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In Sect. 5.1 we considered binary regression models, that is, regression situations where the response is observed in two categories. In many applications, from social science to medicine, response variables often have more than two categories. For example, consumers may choose between different brands of a product or they may express their opinion about some product in ordered categories ranging from “very satisfied” to “not satisfied at all.” Similarly, voters choose between several parties or they assess the quality of candidates in ordered categories. In medicine, we may, for example, not only distinguish between “infection” and “no infection” but also between several types of infection, as in Example 6.1 below.

Linear models are well suited for regression analyses when the response variable is continuous and at least approximately normal. In some cases, an appropriate transformation is needed to ensure approximate normality of the response. In addition, the expectation of the response is assumed to be a linear combination of covariates. Again, these covariates may be transformed before being included in the linear predictor.

This chapter discusses several extensions of the classical linear model. We first describe in Sect. 4.1 the general linear model and its applications. This model allows for correlated errors and heteroscedastic variances of the errors. Section 4.2 discusses several techniques to regularize the least squares estimator. Such a regularization may be useful in cases where the design matrix is highly collinear or even rank deficient. Moreover, regularization techniques allow for built-in variable selection. Section 4.4 describes Bayesian linear models as an alternative to the frequentist linear model framework. In modern statistics, Bayesian approaches have become increasingly more important and widely used.

The following two chapters will focus on the theory and application of linear regression models, which play a major role in statistics. We already studied some examples in Sect. 2.2. In addition to the direct application of linear regression models, they are also the basis of a variety of more complex regression methods.

In the previous chapter, we illustrated how to flexibly model and estimate the effect of a continuous covariate z on the response variable y without specifying a restrictive functional form of the effect f(z).

Following a request from the DG RELEX in April 2008 for support in the planning of the EU mission to Darfur, the GMES-LIMES project partners in the Humanitarian Relief & Reconstruction cluster combined their expertise to contribute their support through the provision of satellite imagery based maps and information. Detailed damage assessment maps were produced for three villages that had been burnt down by militias early in 2008. Analyses were also carried out on the evolution of two large IDP camps, focussing on the population growth and densities within both the camps and the surrounding villages. In addition, rapid mapping techniques adapted to the complex humanitarian situation were applied in analysing the effects of militia raids on the three villages in West Darfur and for monitoring the evolution of the IDP camps between 2002 and 2008. The impact of the camps on the surrounding environment was also analysed using medium-resolution MODIS time series data (2000—2008).

Eine Verbraucherzentrale mochte uberprufen, ob ein bestimmtes Milchprodukt Ubelkeit bei den Konsumenten auslost. In einer Studie mit zehn Personen wird bei sieben Personen nach dem Genus dieses Milchprodukts eine auftretende Ubelkeit registriert. Uberprufen Sie zum Signifikanzniveau α = 0.05 die statistische Nullhypothese, das der Anteil der Personen mit Ubelkeitssymptomen nach dem Genus dieses Produkts in der Grundgesamtheit hochstens 60 % betragt. Geben Sie zunachst das zugehorige statistische Testproblem an.

Im vorhergehenden Kapitel wurde gezeigt, wie sich im Rahmen der nichtparametrischen Regression der Einfluss einer metrischen Kovariablen z auf die Zielvariable y ohne Vorgabe einer restriktiven funktionalen Form des Effekts f(z) flexibel modellieren und schatzen lasst, und wie man die Konzepte fur zwei metrische Kovariablen (z1, z2) oder eine geografisch-raumliche Lokationsvariable s erweitern kann. Wie wir in Kapitel 3 und vielen Beispielen, etwa zum Mietspiegel, zur Unterernahrung in Afrika, zum Kredit-Scoring und zur Patenterteilung gesehen haben, liegt in Anwendungen haufig folgende Situation vor: Fur einen Teil der Kovariablen lasst sich der Einfluss auf die Zielvariable adaquat durch einen linearen Pradiktor beschreiben.

Lineare Modelle eignen sich besonders fur Regressionsanalysen, bei denen die Zielvariable stetig ist und – moglicherweise nach einer geeigneten Transformation – zumindest approximativ durch eine Normalverteilung modelliert werden kann. Zusatzlich muss sich der Erwartungswert der Zielvariablen durch eine Linearkombination von – moglicherweise ebenfalls transformierten – Kovariablen darstellen lassen. In vielen Anwendungen ist die Zielvariable jedoch nicht stetig, sondern binar bzw. kategorial oder eine Zahlvariable.

