Transferability of Regional Permafrost Disturbance Susceptibility Modelling Using Generalized Linear and Generalized Additive Models

To effectively assess and mitigate risk of permafrost disturbance, disturbance-p rone areas can be predicted through the application of susceptibility models. In this study we developed regional susceptibility models for permafrost disturbances using a field disturbance inventory to test the transferability of the model to a broader region in the Canadian High Arctic. Resulting maps of susceptibility were then used to explore the effect of terrain variables on the occurrence of disturbances within this region. To account for a large range of landscape charac- teristics, the model was calibrated using two locations: Sabine Peninsula, Melville Island, NU, and Fosheim Pen- insula, Ellesmere Island, NU. Spatial patterns of disturbance were predicted with a generalized linear model (GLM) and generalized additive model (GAM), each calibrated using disturbed and randomized undisturbed lo- cations from both locations and GIS-derived terrain predictor variables including slope, potential incoming solar radiation, wetness index, topographic position index, elevation, and distance to water. Each model was validated for the Sabine and Fosheim Peninsulas using independent data sets while the transferability of the model to an independent site was assessed at Cape Bounty, Melville Island, NU. The regional GLM and GAM validated well for both calibration sites (Sabine and Fosheim) with the area under the receiver operating curves (AUROC) N 0.79. Both models were applied directly to Cape Bounty without calibration and validated equally with AUROC's of 0.76; however, each model predicted disturbed and undisturbed samples differently. Addition- ally, the sensitivity of the transferred model was assessed using data sets with different sample sizes. Results in- dicated that models based on larger sample sizes transferred more consistently and captured the variability within the terrain attributes in the respective study areas. Terrain attributes associated with the initiation of dis- turbances were similar regardless of the location. Disturbances commonly occurred on slopes between 4 and 15°, below Holocene marine limit, and in areas with low potential incoming solar radiation

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Transferability of Regional Permafrost Disturbance Susceptibility Modelling Using Generalized Linear and Generalized Additive Models

To effectively assess and mitigate risk of permafrost disturbance, disturbance-p rone areas can be predicted through the application of susceptibility models. In this study we developed regional susceptibility models for permafrost disturbances using a field disturbance inventory to test the transferability of the model to a broader region in the Canadian High Arctic. Resulting maps of susceptibility were then used to explore the effect of terrain variables on the occurrence of disturbances within this region. To account for a large range of landscape charac- teristics, the model was calibrated using two locations: Sabine Peninsula, Melville Island, NU, and Fosheim Pen- insula, Ellesmere Island, NU. Spatial patterns of disturbance were predicted with a generalized linear model (GLM) and generalized additive model (GAM), each calibrated using disturbed and randomized undisturbed lo- cations from both locations and GIS-derived terrain predictor variables including slope, potential incoming solar radiation, wetness index, topographic position index, elevation, and distance to water. Each model was validated for the Sabine and Fosheim Peninsulas using independent data sets while the transferability of the model to an independent site was assessed at Cape Bounty, Melville Island, NU. The regional GLM and GAM validated well for both calibration sites (Sabine and Fosheim) with the area under the receiver operating curves (AUROC) N 0.79. Both models were applied directly to Cape Bounty without calibration and validated equally with AUROC's of 0.76; however, each model predicted disturbed and undisturbed samples differently. Addition- ally, the sensitivity of the transferred model was assessed using data sets with different sample sizes. Results in- dicated that models based on larger sample sizes transferred more consistently and captured the variability within the terrain attributes in the respective study areas. Terrain attributes associated with the initiation of dis- turbances were similar regardless of the location. Disturbances commonly occurred on slopes between 4 and 15°, below Holocene marine limit, and in areas with low potential incoming solar radiation

Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Principal components and generalized linear modeling in the correlation between hospital admissions and air pollution

OBJECTIVE To analyze the association between concentrations of air pollutants and admissions for respiratory causes in children. METHODS Ecological time series study. Daily figures for hospital admissions of children aged < 6, and daily concentrations of air pollutants (PM10, SO2, NO2, O3 and CO) were analyzed in the Região da Grande Vitória, ES, Southeastern Brazil, from January 2005 to December 2010. For statistical analysis, two techniques were combined: Poisson regression with generalized additive models and principal model component analysis. Those analysis techniques complemented each other and provided more significant estimates in the estimation of relative risk. The models were adjusted for temporal trend, seasonality, day of the week, meteorological factors and autocorrelation. In the final adjustment of the model, it was necessary to include models of the Autoregressive Moving Average Models (p, q) type in the residuals in order to eliminate the autocorrelation structures present in the components. RESULTS For every 10:49 μg/m3 increase (interquartile range) in levels of the pollutant PM10 there was a 3.0% increase in the relative risk estimated using the generalized additive model analysis of main components-seasonal autoregressive – while in the usual generalized additive model, the estimate was 2.0%. CONCLUSIONS Compared to the usual generalized additive model, in general, the proposed aspect of generalized additive model − principal component analysis, showed better results in estimating relative risk and quality of fit.

