanto ao desempenho do modelo k- SST em extensa faixa de números de Reynolds, segundo o qual se identificaram as deficiências de modelagem para este escoamento. A modelagem adaptativa das escalas (SAS) e o modelo de transição por correlações locais (LCTM), ambos combinados ao SST, melhoraram a aderência aos resultados experimentais para este escoamento, em uma contribuição original deste trabalho. A aplicação de técnicas de verificação e validação possibilitou a estimação de incertezas e erros para os modelos e números de Reynolds e também de identificada como outra contribuição deste trabalho. A combinação da modelagem em SST, SAS e LCTM com movimentos impostos de realizada para números de Reynolds moderados, diferentes frequências e amplitudes de vibração, algo que poucas publicações abordam em detalhes. Com relação aos movimentos livres, este trabalho traz contribuições com a aplicação dos modelos SST e SAS ao estudo de vibrações induzidas por vórtices em dois graus de liberdade, baixa razão de massa e números de Reynolds moderados, mais altos do que normalmente observados na literatura. Por fim, a investigação da importância relativa de efeitos da turbulência aos casos de movimentos livres e impostos, com relação ao caso de cilindro estacionário, comprovou a conjetura formulada na parte inicial deste trabalho, no que tange à escolha do modelo de turbulência em determinadas aplicações. Tal escolha mostrou-se menos decisiva no caso do cilindro em movimento imposto e ainda menos nos movimentos livres, em comparação ao caso estacionário, uma vez que a resposta em movimentos do corpo filtra grande parte dos efeitos turbulentos de ordem superior. Esta observação mostra-se relevante, uma vez que pode permitir simplificações na modelagem e aplicação de ferramentas de CFD em uma classe importante de projetos de engenharia. / This thesis presents the development, implementation and application of turbulence and laminar-turbulent transition models and fuid-structure capabilities to address the vortexshedding and vortex-induced vibrations of a rigid cylinder. These numerical developments have been carried out in the computational fuid dynamics (CFD) code ReFRESCO. In the current work, an investigation of the performance of the turbulence modeling with k- SST in a broad range of Reynolds numbers is carried out identifying its modeling deficiencies for this fow. The implementation and systematic application of the scale adaptive simulations (SAS) and the local correlation transition model (LCTM), both combined with the SST, have improved the agreement with experimental results for the cylinder ow, in a novel contribution of this work. The application of verification and validation technique has allowed the estimation of numerical errors and uncertainties for the diferent models. That is also identified as a contribution of this thesis. The combination of SST modeling with imposed motions is carried out as well as with the SAS and LCTM for moderate Reynolds numbers, diferent vibration frequencies and amplitudes, which is considered novel, as few publications address this issue in extent. Regarding the free-moving cylinder capabilities, the present work brings contributions with the application of SST and SASSST with free-moving cylinder for the study of VIV of two degrees of-freedom, low mass ratio and moderate Reynolds numbers, higher than commonly seen in the literature. Finally, the investigation of the relative importance of turbulence effects on the freemoving cylinder and the imposed-motions case, with respect to the fixed case is carried out. A natural conjecture that has been raised early on this work and proved correct is that, for engineering applications, the choice of turbulence modeling strategy is less decisive when the cylinder is moving with prescribed motion and even less stringent, for free motions as the body response filters most of the higher order turbulence effects. That is a relevant observation as it might allow modeling simplifications and the application of CFD tools to a range of engineering problems.

