Environmental and Ecological Statistics – serie

One of our greatest current challenges is the preservation and remediation of ecosystem integrity. This requires monitoring and assessment over large geographic areas, repeatedly over time, and cannot be practically fulfilled by field measurements alone. Remotely sensed imagery plays a crucial role by its ability to monitor large spatially continuous areas. This technology increasingly provides extensive spatial-temporal data; however, the challenge is to extract meaningful environmental information from such extensive data. This book presents a new method for assessing spatial pattern in raster land cover maps based on satellite imagery in a way that incorporates multiple pixel resolutions. This is combined with more conventional single-resolution measurements of spatial pattern and simple non-spatial land cover proportions to assess predictability of both surface water quality and ecological integrity within watersheds of the state of Pennsylvania (USA).

We offer here a non-conventional approach to muhivariate ima- structured data for which the basis is well tested but the analytical ramifi­ cations are still unfolding. Although we do not formally pursue them, there are several parallels with the nature of neural networks. We employ a systematic set of statistical heuristics for modeling multivariate image data in a quasi-perceptual manner. When the human eye perceives a scene, the elements of the scene are segregated heuristically into compo­ nents according to similarity and dissimilarity, and then the relationships among the components are interpreted. Similarly, we segregate or seg­ ment the scene into hierarchically organized components that are subject to subsequent statistical analysis in many modes for interpretive purposes. We refer to the segregated scene segments as patterns, since they provide a basis for perception of pattern. Since they are also hierarchically organ­ ized, we refer to them further as polypatterns. This leads us to our acro­ nym of Progressively Segmented Image Modeling As Poly-Patterns (PSIMAPP). Likewise, we formalize our approach in terms of pattern processes and segmentation sequences. In alignment with the terminology of image analysis, we refer to our multivariate measures as being signal bands.

Demography can be considered the key to understanding much of biology. It is the demographic processes of birth and death which govern the spread of populations through environmentsand the spread of genes through populations. An understa- ing of demographycan yield not only an understanding of population size and p- ulation change, it can help us to understand the form and function of life histories; whenorganismsmature,whentheybreed,and whentheydie. Demographicinsights allow us to see how populations function, how they interact with their changing environment, and how they adapt. The analysis of demographic processes in free-living organisms is however no simple task and involves considerable challenges in observation and analysis. Some 20yearsago,therewasaconcertedefforttopromoteinter-disciplinarycollaboration between biologists and statisticians to address these challenges and thereby to f- ther our understanding of demographic processes in natural populations. Although many diverse organisms can be studied in the wild, birds have proved particularly amenable with large numbers being marked and followed by large networks of - servers.Itwas nocoincidencethenthatthe EuropeanUnionforBird Ringing(EUR- ING) played a leading role in these initiatives, teaming up in the mid-1980swith the Mathematical Ecology Group of the Biometric Society, and the British Ecological Society, to bring together experts from diverse ?elds to address the challenges in hand. Twenty years on, progresshas been considerable and we now have signi?cant insights into demographic processes thanks to the wide range of quantitative tools and systematically collected datasets which have been built up over this period.

One of our greatest current challenges is the preservation and remediation of ecosystem integrity. This requires monitoring and assessment over large geographic areas, repeatedly over time, and cannot be practically fulfilled by field measurements alone. Remotely sensed imagery plays a crucial role by its ability to monitor large spatially continuous areas. This technology increasingly provides extensive spatial-temporal data; however, the challenge is to extract meaningful environmental information from such extensive data. This book presents a new method for assessing spatial pattern in raster land cover maps based on satellite imagery in a way that incorporates multiple pixel resolutions. This is combined with more conventional single-resolution measurements of spatial pattern and simple non-spatial land cover proportions to assess predictability of both surface water quality and ecological integrity within watersheds of the state of Pennsylvania (USA).

We offer here a non-conventional approach to muhivariate ima- structured data for which the basis is well tested but the analytical ramifi­ cations are still unfolding. Although we do not formally pursue them, there are several parallels with the nature of neural networks. We employ a systematic set of statistical heuristics for modeling multivariate image data in a quasi-perceptual manner. When the human eye perceives a scene, the elements of the scene are segregated heuristically into compo­ nents according to similarity and dissimilarity, and then the relationships among the components are interpreted. Similarly, we segregate or seg­ ment the scene into hierarchically organized components that are subject to subsequent statistical analysis in many modes for interpretive purposes. We refer to the segregated scene segments as patterns, since they provide a basis for perception of pattern. Since they are also hierarchically organ­ ized, we refer to them further as polypatterns. This leads us to our acro­ nym of Progressively Segmented Image Modeling As Poly-Patterns (PSIMAPP). Likewise, we formalize our approach in terms of pattern processes and segmentation sequences. In alignment with the terminology of image analysis, we refer to our multivariate measures as being signal bands.

Sampling consists of selection, acquisition, and quantification of a part of the population. While selection and acquisition apply to physical sampling units of the population, quantification pertains only to the variable of interest, which is a particular characteristic of the sampling units. A sampling procedure is expected to provide a sample that is representative with respect to some specified criteria. Composite sampling, under idealized conditions, incurs no loss of information for estimating the population means. But an important limitation to the method has been the loss of information on individual sample values, such as, the extremely large value. In many of the situations where individual sample values are of interest or concern, composite sampling methods can be suitably modified to retrieve the information on individual sample values that may be lost due to compositing. This book presents statistical solutions to issues that arise in the context of applications of composite sampling.

This book provides axioms of partial order and some basic material, for example consequences of “criss-crossing” of data profiles, the role of aggregations of the indicators and the powerful method of formal concept analysis. The interested reader will learn how to apply fuzzy methods in partial order analysis and what ‘antagonistic indicator’ means.

Sampling consists of selection, acquisition, and quantification of a part of the population. While selection and acquisition apply to physical sampling units of the population, quantification pertains only to the variable of interest, which is a particular characteristic of the sampling units. A sampling procedure is expected to provide a sample that is representative with respect to some specified criteria. Composite sampling, under idealized conditions, incurs no loss of information for estimating the population means. But an important limitation to the method has been the loss of information on individual sample values, such as, the extremely large value. In many of the situations where individual sample values are of interest or concern, composite sampling methods can be suitably modified to retrieve the information on individual sample values that may be lost due to compositing. This book presents statistical solutions to issues that arise in the context of applications of composite sampling.

This book provides axioms of partial order and some basic material, for example consequences of “criss-crossing” of data profiles, the role of aggregations of the indicators and the powerful method of formal concept analysis. The interested reader will learn how to apply fuzzy methods in partial order analysis and what ‘antagonistic indicator’ means.

This monograph is multivariate, multi-perspective and multipurpose.  We intend to be innovatively integrative through statistical synthesis.  Innovation requires capacity to operate in ways that are not ordinary, which means that conventional computations and generic graphics will not meet the needs of an adaptive approach.  Flexible formulation and special schematics are essential elements that must be manageable and economical.