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More than three quarters of the world’s economic activity is concentrated in cities. But what drives people and firms to agglomerate in urban areas? Clearly, some places may offer inherent benefits due to the location itself, such as a mild climate or the presence of natural harbours, but that does not tell the whole story. Rather urban areas also offer spaces for interaction among people and firms as well as the proximity to potential partners, customers, and competitors, which could have a significant impact on the appeal of a location for a firm. Using multiple novel methods based on a unique detailed geographical dataset, this dissertation explores how a location’s attractiveness is impacted by the presence of nearby firms in three studies. The first study explores the influence of the density of economic activity on wages at a given location and attempts to disentangle the separate mechanisms that could be at work. The second study is concerned with the locations of foreign-owned firms and more specifically whether foreign-owned firms are more influenced by agglomeration benefits than domestic firms. The final study switches from modelling the effects of location to modelling the location patterns themselves using economic theory-based spatial point processes. The results of these studies make significant contributions to empirical research both in economic geography and international business as a set of theoretical propositions are tested on a very detailed dataset using an advanced methodology. The results could also be of interest for practitioners as the importance of location decisions is further reinforced, as well as for policymakers as the analyses explore not only the benefits but also the detriments of agglomeration. Sergiy Protsiv is a researcher at the Center for Strategy and Competitiveness at the Stockholm School of Economics. He participated in several projects on clusters and regional development, most notably the European Cluster Observatory. / <p>Diss. Stockholm : Handelshögskolan, 2012</p>

<p>This thesis consits of four papers dealing with distance based (non-Euclidean) tests for spatial clustering in inhomogeneous populations. </p><p>The density adjusted distance (DAD), which considers the underlying density, is defined in the first paper. The proposed distance can be used together with any of the old distance based methods developed for traditional homogeneous spatial patterns. </p><p>The test statistics in distance based tests can all be seen as a weighted sum of distance measures for distances between <i>n</i> cases with known co-ordinates. DAD based test statistics are developed and their performance is compared with the performance of previously suggested tests by simulation in the second paper. The tests are compared in different types of data set and for various kinds of clustering. It is shown that no test is the optimal choice for all alternative hypotheses and that the tests are unequally sensitive to the structure of the underlying data. Tests based on the DAD are often a good alternative. </p><p>Test statistics and graphical tools for the Empirical Distribution Function of DAD are developed and examined in the third paper. We show that the result of an EDF test combined with EDF plots provides more information about the possible nature of clustering in a sample than the result of a parametric test only. </p>

This thesis consits of four papers dealing with distance based (non-Euclidean) tests for spatial clustering in inhomogeneous populations. The density adjusted distance (DAD), which considers the underlying density, is defined in the first paper. The proposed distance can be used together with any of the old distance based methods developed for traditional homogeneous spatial patterns. The test statistics in distance based tests can all be seen as a weighted sum of distance measures for distances between n cases with known co-ordinates. DAD based test statistics are developed and their performance is compared with the performance of previously suggested tests by simulation in the second paper. The tests are compared in different types of data set and for various kinds of clustering. It is shown that no test is the optimal choice for all alternative hypotheses and that the tests are unequally sensitive to the structure of the underlying data. Tests based on the DAD are often a good alternative. Test statistics and graphical tools for the Empirical Distribution Function of DAD are developed and examined in the third paper. We show that the result of an EDF test combined with EDF plots provides more information about the possible nature of clustering in a sample than the result of a parametric test only.

