Microscopy image segmentation by active contour models

In this thesis a semi-automated cell analysis system is described through image processing. To achieve this, an image processing algorithm was studied in order to segment cells in a semi-automatic way. The main goal of this analysis is to increase the performance of cell image segmentation process, without affecting the results in a significant way. Even though, a totally manual system has the ability of producing the best results, it has the disadvantage of taking too long and being repetitive, when a large number of images need to be processed. An active contour algorithm was tested in a sequence of images taken by a microscope. This algorithm, more commonly known as snakes, allowed the user to define an initial region in which the cell was incorporated. Then, the algorithm would run several times, making the initial region contours to converge to the cell boundaries. With the final contour, it was possible to extract region properties and produce statistical data. This data allowed to say that this algorithm produces similar results to a purely manual system but at a faster rate. On the other hand, it is slower than a purely automatic way but it allows the user to adjust the contour, making it more versatile and tolerant to image variations.

Extreme value Birnbaum-Saunders regression models applied to environmental data

Extreme value models are widely used in different areas. The Birnbaum–Saunders distribution is receiving considerable attention due to its physical arguments and its good properties. We propose a methodology based on extreme value Birnbaum–Saunders regression models, which includes model formulation, estimation, inference and checking. We further conduct a simulation study for evaluating its performance. A statistical analysis with real-world extreme value environmental data using the methodology is provided as illustration.

Specification and testing of multiplicative time-varying GARCH models with applications

In this article, we develop a specification technique for building multiplicative time-varying GARCH models of Amado and Teräsvirta (2008, 2013). The variance is decomposed into an unconditional and a conditional component such that the unconditional variance component is allowed to evolve smoothly over time. This nonstationary component is defined as a linear combination of logistic transition functions with time as the transition variable. The appropriate number of transition functions is determined by a sequence of specification tests. For that purpose, a coherent modelling strategy based on statistical inference is presented. It is heavily dependent on Lagrange multiplier type misspecification tests. The tests are easily implemented as they are entirely based on auxiliary regressions. Finite-sample properties of the strategy and tests are examined by simulation. The modelling strategy is illustrated in practice with two real examples: an empirical application to daily exchange rate returns and another one to daily coffee futures returns.

Estimation of statistical cure from cancer using population-based data

Dissertação de mestrado em Estatística

DESARROLLO DE APLICACIONES ESTADÍSTICAS PARA LA AGRICULTURA DE PRECISIÓN. STATISTICAL APPLICATIONS FOR PRECISION AGRICULTURE