The advancement of feature recognition and advanced image analysis techniques facilitates the extraction of thematic information, for policy making support and informed decisions. As a strong driver, the availability of VHSR data and the ever increasing use of geo-information for all kinds of spatially relevant management issues have catalyzed the development of new methods to exploit image information more ‘intelligently’. This chapter highlights some of the recent developments from both technology and policy and poses a synthetic view on an upcoming paradigm in image analysis and the extraction of geo-spatial information. It starts from a review of requirements from international initiatives like GMES (Global Monitoring of Environment and Security), followed by a discussion the possible answers from OBIA including a detailed portrait of the methodological framework of class modeling. The chapter closes with a short reflection on the required adaptation of standard methods of accuracy assessment and change detection, as well as on the evaluation of delineated and classified objects against the ultimate benchmark, our human perception.

As a synthesis of a series of studies carried out by the authors this chapter discusses domain-specific class modelling which utilizes a priori knowledge on the specific scale domains of the target features addressed. Two near-natural forest settings served as testing environment for a combined use of airborne laser scanning (ALS) and optical image data to perform automated tree-crown delineation. The primary methodological aim was to represent the entire image data product in a single, spatially contiguous, set of scale-specific objects (one-level-representation, OLR). First, by high-level (broad-scale) segmentation an initial set of image regions was created. The regions, characterised by homogenous spectral behaviour and uniform ALS-based height information, represented different image object domains (in this case: areas of specific forest characteristics). The regions were then treated independently to perform domain-specific class modelling (i.e. the characteristics of each region controlled the generation of lower level objects). The class modelling was undertaken using Cognition Network Language (CNL), which allows for addressing single objects and enables supervising the object generation process through the provision of programming functions like branching and looping. Altogether, the single processes of segmentation and classification were coupled in a cyclic approach. Finally, representing the entire scene content in a scale finer than the initial regional level, has accomplished OLR. Building upon the preceding papers, we endeavoured to improve the algorithms for tree crown delineation and also extended the underlying workflow. The transferability of our approach was evaluated by (1) shifting the geographical setting from a hilly study area (National Park Bavarian Forest, South-Eastern Germany) to a mountainous site (Montafon area, Western Austria); and (2) by applying it to different data sets, wherein the latter differ from the initial ones in terms of spectral resolution (line scanner RGBI data vs. false colour infrared orthophotos) and spatial resolution (0.5 m vs. 0.25 m), as well as ALS point density, which was ten times higher in the original setting. Only minor adaptations had to be done. Additional steps, however, were necessary targeting the data sets of different resolution. In terms of accuracy, in both study areas 90% of the evaluated trees were correctly detected (concerning the location of trees). The following classification of tree types reached an accuracy of 75% in the first study area. It was not evaluated for the second study area which was nearly exclusively covered by coniferous trees.

Driven by vegetation and environmental changes caused by global warming and an ongoing loss of biodiversity, there is an increasing demand for updated image data in a high time rate. These requirements, as well as economic reasons, ask for automated image analysis techniques. This article presents a synthesis of two complementary, preceding studies (Preiner et al., 2006; Weinke and Lang, 2006) on semi-automated habitat delineation. The work has been carried out in two neighboring study sites, which are situated in the Berchtesgaden National Park, in the Alpine region of south-eastern Germany. Both test sites represent a mountainous area, characterized by a high bio- and habitat diversity and a cliffy relief. The NPB has been involved in the European Interreg-IIIb project HABITALP (Alpine Habitat Diversity), which came up with harmonized methods for trans-Alpine monitoring of habitat diversity and environmental changes by standardized, comparative habitat interpretation on color infrared (CIR) aerial photographs. The work presented evaluates the potential of object-based image analysis (OBIA) for partly automising this process. In both studies we used pan-sharpened data from the same QuickBird scene. First, two different approaches, i.e. iterative one-level representation (OLR) strategy and multi-scale segmentation/object relationship modeling (MSS/ORM), are described. Both are meant for dealing with high spectral and spatial variability. They are discussed in the light of specific settings: whereas iterative OLR was used for delineating homogeneous, but differently scaled single habitat types, MSS/ORM proved suitable for classifying hierarchically structured patches of mountain pine (Pinus mugo). Second, based on the results from iterative OLR, a spatial overlay method (‘virtual overlay’, cf. Schopfer and Lang, 2006) is applied to characterize habitat fate. The aim is to tell ‘real’ object changes from differences originating from different ways of delineation, i.e. visual interpretation in the year 2003 vs. automated delineation in 2005. The results showed that both strategies in combination with object-oriented image analysis software are suited to delineate habitats similar to the habitats as addressed by the HABITALP project.