<p>This dissertation focuses on solving some common problems associated with ecological field studies. In the core of the statistical methodology, lies spatial modeling that provides greater flexibility and improved predictive performance over existing algorithms. The applications involve prevalence datasets for hundreds of plants over a large area in the Cape Floristic Region (CFR) of South Africa.</p><p>In Chapter 2, we begin with modeling the categorical abundance data with a multi level spatial model using background information such as environmental and soil-type factors. The empirical pattern is formulated as a degraded version of the potential pattern, with the degradation effect accomplished in two stages. First, we adjust for land use transformation and then we adjust for measurement error, hence misclassification error, to yield the observed abundance classifications. With data on a regular grid over CFR, the analysis is done with a conditionally autoregressive prior on spatial random effects. With around ~ 37000 cells to work with, a novel paralleilization algorithm is developed for updating the spatial parameters to efficiently estimate potential and transformed abundance surfaces over the entire region.</p><p>In Chapter 3, we focus on a different but increasingly common type of prevalence data in the so called <italic>presence-only</italic> setting. We detail the limitations associated with a usual presence-absence analysis for this data and advocate modeling the data as a point pattern realization. The underlying intensity surface is modeled with a point-level spatial Gaussian process prior, after taking into account sampling bias and change in land-use pattern. The large size of the region enforces using an computational approximation with a bias-corrected predictive process. We compare our methodology against the the most commonly used maximum entropy method, to highlight the improvement in predictive performance.</p><p>In Chapter 4, we develop a novel hierarchical model for analyzing noisy point pattern datasets, that arise commonly in ecological surveys due to multiple sources of bias, as discussed in previous chapters. The effect of the noise leads to displacements of locations as well as potential loss of points inside a bounded domain. Depending on the assumption on existence of locations outside the boundary, a couple of different models -- <italic>island</italic> and <italic>subregion</italic>, are specified. The methodology assumes informative knowledge of the scale of measurement error, either pre-specified or learned from a training sample. Its performance is tested against different scales of measurement error related to the data collection techniques in CFR.</p><p>In Chapter 5, we suggest an alternative model for prevalence data, different from the one in Chapter 3, to avoid numerical approximation and subsequent computational complexities for a large region. A mixture model, similar to the one in Chapter 4 is used, with potential dependence among the weights and locations of components. The covariates as well as a spatial process are used to model the dependence. A novel birth-death algorithm for the number of components in the mixture is under construction.</p><p>Lastly, in Chapter 6, we proceed to joint modeling of multiple-species datasets. The challenge is to infer about inter-species competition with a large number of populations, possibly running into several hundreds. Our contribution involves applying hierarchical Dirichlet process to cluster the presence localities and subsequently developing measures of range overlap from posterior draws. This kind of simultaneous inference can potentially have implications for questions related to biodiversity and conservation studies. .</p> / Dissertation

<p>The modelling and analysis of complex stochastic systems with increasingly large data sets, state-spaces and parameters provides major stimulus to research in Bayesian nonparametric methods and Bayesian computation. This dissertation presents advances in both nonparametric modelling and statistical computation stimulated by challenging problems of analysis in complex spatio-temporal systems and core computational issues in model fitting and model assessment. The first part of the thesis, represented by chapters 2 to 4, concerns novel, nonparametric Bayesian mixture models for spatial point processes, with advances in modelling, computation and applications in biological contexts. Chapter 2 describes and develops models for spatial point processes in which the point outcomes are latent, where indirect observations related to the point outcomes are available, and in which the underlying spatial intensity functions are typically highly heterogenous. Spatial intensities of inhomogeneous Poisson processes are represented via flexible nonparametric Bayesian mixture models. Computational approaches are presented for this new class of spatial point process mixtures and extended to the context of unobserved point process outcomes. Two examples drawn from a central, motivating context, that of immunofluorescence histology analysis in biological studies generating high-resolution imaging data, demonstrate the modelling approach and computational methodology. Chapters 3 and 4 extend this framework to define a class of flexible Bayesian nonparametric models for inhomogeneous spatio-temporal point processes, adding dynamic models for underlying intensity patterns. Dependent Dirichlet process mixture models are introduced as core components of this new time-varying spatial model. Utilizing such nonparametric mixture models for the spatial process intensity functions allows the introduction of time variation via dynamic, state-space models for parameters characterizing the intensities. Bayesian inference and model-fitting is addressed via novel particle filtering ideas and methods. Illustrative simulation examples include studies in problems of extended target tracking and substantive data analysis in cell fluorescent microscopic imaging tracking problems.</p><p>The second part of the thesis, consisting of chapters 5 and chapter 6, concerns advances in computational methods for some core and generic Bayesian inferential problems. Chapter 5 develops a novel approach to estimation of upper and lower bounds for marginal likelihoods in Bayesian modelling using refinements of existing variational methods. Traditional variational approaches only provide lower bound estimation; this new lower/upper bound analysis is able to provide accurate and tight bounds in many problems, so facilitates more reliable computation for Bayesian model comparison while also providing a way to assess adequacy of variational densities as approximations to exact, intractable posteriors. The advances also include demonstration of the significant improvements that may be achieved in marginal likelihood estimation by marginalizing some parameters in the model. A distinct contribution to Bayesian computation is covered in Chapter 6. This concerns a generic framework for designing adaptive MCMC algorithms, emphasizing the adaptive Metropolized independence sampler and an effective adaptation strategy using a family of mixture distribution proposals. This work is coupled with development of a novel adaptive approach to computation in nonparametric modelling with large data sets; here a sequential learning approach is defined that iteratively utilizes smaller data subsets. Under the general framework of importance sampling based marginal likelihood computation, the proposed adaptive Monte Carlo method and sequential learning approach can facilitate improved accuracy in marginal likelihood computation. The approaches are exemplified in studies of both synthetic data examples, and in a real data analysis arising in astro-statistics.</p><p>Finally, chapter 7 summarizes the dissertation and discusses possible extensions of the specific modelling and computational innovations, as well as potential future work.</p> / Dissertation