Esta tese apresenta o desenvolvimento e aplicação de modelos de turbulência, transição laminar-turbulenta e de interações fluido-estrutura ao escoamento externo em cilindro rígido estacionário e em vibrações induzidas por vórtices. Tais desenvolvimentos foram realizados no código ReFRESCO, baseado em técnicas de dinâmica de fluidos computacional (CFD). Realizou-se um estudo quanto ao desempenho do modelo k- SST em extensa faixa de números de Reynolds, segundo o qual se identificaram as deficiências de modelagem para este escoamento. A modelagem adaptativa das escalas (SAS) e o modelo de transição por correlações locais (LCTM), ambos combinados ao SST, melhoraram a aderência aos resultados experimentais para este escoamento, em uma contribuição original deste trabalho. A aplicação de técnicas de verificação e validação possibilitou a estimação de incertezas e erros para os modelos e números de Reynolds e também de identificada como outra contribuição deste trabalho. A combinação da modelagem em SST, SAS e LCTM com movimentos impostos de realizada para números de Reynolds moderados, diferentes frequências e amplitudes de vibração, algo que poucas publicações abordam em detalhes. Com relação aos movimentos livres, este trabalho traz contribuições com a aplicação dos modelos SST e SAS ao estudo de vibrações induzidas por vórtices em dois graus de liberdade, baixa razão de massa e números de Reynolds moderados, mais altos do que normalmente observados na literatura. Por fim, a investigação da importância relativa de efeitos da turbulência aos casos de movimentos livres e impostos, com relação ao caso de cilindro estacionário, comprovou a conjetura formulada na parte inicial deste trabalho, no que tange à escolha do modelo de turbulência em determinadas aplicações. Tal escolha mostrou-se menos decisiva no caso do cilindro em movimento imposto e ainda menos nos movimentos livres, em comparação ao caso estacionário, uma vez que a resposta em movimentos do corpo filtra grande parte dos efeitos turbulentos de ordem superior. Esta observação mostra-se relevante, uma vez que pode permitir simplificações na modelagem e aplicação de ferramentas de CFD em uma classe importante de projetos de engenharia. / This thesis presents the development, implementation and application of turbulence and laminar-turbulent transition models and fuid-structure capabilities to address the vortexshedding and vortex-induced vibrations of a rigid cylinder. These numerical developments have been carried out in the computational fuid dynamics (CFD) code ReFRESCO. In the current work, an investigation of the performance of the turbulence modeling with k- SST in a broad range of Reynolds numbers is carried out identifying its modeling deficiencies for this fow. The implementation and systematic application of the scale adaptive simulations (SAS) and the local correlation transition model (LCTM), both combined with the SST, have improved the agreement with experimental results for the cylinder ow, in a novel contribution of this work. The application of verification and validation technique has allowed the estimation of numerical errors and uncertainties for the diferent models. That is also identified as a contribution of this thesis. The combination of SST modeling with imposed motions is carried out as well as with the SAS and LCTM for moderate Reynolds numbers, diferent vibration frequencies and amplitudes, which is considered novel, as few publications address this issue in extent. Regarding the free-moving cylinder capabilities, the present work brings contributions with the application of SST and SASSST with free-moving cylinder for the study of VIV of two degrees of-freedom, low mass ratio and moderate Reynolds numbers, higher than commonly seen in the literature. Finally, the investigation of the relative importance of turbulence effects on the freemoving cylinder and the imposed-motions case, with respect to the fixed case is carried out. A natural conjecture that has been raised early on this work and proved correct is that, for engineering applications, the choice of turbulence modeling strategy is less decisive when the cylinder is moving with prescribed motion and even less stringent, for free motions as the body response filters most of the higher order turbulence effects. That is a relevant observation as it might allow modeling simplifications and the application of CFD tools to a range of engineering problems.