A partir de las últimas décadas se ha impulsado el desarrollo y la utilización de los Sistemas de Información Geográficos (SIG) y los Sistemas de Posicionamiento Satelital (GPS) orientados a mejorar la eficiencia productiva de distintos sistemas de cultivos extensivos en términos agronómicos, económicos y ambientales. Estas nuevas tecnologías permiten medir variabilidad espacial de propiedades del sitio como conductividad eléctrica aparente y otros atributos del terreno así como el efecto de las mismas sobre la distribución espacial de los rendimientos. Luego, es posible aplicar el manejo sitio-específico en los lotes para mejorar la eficiencia en el uso de los insumos agroquímicos, la protección del medio ambiente y la sustentabilidad de la vida rural. En la actualidad, existe una oferta amplia de recursos tecnológicos propios de la agricultura de precisión para capturar variación espacial a través de los sitios dentro del terreno. El óptimo uso del gran volumen de datos derivado de maquinarias de agricultura de precisión depende fuertemente de las capacidades para explorar la información relativa a las complejas interacciones que subyacen los resultados productivos. La covariación espacial de las propiedades del sitio y el rendimiento de los cultivos ha sido estudiada a través de modelos geoestadísticos clásicos que se basan en la teoría de variables regionalizadas. Nuevos desarrollos de modelos estadísticos contemporáneos, entre los que se destacan los modelos lineales mixtos, constituyen herramientas prometedoras para el tratamiento de datos correlacionados espacialmente. Más aún, debido a la naturaleza multivariada de las múltiples variables registradas en cada sitio, las técnicas de análisis multivariado podrían aportar valiosa información para la visualización y explotación de datos georreferenciados. La comprensión de las bases agronómicas de las complejas interacciones que se producen a la escala de lotes en producción, es hoy posible con el uso de éstas nuevas tecnologías. Los objetivos del presente proyecto son: (l) desarrollar estrategias metodológicas basadas en la complementación de técnicas de análisis multivariados y geoestadísticas, para la clasificación de sitios intralotes y el estudio de interdependencias entre variables de sitio y rendimiento; (ll) proponer modelos mixtos alternativos, basados en funciones de correlación espacial de los términos de error que permitan explorar patrones de correlación espacial de los rendimientos intralotes y las propiedades del suelo en los sitios delimitados. From the last decades the use and development of Geographical Information Systems (GIS) and Satellite Positioning Systems (GPS) is highly promoted in cropping systems. Such technologies allow measuring spatial variability of site properties including electrical conductivity and others soil features as well as their impact on the spatial variability of yields. Therefore, site-specific management could be applied to improve the efficiency in the use of agrochemicals, the environmental protection, and the sustainability of the rural life. Currently, there is a wide offer of technological resources to capture spatial variation across sites within field. However, the optimum use of data coming from the precision agriculture machineries strongly depends on the capabilities to explore the information about the complex interactions underlying the productive outputs. The covariation between spatial soil properties and yields from georeferenced data has been treated in a graphical manner or with standard geostatistical approaches. New statistical modeling capabilities from the Mixed Linear Model framework are promising to deal with correlated data such those produced by the precision agriculture. Moreover, rescuing the multivariate nature of the multiple data collected at each site, several multivariate statistical approaches could be crucial tools for data analysis with georeferenced data. Understanding the basis of complex interactions at the scale of production field is now within reach the use of these new techniques. Our main objectives are: (1) to develop new statistical strategies, based on the complementarities of geostatistics and multivariate methods, useful to classify sites within field grown with grain crops and analyze the interrelationships of several soil and yield variables, (2) to propose mixed linear models to predict yield according spatial soil variability and to build contour maps to promote a more sustainable agriculture.

Modeling sequencing errors by combining Hidden Markov models.

Among the largest resources for biological sequence data is the large amount of expressed sequence tags (ESTs) available in public and proprietary databases. ESTs provide information on transcripts but for technical reasons they often contain sequencing errors. Therefore, when analyzing EST sequences computationally, such errors must be taken into account. Earlier attempts to model error prone coding regions have shown good performance in detecting and predicting these while correcting sequencing errors using codon usage frequencies. In the research presented here, we improve the detection of translation start and stop sites by integrating a more complex mRNA model with codon usage bias based error correction into one hidden Markov model (HMM), thus generalizing this error correction approach to more complex HMMs. We show that our method maintains the performance in detecting coding sequences.

The Estimation of Technical Efficiency Effects Models with an Example Applied to the Thai Manufacturing Sector

This paper does two things. First, it presents alternative approaches to the standard methods of estimating productive efficiency using a production function. It favours a parametric approach (viz. the stochastic production frontier approach) over a nonparametric approach (e.g. data envelopment analysis); and, further, one that provides a statistical explanation of efficiency, as well as an estimate of its magnitude. Second, it illustrates the favoured approach (i.e. the ‘single stage procedure’) with estimates of two models of explained inefficiency, using data from the Thai manufacturing sector, after the crisis of 1997. Technical efficiency is modelled as being dependent on capital investment in three major areas (viz. land, machinery and office appliances) where land is intended to proxy the effects of unproductive, speculative capital investment; and both machinery and office appliances are intended to proxy the effects of productive, non-speculative capital investment. The estimates from these models cast new light on the five-year long, post-1997 crisis period in Thailand, suggesting a structural shift from relatively labour intensive to relatively capital intensive production in manufactures from 1998 to 2002.

What Belongs Where? Variable Selection for Zero-Inflated Count Models with an Application to the Demand for Health Care

This paper develops stochastic search variable selection (SSVS) for zero-inflated count models which are commonly used in health economics. This allows for either model averaging or model selection in situations with many potential regressors. The proposed techniques are applied to a data set from Germany considering the demand for health care. A package for the free statistical software environment R is provided.