The use of spatial statistics to investigate ecological processes in plant communities is becoming increasingly widespread. In diverse communities such as tropical rainforests, analysis of spatial structure may help to unravel the various processes that act and interact to maintain high levels of diversity. In particular, a number of contrasting mechanisms have been suggested to explain species coexistence, and these differ greatly in their practical implications for the ecology and conservation of tropical forests. Traditional first-order measures of community structure have proved unable to distinguish these mechanisms in practice, but statistics that describe spatial structure may be able to do so. This is of great interest and relevance as spatially explicit data become available for a range of ecological communities and analysis methods for these data become more accessible. This thesis investigates the potential for inference about underlying ecological processes in plant communities using spatial statistics. Current methodologies for spatial analysis are reviewed and extended, and are used to characterise the spatial signals of the principal theorised mechanisms of coexistence. The sensitivity of a range of spatial statistics to these signals is assessed, and the strength of such signals in natural communities is investigated. The spatial signals of the processes considered here are found to be strong and robust to modelled stochastic variation. Several new and existing spatial statistics are found to be sensitive to these signals, and offer great promise for inference about underlying processes from empirical data. The relative strengths of particular processes are found to vary between natural communities, with any one theory being insufficient to explain observed patterns. This thesis extends both understanding of species coexistence in diverse plant communities and the methodology for assessing underlying process in particular cases. It demonstrates that the potential of spatial statistics in ecology is great and largely unexplored.

Remediation of unexploded ordnance (UXO) and prioritization of excavation procedures for archaeological artifacts using electromagnetic (EM) induction are studied in this dissertation. Lowering of the false alarm rates that require excavation and artifact excavation prioritization can reduce the costs associated with unnecessary procedures. Data were taken over 5 areas at the San Jacinto Battleground near Houston, Texas, using an EM-63 metal detection instrument. The areas were selected using the archaeological concepts of cultural and natural formation processes applied to what is thought to be areas that were involved in the 1836 Battle of San Jacinto. Innovative use of a Statistical Point Pattern Analysis (PPA) is employed to identify clustering of EM anomalies. The K-function uses point {x,y} data to look for possible clusters in relation to other points in the data set. The clusters once identified using K-function will be further examined for classification and prioritization using the Weighted K-function. The Weighted K-function uses a third variable such as millivolt values or time decay to aid in segregation and prioritization of anomalies present. Once the anomalies of interest are identified, their locations are determined using the Gi-Statistics Technique. The Gi*-Statistic uses the individual Cartesian{x, y} points as origin locations to establish a range of distances to other cluster points in the data set. The segregation and location of anomalies supplied by this analysis will have several benefits. Prioritization of excavations will narrow down what areas should be excavated first. Anomalies of interest can be located to guide excavation procedures within the areas surveyed. Knowing what anomalies are of greater importance than others will help to lower false alarm rates for UXO remediation or for archaeological artifact selection. Knowing significant anomaly location will reduce the number of excavations which will subsequently save time and money. The procedures and analyses presented here are an interdisciplinary compilation of geophysics, archaeology and statistical analysis brought together for the first time to examine problems associated with UXO remediation as well as archaeological artifact selection at historic battlegrounds using electromagnetic data.