Un système embarqué est un système électronique et informatique autonome dédié à une tâche précise. Dans le secteur de l’automobile, le nombre de systèmes embarqués dans les voitures a considérablement augmenté au cours de ces dernières années et va certainement continuer à augmenter. Ces systèmes sont dédiés entre autres, à la sécurité, au confort de conduite,et à l’assistance à la conduite. Cette croissance des systèmes est associée avec une croissance en taille des logiciels qui les contrôlent. En conséquence, leur gestion(système et logiciel) devient de plus en plus complexe et problématique. Par ailleurs, la concurrence dans le secteur automobile est très féroce et les temps de mise sur le marché sont de plus en plus courts. Ainsi, pour garantir le bon fonctionnement des systèmes en général et du logiciel en particulier, étant donné leur complexité,et aussi les délais courts de mise sur le marché des produits automobiles, de nouvelles méthodes de développement doivent être considérées. Ainsi, de nombreuses méthodes de développement, incluant de nouveaux standards (de développement) et approches automatiques ont émergé au cours de ces dernières années. Dans le cas particulier de la vérification et validation de logiciel, une des activités critiques qui a connu une avancée significative est la génération de cas de test, avec l’avènement d’approches automatiques.Malgré cela, ces approches peinent souvent à s’imposer en milieu industriel. Une des raisons est que celles ci sont souvent peu adaptées ou peu utilisées dans un contexte industriel.Dans ce contexte, cette thèse vise à proposer une approche de vérification et de validation de logiciels embarqués, basée sur la génération automatique de cas de test. Pour cela, nous avons mis en place une approche permettant de représenter sous forme de modèles abstraits les spécifications d’un logiciel, puis de générer à partir de ces modèles un ensemble de cas de test en considérant en particulier le critère de couverture MC/DC. / An embedded system is a system that performs a specific task and has a computer embedded inside. In the automotive sector, the amount of embedded systems in the vehicle has risen dramatically in recent years and is set to increase. They deal essentially with safety, comfort, and driving assistance. Furthermore, the increase in number and complexity of the systems is associated with a growth in software. As a consequence, their management (system and software) have become more and more complex and problematic. Also, the competition and time-to-market in the automotive industry are very tough. Thus, to guarantee the efficiency and reliability of the embedded systems in the vehicle in general and the software in particular, in view of the complexity as well as the competition and time-to-market law, new development methods should be considered. Therefore, new development methods including new standards, and automatic approaches have emerged over the last years. In the particular case of embedded software verification and validation, one of the most critical activities that has experienced a significant progress is test case generation with the advent of automatic approaches. Despite this, these approaches are not widely used or are not well adapted in industrial context. In that context, our goal in this PhD. thesis is to propose a new verification and validation approach, based on automatic test case generation of embedded embedded. Thus, we have set up an approach that automatically generates test cases, with respect to the MC/DC criterion, from abstract models of the software specifications expressed in the form of state-transition models.

A transição energética residencial começou a receber especial atenção da comunidade científica nos anos 1970 e 1980, quando se acreditava na ocorrência iminente da Crise da Lenha. Na época, temia-se que o corrente ritmo de consumo de biomassas sólidas em países em desenvolvimento ultrapassaria a capacidade de produção primária dos ambientes naturais, com sérias consequências para as camadas menos abastadas da população destes locais, que se veriam em uma situação de escassez de fontes de energia. Apesar de esta crise nunca haver, de fato, se concretizado, a preocupação com a sua potencial ocorrência estimulou o desenvolvimento de modelos que visavam à interpretação do fenômeno da transição energética residencial decorrente do processo de urbanização e aumento de renda dos usuários finais. Tal interesse culminou na elaboração do modelo da Escada Energética que, de uma maneira geral, previa que o abandono de fontes de energia tradicionais e a adoção de fontes de energia modernas era o resultado do aumento do status social da população. Inicialmente, a Escada Energética se estabeleceu como principal modelo de transição energética residencial. À medida que novos estudos foram desenvolvidos, entretanto, evidências passaram a sugerir que diversos fatores envolvidos na transição energética em países em desenvolvimento não podiam ser explicados pelo modelo. Estas evidências subsidiaram a concepção do modelo do Acúmulo de Combustíveis, segundo o qual a diversificação, e não a substituição, de energéticos seria o resultado do desenvolvimento social da população. Atualmente, não existe consenso sobre qual modelo melhor reflete o fenômeno da transição energética residencial. Como consequência, políticas públicas de acesso a energia e serviços energéticos limpos baseadas