Microstructure Order Flow: Statistical and Economic Evaluation of Nonlinear Forecasts

In this paper we propose a novel empirical extension of the standard market microstructure order flow model. The main idea is that heterogeneity of beliefs in the foreign exchange market can cause model instability and such instability has not been fully accounted for in the existing empirical literature. We investigate this issue using two di¤erent data sets and focusing on out- of-sample forecasts. Forecasting power is measured using standard statistical tests and, additionally, using an alternative approach based on measuring the economic value of forecasts after building a portfolio of assets. We nd there is a substantial economic value on conditioning on the proposed models.

Spatial Interactions in Hedonic Pricing Models: The Urban Housing Market of Aveiro, Portugal

Spatial heterogeneity, spatial dependence and spatial scale constitute key features of spatial analysis of housing markets. However, the common practice of modelling spatial dependence as being generated by spatial interactions through a known spatial weights matrix is often not satisfactory. While existing estimators of spatial weights matrices are based on repeat sales or panel data, this paper takes this approach to a cross-section setting. Specifically, based on an a priori definition of housing submarkets and the assumption of a multifactor model, we develop maximum likelihood methodology to estimate hedonic models that facilitate understanding of both spatial heterogeneity and spatial interactions. The methodology, based on statistical orthogonal factor analysis, is applied to the urban housing market of Aveiro, Portugal at two different spatial scales.

An Introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

Modelling dependence in a ratemaking procedure with multivariate Poisson regression models

When actuaries face with the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce different regression models in order to relax the independence assumption, including zero-inflated models to account for excess of zeros and overdispersion. These models have been largely ignored to multivariate Poisson date, mainly because of their computational di±culties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claims. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models and their zero-inflated versions.

Species distribution models for conservation-oriented studies in Switzerland : filling data and tools gaps