Estimation and hypothesis testing in mixed linear models

Dissertação apresentada para obtenção do Grau de Doutor em Matemática, Estatística, pela Universidade Nova de Lisboa, faculdade de Ciências e Tecnologia

Hierarchical Mixtures of Experts and the EM Algorithm

We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's). Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain.

Posterior Simulation in the Generalized Linear Model with Semiparmetric Random Effects

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model, normal base measures and Gibbs sampling procedures based on the Pólya urn scheme are often used to simulate posterior draws. These algorithms are applicable in the conjugate case when (for a normal base measure) the likelihood is normal. In the non-conjugate case, the algorithms proposed by MacEachern and Müller (1998) and Neal (2000) are often applied to generate posterior samples. Some common problems associated with simulation algorithms for non-conjugate MDP models include convergence and mixing difficulties. This paper proposes an algorithm based on the Pólya urn scheme that extends the Gibbs sampling algorithms to non-conjugate models with normal base measures and exponential family likelihoods. The algorithm proceeds by making Laplace approximations to the likelihood function, thereby reducing the procedure to that of conjugate normal MDP models. To ensure the validity of the stationary distribution in the non-conjugate case, the proposals are accepted or rejected by a Metropolis-Hastings step. In the special case where the data are normally distributed, the algorithm is identical to the Gibbs sampler.

An upper bound on the Bayesian error bars for generalized linear regression

In the Bayesian framework, predictions for a regression problem are expressed in terms of a distribution of output values. The mode of this distribution corresponds to the most probable output, while the uncertainty associated with the predictions can conveniently be expressed in terms of error bars. In this paper we consider the evaluation of error bars in the context of the class of generalized linear regression models. We provide insights into the dependence of the error bars on the location of the data points and we derive an upper bound on the true error bars in terms of the contributions from individual data points which are themselves easily evaluated.

A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: bf(1) we allow for em non-linear projection manifolds (the basic building block is the Generative Topographic Mapping -- GTM), bf(2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, bf(3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold's local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.

Linear models of simple cells: Correspondence to real cell responses and space spanning properties

Despite their limitations, linear filter models continue to be used to simulate the receptive field properties of cortical simple cells. For theoreticians interested in large scale models of visual cortex, a family of self-similar filters represents a convenient way in which to characterise simple cells in one basic model. This paper reviews research on the suitability of such models, and goes on to advance biologically motivated reasons for adopting a particular group of models in preference to all others. In particular, the paper describes why the Gabor model, so often used in network simulations, should be dropped in favour of a Cauchy model, both on the grounds of frequency response and mutual filter orthogonality.

Optimal designs for multivariate linear models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

Generalized factor models: a bayesian approach

There is recent interest in the generalization of classical factor models in which the idiosyncratic factors are assumed to be orthogonal and there are identification restrictions on cross-sectional and time dimensions. In this study, we describe and implement a Bayesian approach to generalized factor models. A flexible framework is developed to determine the variations attributed to common and idiosyncratic factors. We also propose a unique methodology to select the (generalized) factor model that best fits a given set of data. Applying the proposed methodology to the simulated data and the foreign exchange rate data, we provide a comparative analysis between the classical and generalized factor models. We find that when there is a shift from classical to generalized, there are significant changes in the estimates of the structures of the covariance and correlation matrices while there are less dramatic changes in the estimates of the factor loadings and the variation attributed to common factors.