nestas diferentes interpretações possuem características e resultados distintos. Neste contexto, o presente trabalho pretende contribuir para a discussão sobre qual modelo de transição energética melhor reflete a realidade dos consumidores residenciais de energia de países em desenvolvimento a partir da apresentação de dois estudos de caso que retratam diferentes facetas da questão. As análises elaboradas indicam que o modelo do Acúmulo de Combustíveis consegue representar com maior fidelidade o fenômeno da transição energética residencial e que políticas públicas estruturadas segundo seu arcabouço teórico podem contribuir mais eficazmente para a melhoria das condições de vida da população. / The residential energy transition began to receive special attention from the scientific community in 70s and 80s, when a Fuelwood crisis was believed to be imminent. At the time, it was feared that the current rhythm of solid biomass consumption would not keep pace with the primary productivity of the forests and other sources of fuelwood, with severe consequences striking the least wealthy households, who would face an energy shortage. Although the referred crisis never really happened, the concern with its potential occurrence stimulated the development of models aiming at interpreting the energy transition phenomenon provoked by the urbanization process and the increase in income of households. Such interest culminated in the elaboration of the Energy Ladder model, which indicated that the abandonment of traditional energy sources and the adoption of modern ones was the result of the increase of the social status of the population. Initially, the Energy Ladder established itself as the main residential energy transition model. As new studies were being developed, however, evidences suggesting that different factors related to the energy transition in developing countries couldnt be explained by the model were found. These evidences supported the conception of the Fuel Staking model, according to which diversification, instead of substitution, resulted from the social development of the population. Currently, there is no consensus on which model better represents the residential energy transition. As a consequence, public policies focused on clean energy and energy services access based on these different interpretations have different characteristics and results. In such context, this work intends to contribute to the discussion on which energy transition model better reflects the reality of households in developing countries by presenting two case studies showing different aspects of the thematic. The analysis presented suggests that the Fuel Stacking model can better represent the residential energy transition phenomenon and that public policies structured according to its theoretical framework are more effective in contributing to increase the living standards of the population.

This study tested the performance of classification, regression, and ordination techniques to evaluate the spatiotemporal dynamics of threats to big sagebrush ecological sites. The research was focused on invasion by annual exotic grasses and encroachment by woodlands. We sought to identify those areas that have had a persistent coverage of cheatgrass (Bromus tectorum) in big sagebrush ecological sites. We took advantage of the contrast in greenness between multi-temporal (within one year) remotely sensed vegetation indices captured in the spring and summer to find a distinct phenological signature that allowed mapping cheatgrass. We utilized support vector machines (SVM) to classify three temporal scenarios for which field data sets were available. SVM performed very well with accuracies of 70% (producer's) and 95% (user's) for the class of interest (presence of cheatgrass). This was the focus of chapter 2. In chapter 3 we report the development of vegetation continuous fields (VCF) for three years of interest 1996, 2001, and 2007 in order to detect active woodland encroachment. We prepared VCF for shrubs, trees, herbaceous vegetation, and bare ground using a suite of remotely sensed spectral reflectance, vegetation indices, and transformations. We compared the performance of multivariate regression trees (MRT) and random forests (RF) to develop the VCF multi-temporal series. RF outperformed MRT in both accuracy and ability to appropriately map the continuum of percent cover across large landscapes. We estimate that 17,570 hectares of big sagebrush lands showed encroachment by woodlands. Our goal in chapter 4 was to develop a similarity index for large rangeland landscapes. Trend assessments field sites and a long-term annual series (1984 - 2008) of remotely sensed imagery were used in conjunction with multidimensional scaling (MDS) to measure ecological distance to undesired states such as invasion by exotic annuals and encroachment by woodlands. In this chapter our units of analysis were soil-mapping units, which were predominantly composed of one ecological site (>60%). Our MDS results show that different ecological sites can be identified in the reduced MDS statistical space. The observed transitions and trajectories of mountain, Wyoming, and basin big sagebrush sites correlated well with the ecological expectation in semiarid lands. We anticipate that managers can use our protocols to update ecological site descriptions and state and transition models from a remotely sensed perspective.