SUMMARYSpecies distribution models (SDMs) represent nowadays an essential tool in the research fields of ecology and conservation biology. By combining observations of species occurrence or abundance with information on the environmental characteristic of the observation sites, they can provide information on the ecology of species, predict their distributions across the landscape or extrapolate them to other spatial or time frames. The advent of SDMs, supported by geographic information systems (GIS), new developments in statistical models and constantly increasing computational capacities, has revolutionized the way ecologists can comprehend species distributions in their environment. SDMs have brought the tool that allows describing species realized niches across a multivariate environmental space and predict their spatial distribution. Predictions, in the form of probabilistic maps showing the potential distribution of the species, are an irreplaceable mean to inform every single unit of a territory about its biodiversity potential. SDMs and the corresponding spatial predictions can be used to plan conservation actions for particular species, to design field surveys, to assess the risks related to the spread of invasive species, to select reserve locations and design reserve networks, and ultimately, to forecast distributional changes according to scenarios of climate and/or land use change.By assessing the effect of several factors on model performance and on the accuracy of spatial predictions, this thesis aims at improving techniques and data available for distribution modelling and at providing the best possible information to conservation managers to support their decisions and action plans for the conservation of biodiversity in Switzerland and beyond. Several monitoring programs have been put in place from the national to the global scale, and different sources of data now exist and start to be available to researchers who want to model species distribution. However, because of the lack of means, data are often not gathered at an appropriate resolution, are sampled only over limited areas, are not spatially explicit or do not provide a sound biological information. A typical example of this is data on 'habitat' (sensu biota). Even though this is essential information for an effective conservation planning, it often has to be approximated from land use, the closest available information. Moreover, data are often not sampled according to an established sampling design, which can lead to biased samples and consequently to spurious modelling results. Understanding the sources of variability linked to the different phases of the modelling process and their importance is crucial in order to evaluate the final distribution maps that are to be used for conservation purposes.The research presented in this thesis was essentially conducted within the framework of the Landspot Project, a project supported by the Swiss National Science Foundation. The main goal of the project was to assess the possible contribution of pre-modelled 'habitat' units to model the distribution of animal species, in particular butterfly species, across Switzerland. While pursuing this goal, different aspects of data quality, sampling design and modelling process were addressed and improved, and implications for conservation discussed. The main 'habitat' units considered in this thesis are grassland and forest communities of natural and anthropogenic origin as defined in the typology of habitats for Switzerland. These communities are mainly defined at the phytosociological level of the alliance. For the time being, no comprehensive map of such communities is available at the national scale and at fine resolution. As a first step, it was therefore necessary to create distribution models and maps for these communities across Switzerland and thus to gather and collect the necessary data. In order to reach this first objective, several new developments were necessary such as the definition of expert models, the classification of the Swiss territory in environmental domains, the design of an environmentally stratified sampling of the target vegetation units across Switzerland, the development of a database integrating a decision-support system assisting in the classification of the relevés, and the downscaling of the land use/cover data from 100 m to 25 m resolution.The main contributions of this thesis to the discipline of species distribution modelling (SDM) are assembled in four main scientific papers. In the first, published in Journal of Riogeography different issues related to the modelling process itself are investigated. First is assessed the effect of five different stepwise selection methods on model performance, stability and parsimony, using data of the forest inventory of State of Vaud. In the same paper are also assessed: the effect of weighting absences to ensure a prevalence of 0.5 prior to model calibration; the effect of limiting absences beyond the environmental envelope defined by presences; four different methods for incorporating spatial autocorrelation; and finally, the effect of integrating predictor interactions. Results allowed to specifically enhance the GRASP tool (Generalized Regression Analysis and Spatial Predictions) that now incorporates new selection methods and the possibility of dealing with interactions among predictors as well as spatial autocorrelation. The contribution of different sources of remotely sensed information to species distribution models was also assessed. The second paper (to be submitted) explores the combined effects of sample size and data post-stratification on the accuracy of models using data on grassland distribution across Switzerland collected within the framework of the Landspot project and supplemented with other important vegetation databases. For the stratification of the data, different spatial frameworks were compared. In particular, environmental stratification by Swiss Environmental Domains was compared to geographical stratification either by biogeographic regions or political states (cantons). The third paper (to be submitted) assesses the contribution of pre- modelled vegetation communities to the modelling of fauna. It is a two-steps approach that combines the disciplines of community ecology and spatial ecology and integrates their corresponding concepts of habitat. First are modelled vegetation communities per se and then these 'habitat' units are used in order to model animal species habitat. A case study is presented with grassland communities and butterfly species. Different ways of integrating vegetation information in the models of butterfly distribution were also evaluated. Finally, a glimpse to climate change is given in the fourth paper, recently published in Ecological Modelling. This paper proposes a conceptual framework for analysing range shifts, namely a catalogue of the possible patterns of change in the distribution of a species along elevational or other environmental gradients and an improved quantitative methodology to identify and objectively describe these patterns. The methodology was developed using data from the Swiss national common breeding bird survey and the article presents results concerning the observed shifts in the elevational distribution of breeding birds in Switzerland.The overall objective of this thesis is to improve species distribution models as potential inputs for different conservation tools (e.g. red lists, ecological networks, risk assessment of the spread of invasive species, vulnerability assessment in the context of climate change). While no conservation issues or tools are directly tested in this thesis, the importance of the proposed improvements made in species distribution modelling is discussed in the context of the selection of reserve networks.RESUMELes modèles de distribution d'espèces (SDMs) représentent aujourd'hui un outil essentiel dans les domaines de recherche de l'écologie et de la biologie de la conservation. En combinant les observations de la présence des espèces ou de leur abondance avec des informations sur les caractéristiques environnementales des sites d'observation, ces modèles peuvent fournir des informations sur l'écologie des espèces, prédire leur distribution à travers