The ghost of past species occurrence: improving species distribution models for presence-only data

1. Model-based approaches have been used increasingly in conservation biology over recent years. Species presence data used for predictive species distribution modelling are abundant in natural history collections, whereas reliable absence data are sparse, most notably for vagrant species such as butterflies and snakes. As predictive methods such as generalized linear models (GLM) require absence data, various strategies have been proposed to select pseudo-absence data. However, only a few studies exist that compare different approaches to generating these pseudo-absence data. 2. Natural history collection data are usually available for long periods of time (decades or even centuries), thus allowing historical considerations. However, this historical dimension has rarely been assessed in studies of species distribution, although there is great potential for understanding current patterns, i.e. the past is the key to the present. 3. We used GLM to model the distributions of three 'target' butterfly species, Melitaea didyma, Coenonympha tullia and Maculinea teleius, in Switzerland. We developed and compared four strategies for defining pools of pseudo-absence data and applied them to natural history collection data from the last 10, 30 and 100 years. Pools included: (i) sites without target species records; (ii) sites where butterfly species other than the target species were present; (iii) sites without butterfly species but with habitat characteristics similar to those required by the target species; and (iv) a combination of the second and third strategies. Models were evaluated and compared by the total deviance explained, the maximized Kappa and the area under the curve (AUC). 4. Among the four strategies, model performance was best for strategy 3. Contrary to expectations, strategy 2 resulted in even lower model performance compared with models with pseudo-absence data simulated totally at random (strategy 1). 5. Independent of the strategy model, performance was enhanced when sites with historical species presence data were not considered as pseudo-absence data. Therefore, the combination of strategy 3 with species records from the last 100 years achieved the highest model performance. 6. Synthesis and applications. The protection of suitable habitat for species survival or reintroduction in rapidly changing landscapes is a high priority among conservationists. Model-based approaches offer planning authorities the possibility of delimiting priority areas for species detection or habitat protection. The performance of these models can be enhanced by fitting them with pseudo-absence data relying on large archives of natural history collection species presence data rather than using randomly sampled pseudo-absence data.

Alternative ways to estimate change points in multinomial sequences. An application to an authorship attribution problem

The statistical analysis of literary style is the part of stylometry that compares measurable characteristicsin a text that are rarely controlled by the author, with those in other texts. When thegoal is to settle authorship questions, these characteristics should relate to the author’s style andnot to the genre, epoch or editor, and they should be such that their variation between authors islarger than the variation within comparable texts from the same author.For an overview of the literature on stylometry and some of the techniques involved, see for exampleMosteller and Wallace (1964, 82), Herdan (1964), Morton (1978), Holmes (1985), Oakes (1998) orLebart, Salem and Berry (1998).Tirant lo Blanc, a chivalry book, is the main work in catalan literature and it was hailed to be“the best book of its kind in the world” by Cervantes in Don Quixote. Considered by writterslike Vargas Llosa or Damaso Alonso to be the first modern novel in Europe, it has been translatedseveral times into Spanish, Italian and French, with modern English translations by Rosenthal(1996) and La Fontaine (1993). The main body of this book was written between 1460 and 1465,but it was not printed until 1490.There is an intense and long lasting debate around its authorship sprouting from its first edition,where its introduction states that the whole book is the work of Martorell (1413?-1468), while atthe end it is stated that the last one fourth of the book is by Galba (?-1490), after the death ofMartorell. Some of the authors that support the theory of single authorship are Riquer (1990),Chiner (1993) and Badia (1993), while some of those supporting the double authorship are Riquer(1947), Coromines (1956) and Ferrando (1995). For an overview of this debate, see Riquer (1990).Neither of the two candidate authors left any text comparable to the one under study, and thereforediscriminant analysis can not be used to help classify chapters by author. By using sample textsencompassing about ten percent of the book, and looking at word length and at the use of 44conjunctions, prepositions and articles, Ginebra and Cabos (1998) detect heterogeneities that mightindicate the existence of two authors. By analyzing the diversity of the vocabulary, Riba andGinebra (2000) estimates that stylistic boundary to be near chapter 383.Following the lead of the extensive literature, this paper looks into word length, the use of the mostfrequent words and into the use of vowels in each chapter of the book. Given that the featuresselected are categorical, that leads to three contingency tables of ordered rows and therefore tothree sequences of multinomial observations.Section 2 explores these sequences graphically, observing a clear shift in their distribution. Section 3describes the problem of the estimation of a suden change-point in those sequences, in the followingsections we propose various ways to estimate change-points in multinomial sequences; the methodin section 4 involves fitting models for polytomous data, the one in Section 5 fits gamma modelsonto the sequence of Chi-square distances between each row profiles and the average profile, theone in Section 6 fits models onto the sequence of values taken by the first component of thecorrespondence analysis as well as onto sequences of other summary measures like the averageword length. In Section 7 we fit models onto the marginal binomial sequences to identify thefeatures that distinguish the chapters before and after that boundary. Most methods rely heavilyon the use of generalized linear models