[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] This thesis is a new proposal for analysing spatial point patterns in spatial statistics using the outputs of popular techniques of (classical, non-spatial, multivariate) cluster analysis. The outputs of a chosen hierarchical algorithm, named fusion distances, are applied to investigate important spatial characteristics of a given point pattern. The fusion distances may be regarded as a missing link between the fields of spatial statistics and multivariate cluster analysis. Up to now, these two fields have remained rather separate because of fundamental differences in approach. It is shown that fusion distances are very good at discriminating different types of spatial point patterns. A detailed study on the power of the Monte Carlo test under the null hypothesis of Complete Spatial Randomness (the benchmark of spatial statistics) against chosen alternative models is also conducted. For instance, the test (based on the fusion distance) is very powerful for some arbitrary values of the parameters of the alternative. A new general approach is developed for analysing a given point pattern using several graphical techniques for exploratory data analysis and inference. The new strategy is applied to univariate and multivariate point patterns. A new extension of a popular strategy in spatial statistics, named the analysis of the local configuration, is also developed. This new extension uses the fusion distances, and analyses a localised neighbourhood of a given point of the point pattern. New spatial summary function and statistics, named the fusion distance function H(t), area statistic A, statistic S, and spatial Rg index, are introduced, and proven to be useful tools for identifying relevant features of spatial point patterns. In conclusion, the new methodology using the outputs of hierarchical clustering algorithms can be considered as an essential complement to the existing approaches in spatial statistics literature.

An important prerequisite for running a successful insurance business is to predict risk. By forecasting the future in as much detail as possible, competitive advantages are created in terms of price differentiation. This work aims at using spatial point processes to provide a proposal for how the geographical position of the customer can be used in developing risk differentiation tools. For spatial variation in claim frequency an approach is presented which is common in spatial epidemiology by considering a group of policyholders, with and without claims, as a realisation of a multivariate Poisson point process in two dimensions. Claim costs are then included by considering the claims as a realisation of a point process with continuous marks. To describe the spatial variation in relative risk, demographic and socio-economic information from Swedish agencies have been used. The insurance data that have been used come from the insurance company If Skadeförsäkring AB, where also the work has been carried out. The result demonstrates problems with parametric modelling of the intensity of policyholders, which makes it difficult to validate the spatial varying intensity of claim frequency. Therefore different proposals of non-parametric estimation are discussed. Further, there are no tendencies that the selected information is able to explain the variation in claim costs. / En viktig förutsättning för att kunna bedriva en framgångsrik försäkringsverksamhet är att prediktera risk. Genom att på en så detaljerad nivå som möjligt kunna förutse framtiden skapas konkurrensfördelar i form av prisdifferentiering. Målet med detta arbete är att med hjälp av spatiala punktprocesser ge ett förslag på hur kunders geografiska position kan utvecklas som riskdifferentieringsverktyg. För spatial variation i skadefrekvens presenteras ett tillvägagångssätt som är vanligt inom spatial epidemiologi genom att betrakta en grupp försäkringstagare, med och utan skador, som en realisering av en multivariat Poissonprocess i två dimensioner. Skadekostnaderna inkluderas sedan genom att betrakta skadorna som en punktprocess med kontinuerliga märken. För att beskriva spatial variation i relativ risk används demografisk och socioekonomisk information från svenska myndigheter. De försäkringsdata som använts kommer från If Skadeförsäkring AB, där också arbetet har utförts. Resultatet påvisar problem med att parametriskt modellera intensiteten för försäkringstagare, vilket medför svårigheter att validera den skattade spatiala variationen i skadefrekvens, varför olika ickeparametriska förslag diskuteras. Vidare upptäcktes inga tendenser till att variationen i skadekostnad kan förklaras med den utvalda informationen.