le paysage ou l'extrapoler dans l'espace et le temps. Le déploiement des SDMs, soutenu par les systèmes d'information géographique (SIG), les nouveaux développements dans les modèles statistiques, ainsi que la constante augmentation des capacités de calcul, a révolutionné la façon dont les écologistes peuvent comprendre la distribution des espèces dans leur environnement. Les SDMs ont apporté l'outil qui permet de décrire la niche réalisée des espèces dans un espace environnemental multivarié et prédire leur distribution spatiale. Les prédictions, sous forme de carte probabilistes montrant la distribution potentielle de l'espèce, sont un moyen irremplaçable d'informer chaque unité du territoire de sa biodiversité potentielle. Les SDMs et les prédictions spatiales correspondantes peuvent être utilisés pour planifier des mesures de conservation pour des espèces particulières, pour concevoir des plans d'échantillonnage, pour évaluer les risques liés à la propagation d'espèces envahissantes, pour choisir l'emplacement de réserves et les mettre en réseau, et finalement, pour prévoir les changements de répartition en fonction de scénarios de changement climatique et/ou d'utilisation du sol. En évaluant l'effet de plusieurs facteurs sur la performance des modèles et sur la précision des prédictions spatiales, cette thèse vise à améliorer les techniques et les données disponibles pour la modélisation de la distribution des espèces et à fournir la meilleure information possible aux gestionnaires pour appuyer leurs décisions et leurs plans d'action pour la conservation de la biodiversité en Suisse et au-delà. Plusieurs programmes de surveillance ont été mis en place de l'échelle nationale à l'échelle globale, et différentes sources de données sont désormais disponibles pour les chercheurs qui veulent modéliser la distribution des espèces. Toutefois, en raison du manque de moyens, les données sont souvent collectées à une résolution inappropriée, sont échantillonnées sur des zones limitées, ne sont pas spatialement explicites ou ne fournissent pas une information écologique suffisante. Un exemple typique est fourni par les données sur 'l'habitat' (sensu biota). Même s'il s'agit d'une information essentielle pour des mesures de conservation efficaces, elle est souvent approximée par l'utilisation du sol, l'information qui s'en approche le plus. En outre, les données ne sont souvent pas échantillonnées selon un plan d'échantillonnage établi, ce qui biaise les échantillons et par conséquent les résultats de la modélisation. Comprendre les sources de variabilité liées aux différentes phases du processus de modélisation s'avère crucial afin d'évaluer l'utilisation des cartes de distribution prédites à des fins de conservation.La recherche présentée dans cette thèse a été essentiellement menée dans le cadre du projet Landspot, un projet soutenu par le Fond National Suisse pour la Recherche. L'objectif principal de ce projet était d'évaluer la contribution d'unités 'd'habitat' pré-modélisées pour modéliser la répartition des espèces animales, notamment de papillons, à travers la Suisse. Tout en poursuivant cet objectif, différents aspects touchant à la qualité des données, au plan d'échantillonnage et au processus de modélisation sont abordés et améliorés, et leurs implications pour la conservation des espèces discutées. Les principaux 'habitats' considérés dans cette thèse sont des communautés de prairie et de forêt d'origine naturelle et anthropique telles que définies dans la typologie des habitats de Suisse. Ces communautés sont principalement définies au niveau phytosociologique de l'alliance. Pour l'instant aucune carte de la distribution de ces communautés n'est disponible à l'échelle nationale et à résolution fine. Dans un premier temps, il a donc été nécessaire de créer des modèles de distribution de ces communautés à travers la Suisse et par conséquent de recueillir les données nécessaires. Afin d'atteindre ce premier objectif, plusieurs nouveaux développements ont été nécessaires, tels que la définition de modèles experts, la classification du territoire suisse en domaines environnementaux, la conception d'un échantillonnage environnementalement stratifié des unités de végétation cibles dans toute la Suisse, la création d'une base de données intégrant un système d'aide à la décision pour la classification des relevés, et le « downscaling » des données de couverture du sol de 100 m à 25 m de résolution. Les principales contributions de cette thèse à la discipline de la modélisation de la distribution d'espèces (SDM) sont rassemblées dans quatre articles scientifiques. Dans le premier article, publié dans le Journal of Biogeography, différentes questions liées au processus de modélisation sont étudiées en utilisant les données de l'inventaire forestier de l'Etat de Vaud. Tout d'abord sont évalués les effets de cinq méthodes de sélection pas-à-pas sur la performance, la stabilité et la parcimonie des modèles. Dans le même article sont également évalués: l'effet de la pondération des absences afin d'assurer une prévalence de 0.5 lors de la calibration du modèle; l'effet de limiter les absences au-delà de l'enveloppe définie par les présences; quatre méthodes différentes pour l'intégration de l'autocorrélation spatiale; et enfin, l'effet de l'intégration d'interactions entre facteurs. Les résultats présentés dans cet article ont permis d'améliorer l'outil GRASP qui intègre désonnais de nouvelles méthodes de sélection et la possibilité de traiter les interactions entre variables explicatives, ainsi que l'autocorrélation spatiale. La contribution de différentes sources de données issues de la télédétection a également été évaluée. Le deuxième article (en voie de soumission) explore les effets combinés de la taille de l'échantillon et de la post-stratification sur le la précision des modèles. Les données utilisées ici sont celles concernant la répartition des prairies de Suisse recueillies dans le cadre du projet Landspot et complétées par d'autres sources. Pour la stratification des données, différents cadres spatiaux ont été comparés. En particulier, la stratification environnementale par les domaines environnementaux de Suisse a été comparée à la stratification géographique par les régions biogéographiques ou par les cantons. Le troisième article (en voie de soumission) évalue la contribution de communautés végétales pré-modélisées à la modélisation de la faune. C'est une approche en deux étapes qui combine les disciplines de l'écologie des communautés et de l'écologie spatiale en intégrant leurs concepts de 'habitat' respectifs. Les communautés végétales sont modélisées d'abord, puis ces unités de 'habitat' sont utilisées pour modéliser les espèces animales. Une étude de cas est présentée avec des communautés prairiales et des espèces de papillons. Différentes façons d'intégrer l'information sur la végétation dans les modèles de répartition des papillons sont évaluées. Enfin, un clin d'oeil aux changements climatiques dans le dernier article, publié dans Ecological Modelling. Cet article propose un cadre conceptuel pour l'analyse des changements dans la distribution des espèces qui comprend notamment un catalogue des différentes formes possibles de changement le long d'un gradient d'élévation ou autre gradient environnemental, et une méthode quantitative améliorée pour identifier et décrire ces déplacements. Cette méthodologie a été développée en utilisant des données issues du monitoring des oiseaux nicheurs répandus et l'article présente les résultats concernant les déplacements observés dans la distribution altitudinale des oiseaux nicheurs en Suisse.L'objectif général de cette thèse est d'améliorer les modèles de distribution des espèces en tant que source d'information possible pour les différents outils de conservation (par exemple, listes rouges, réseaux écologiques, évaluation des risques de propagation d'espèces envahissantes, évaluation de la vulnérabilité des espèces dans le contexte de changement climatique). Bien que ces questions de conservation ne soient pas directement testées dans cette thèse, l'importance des améliorations proposées pour la modélisation de la distribution des espèces est discutée à la fin de ce travail dans le contexte de la sélection de réseaux de réserves.

