Selected Challenges From Spatial Statistics For Spatial Econometricians

Griffith and Paelinck (2011) present selected non-standard spatial statistics and spatial econometrics topics that address issues associated with spatial econometric methodology. This paper addresses the following challenges posed by spatial autocorrelation alluded to and/or derived from the spatial statistics topics of this book: the Gaussian random variable Jacobian term for massive datasets; topological features of georeferenced data; eigenvector spatial filtering-based georeferenced data generating mechanisms; and, interpreting random effects.Artykuł prezentuje wybrane, niestandardowe statystyki przestrzenne oraz zagadnienia ekonometrii przestrzennej. Rozważania teoretyczne koncentrują się na wyzwaniach wynikających z autokorelacji przestrzennej, nawiązując do pojęć Gaussowskiej zmiennej losowej, topologicznych cech danych georeferencyjnych, wektorów własnych, filtrów przestrzennych, georeferencyjnych mechanizmów generowania danych oraz interpretacji efektów losowych

Detection algorithms for spatial data

This dissertation addresses the problem of anomaly detection in spatial data. The problem of landmine detection in airborne spatial data is chosen as the specific detection scenario. The first part of the dissertation deals with the development of a fast algorithm for kernel-based non-linear anomaly detection in the airborne spatial data. The original Kernel RX algorithm, proposed by Kwon et al. [2005a], suffers from the problem of high computational complexity, and has seen limited application. With the aim to reduce the computational complexity, a reformulated version of the Kernel RX, termed the Spatially Weighted Kernel RX (SW-KRX), is presented. It is shown that under this reformulation, the detector statistics can be obtained directly as a function of the centered kernel Gram matrix. Subsequently, a methodology for the fast computation of the centered kernel Gram matrix is proposed. The key idea behind the proposed methodology is to decompose the set of image pixels into clusters, and expediting the computations by approximating the effect of each cluster as a whole. The SW-KRX algorithm is implemented for a special case, and comparative results are compiled for the SW-KRX vis-à-vis the RX anomaly detector. In the second part of the dissertation, a detection methodology for buried mine detection is presented. The methodology is based on extraction of color texture information using cross-co-occurrence features. A feature selection methodology based on Bhattacharya coefficients and principal feature analysis is proposed and detection results with different feature-based detectors are presented, to demonstrate the effectiveness of the proposed methodology in the extraction of useful discriminatory information --Abstract, page iii

Representation of features as images with neighborhood dependencies for compatibility with convolutional neural networks

Deep learning with Convolutional Neural Networks has shown great promise in image-based classification and enhancement but is often unsuitable for predictive modeling using features without spatial correlations. We present a feature representation approach termed REFINED (REpresentation of Features as Images with NEighborhood Dependencies) to arrange high-dimensional vectors in a compact image form conducible for CNN-based deep learning. We consider the similarities between features to generate a concise feature map in the form of a two-dimensional image by minimizing the pairwise distance values following a Bayesian Metric Multidimensional Scaling Approach. We hypothesize that this approach enables embedded feature extraction and, integrated with CNN-based deep learning, can boost the predictive accuracy. We illustrate the superior predictive capabilities of the proposed fra- mework as compared to state-of-the-art methodologies in drug sensitivity prediction scenarios using synthetic datasets, drug chemical descriptors as predictors from NCI60, and both transcriptomic information and drug descriptors as predictors from GDSC

On Issues of Scale and Dependence in Spatial and Spatio-Temporal Data

Recent years have seen a massive increase in the availability of spatial and spatio-temporal datasets. With these data comes a set of practical challenges, especially when researchers use spatial statistical models to generate predictions or synthesize datasets with differing spatial resolutions. At the basis of these models lies the notion of spatial scale which, for a stationary and isotropic covariance, is quantified through a range parameter which captures the distance at which observations are considered independent in space. In this dissertation, we propose a set of statistical methods to investigate issues related to spatial scale, with the goal of providing a better characterization of the dependence structure of a spatial process. These methods are used to generate improved predictions and to generate estimates at the needed spatial resolution. Furthermore, several of the proposed methods account for the sampling mechanism of the data, whether they are derived through surveys or from non-probabilistic samples such as electronic health records (EHRs). In Chapter 2, building upon the Multi-resolution Approximation (M-RA) for large spatial data (Katzfuss, 2017), and leveraging the relationship between levels of the M-RA and the scale of a spatial process, we develop a Bayesian hierarchical model that explores and accommodates non-stationarity in spatial processes. In contrast to existing tests for global non-stationarity, our model can detect regions of local stationarity by specifying a mixture of multivariate normal priors on the basis function weights of the M-RA. Furthermore, our model outperforms other standard spatial statistical models in terms of out-of-sample prediction. In Chapter 3, we present a model for disaggregating to a fine spatio-temporal resolution estimates of proportions derived from the American Community Survey (ACS). We envision that disaggregated estimates will be better proxies of neighborhood exposure than the ACS estimates, which are resolved at either a fine spatial resolution and coarse temporal scale, or at a coarse spatial resolution and fine temporal scale. By characterizing the data as an aggregation of an underlying point-referenced process, we disaggregate the ACS estimates to the 1-year census tract resolution. Crucial to our methodological development is the incorporation of the survey’s design effect. A secondary development is a spatio-temporal version of the M-RA. In Chapter 4, we extend the disaggregation model of the previous chapter to accommodate estimates of count-valued characteristics. This chapter contains a comparison to the model of Bradley et al. (2016) (the BWH model), which addresses a similar problem for purely spatial data. In addition to accommodating spatio-temporal data, our model differs from the BWH model by incorporating the survey design effect into the model specification. We find that our model outperforms the BWH model in terms of prediction accuracy and coverage probability. In Chapter 5, we address the issue of sampling bias in EHR data, which can arise in studies of the association between disease and exposure when both the outcome variable and the exposure process are related to the sampling mechanism. Our method jointly models EHR and publicly available data to approximate sampling probabilities, which are then used to derive sampling weights. We show via simulation studies that we can recover data generating sampling probabilities and reduce bias compared to a naive analysis. To illustrate the utility of our model with clinical data, we present an analysis of smoking and lung cancer using subjects in the Michigan Genomics Initiative.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/153375/1/benedetm_2.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153375/2/benedetm_1.pd