In the near future several new highest resolution, next generation satellites will be launched with panchromatic half-meter resolution imagery, e.g. WorldView 1 and 2. The ever increasing supply of high-resolution imagery seeks for adequate, i.e. more effective, more automated and reliable methods for image processing and interpretation. At the interface of geographic information science and remote sensing, object-based image analysis methodologies provide a solid basis for exploiting imagery more intelligently. Working with image objects enables (1) single feature, specific information extraction, (2) performing complex classifications and multi-scale representations and (3) spatial analysis and modeling. However, deriving image objects from various sources and in different scales implies the problem of generating inconsistent boundaries. To specifically address this challenge, a tool called LIST (landscape interpretation support tool) is used, which, based on a straight-forward principle, analyses the spatial relationships of image objects, i.e. their correspondence and their changes over time. The chapter presents a methodological discussion and preliminary results from an ongoing study on ‘object fate analysis’ (OFA). OFA means the investigation of object transition (change over time) or object correspondence (different delineations or representations). The concept and the application of OFA are illustrated by two case-studies representing both aspects. The first one carried out in medium scale uses Landsat TM and ETM imagery and shows an example of performing change assessment as well as object-based accuracy assessment. The second fine-scale study is based on SPOT 5 scenes and demonstrates how object correspondence can be assessed on two different object representations, machine-based segmentation and manual delineation.

This book brings together a collection of invited interdisciplinary perspec- tives on the recent topic of Object-based Image Analysis (OBIA).

Generalized linear models (GLMs) and semiparametric extensions provide a flexible framework for analyzing the claims process in non-life insurance. Currently, most applications are still based on traditional GLMs, where covariate effects are modelled in form of a linear predictor. However, these models may already be too restrictive if nonlinear effects of metrical covariates are present. Moreover, although data are often collected within longer time periods and come from different geographical regions, effects of space and time are usually totally neglected. We provide a Bayesian semiparametric approach, which allows to simultaneously incorporate effects of space, time and further covariates within a joint model. The method is applied to analyze costs of hospital treatment and accommodation for a large data set from a German health insurance company.

Welche approximativen Verteilungen besitzen die folgenden Zufallsvariablen? (a) Der Frauenanteil an der Gesamtzahl der Beschaftigten liegt im Land NRW bei 41.4 % (Ende Marz 1990). X 1 sei die Anzahl der Frauen unter 100 zufallig ausgewahlten Beschaftigten dieses Landes. (b) Eine Pharmagroshandlung beliefert taglich 500 Apotheken. Die Wahrscheinlichkeit einer Reklamation betragt bei allen Apotheken (unabhangig voneinander) 0.02. X 2 sei die Anzahl der Reklamationen an einem Tag. (c) Der spielsuchtige Willi verbringt seine Abende oft an einem Spielautomaten, bei dem ein Spiel 50 Pfennig kostet. Die Zufallsvariable X = Gewinn (in DM) hat folgende Wahrscheinlichkeitsfunktion: $$ P(X = - 0.5) = 0.6\quad ,\quad P(X = 0) = 0.2\quad ,\quad P(X = 1) = 0.2. $$ . Sei X 3 der Gewinn bei 100 Spielen. (d) Ein Mann, der jeden Morgen mit dem Bus zur Arbeit fahrt, hat oftmals das Pech, das die ankommenden Busse uberfullt sind und weiterfahren. Er weis aus Erfahrung, das die Anzahl der an einem Morgen vorbeifahrenden Busse Poisson-verteilt ist mit Erwartungswert 1. Sei X 4 die Anzahl der pro Halbjahr (=100 Arbeitstage) vorbeifahrenden Busse.

In vielen Anwendungen ist man nicht nur an einem einzigen, sondern an vielen erhobenen Merkmalen interessiert. Beschrankt man sich auf ein Merkmal wie Dauer der Arbeitslosigkeit, so lassen sich zwar die Form der Verteilung, die mittlere Dauer der Arbeitslosigkeit sowie die Varianz untersuchen, wesentliche Fragestellungen jedoch, beispielsweise danach, wie die Dauer der Arbeitslosigkeit von Ausbildungsniveau oder Geschlecht abhangt, lassen sich mit diesem eindimensionalen Datenmaterial nicht beantworten. Dazu ist es notwendig, die Merkmale Dauer, Ausbildungsniveau und Geschlecht gemeinsam zu erheben, d.h. zu einer Person werden mehrere Werte (x, y, z,...), sogenannte mehrdimensionale Daten erhoben. Im folgenden wird ausgefuhrt, wie sich derartige Daten aufbereiten und graphisch darstellen lassen. Wir beschranken uns dabei hauptsachlich auf den zweidimensionalen Fall. In einem weiteren Schritt werden Mase entwickelt, die den Zusammenhang zwischen Merkmalen erfassen. Dabei werden zuerst Methoden fur diskrete bzw. diskretisierte Merkmale behandelt. Anschliesend werden Verfahren fur metrisch skalierte Merkmale vorgestellt.