Estimation of parametric and nonparametric models for univariate claim severity distributions - an approach using R

This paper presents an analysis of motor vehicle insurance claims relating to vehicle damage and to associated medical expenses. We use univariate severity distributions estimated with parametric and non-parametric methods. The methods are implemented using the statistical package R. Parametric analysis is limited to estimation of normal and lognormal distributions for each of the two claim types. The nonparametric analysis presented involves kernel density estimation. We illustrate the benefits of applying transformations to data prior to employing kernel based methods. We use a log-transformation and an optimal transformation amongst a class of transformations that produces symmetry in the data. The central aim of this paper is to provide educators with material that can be used in the classroom to teach statistical estimation methods, goodness of fit analysis and importantly statistical computing in the context of insurance and risk management. To this end, we have included in the Appendix of this paper all the R code that has been used in the analysis so that readers, both students and educators, can fully explore the techniques described

What do we gain from simplicity versus complexity in species distribution models?

Species distribution models (SDMs) are widely used to explain and predict species ranges and environmental niches. They are most commonly constructed by inferring species' occurrence-environment relationships using statistical and machine-learning methods. The variety of methods that can be used to construct SDMs (e.g. generalized linear/additive models, tree-based models, maximum entropy, etc.), and the variety of ways that such models can be implemented, permits substantial flexibility in SDM complexity. Building models with an appropriate amount of complexity for the study objectives is critical for robust inference. We characterize complexity as the shape of the inferred occurrence-environment relationships and the number of parameters used to describe them, and search for insights into whether additional complexity is informative or superfluous. By building 'under fit' models, having insufficient flexibility to describe observed occurrence-environment relationships, we risk misunderstanding the factors shaping species distributions. By building 'over fit' models, with excessive flexibility, we risk inadvertently ascribing pattern to noise or building opaque models. However, model selection can be challenging, especially when comparing models constructed under different modeling approaches. Here we argue for a more pragmatic approach: researchers should constrain the complexity of their models based on study objective, attributes of the data, and an understanding of how these interact with the underlying biological processes. We discuss guidelines for balancing under fitting with over fitting and consequently how complexity affects decisions made during model building. Although some generalities are possible, our discussion reflects differences in opinions that favor simpler versus more complex models. We conclude that combining insights from both simple and complex SDM building approaches best advances our knowledge of current and future species ranges.