High-performance solutions of geographically weighted regression in R

As an established spatial analytical tool, Geographically Weighted Regression (GWR) has been applied across a variety of disciplines. However, its usage can be challenging for large datasets, which are increasingly prevalent in today’s digital world. In this study, we propose two high-performance R solutions for GWR via Multi-core Parallel (MP) and Compute Unified Device Architecture (CUDA) techniques, respectively GWR-MP and GWR-CUDA. We compared GWR-MP and GWR-CUDA with three existing solutions available in Geographically Weighted Models (GWmodel), Multi-scale GWR (MGWR) and Fast GWR (FastGWR). Results showed that all five solutions perform differently across varying sample sizes, with no single solution a clear winner in terms of computational efficiency. Specifically, solutions given in GWmodel and MGWR provided acceptable computational costs for GWR studies with a relatively small sample size. For a large sample size, GWR-MP and FastGWR provided coherent solutions on a Personal Computer (PC) with a common multi-core configuration, GWR-MP provided more efficient computing capacity for each core or thread than FastGWR. For cases when the sample size was very large, and for these cases only, GWR-CUDA provided the most efficient solution, but should note its I/O cost with small samples. In summary, GWR-MP and GWR-CUDA provided complementary high-performance R solutions to existing ones, where for certain data-rich GWR studies, they should be preferred

Towards Predictive Rendering in Virtual Reality

The strive for generating predictive images, i.e., images representing radiometrically correct renditions of reality, has been a longstanding problem in computer graphics. The exactness of such images is extremely important for Virtual Reality applications like Virtual Prototyping, where users need to make decisions impacting large investments based on the simulated images. Unfortunately, generation of predictive imagery is still an unsolved problem due to manifold reasons, especially if real-time restrictions apply. First, existing scenes used for rendering are not modeled accurately enough to create predictive images. Second, even with huge computational efforts existing rendering algorithms are not able to produce radiometrically correct images. Third, current display devices need to convert rendered images into some low-dimensional color space, which prohibits display of radiometrically correct images. Overcoming these limitations is the focus of current state-of-the-art research. This thesis also contributes to this task. First, it briefly introduces the necessary background and identifies the steps required for real-time predictive image generation. Then, existing techniques targeting these steps are presented and their limitations are pointed out. To solve some of the remaining problems, novel techniques are proposed. They cover various steps in the predictive image generation process, ranging from accurate scene modeling over efficient data representation to high-quality, real-time rendering. A special focus of this thesis lays on real-time generation of predictive images using bidirectional texture functions (BTFs), i.e., very accurate representations for spatially varying surface materials. The techniques proposed by this thesis enable efficient handling of BTFs by compressing the huge amount of data contained in this material representation, applying them to geometric surfaces using texture and BTF synthesis techniques, and rendering BTF covered objects in real-time. Further approaches proposed in this thesis target inclusion of real-time global illumination effects or more efficient rendering using novel level-of-detail representations for geometric objects. Finally, this thesis assesses the rendering quality achievable with BTF materials, indicating a significant increase in realism but also confirming the remainder of problems to be solved to achieve truly predictive image generation

Non-decimated wavelet transform in statistical assessment of scaling: Theory and applications

In this thesis, we introduced four novel methods that facilitate the scaling estimation based on NDWT. Chapter 2 introduced an NDWT matrix which is used to perform an NDWT in one or two dimensions. The use of matrix significantly decreased the computation time when 2-D inputs of moderate size are transformed under MATLAB environment, and such reduction of computation time was augmented when the same type of NDWT is performed repeatedly. With 2-D inputs, an NDWT matrix yielded a scale-mixing NDWT, which is more compressive than the standard 2-D NDWT. The retrieval of an original signal after the transform was possible with a weight matrix. An NDWT matrix can handle signals of non-dyadic sizes in one or two dimensions. The proposed NDWT matrix was used for the transforms in Chapters 3-5. Chapter 3 introduced a method for scaling estimation based on a non-decimated wavelet spectrum. A distinctive feature of NDWT, redundancy, enables us to obtain local spectra and improves the accuracy of scaling estimation. For simulated signals with known $H$ values, the method yields estimators of $H$ with lower mean squared errors. We characterized mammographic images with the proposed scaling estimator and anisotropy measures from non-decimated wavelet spectra for breast cancer detection, and obtained the best diagnostic accuracy in excess of 80\%. Some real-life signals are known to possess a theoretical value of the Hurst exponent. Chapter 4 described a Bayesian scaling estimation method that utilizes the value of a theoretical scaling index as a mean of prior distribution and estimates $H$ with MAP estimation. The accuracy of estimators from the proposed method is robust to small misspecification of the prior mean. We applied the method to a turbulence velocity signal and yielded an estimator of $H$ close to the theoretical value. Chapter 5 proposed two methods based on NDWT for robust estimation of Hurst exponent $H$ of 1-D self-similar signals. The redundancy of NDWT, which improved the accuracy of estimation, introduced autocorrelations within the wavelet coefficients. With the two proposed methods, we alleviated the autocorrelation in three ways: taking the logarithm prior to taking the median, relating Hurst exponent to the median instead of mean of the model distribution, and resampling the coefficients.Ph.D

Glosarium Matematika

273 p.; 24 cm