# Modelling spine locations on dendrite trees using inhomogeneous Cox point processes

Spatial Statistics

Published On 2020/10/1

Dendritic spines, which are small protrusions on the dendrites of a neuron, are of interest in neuroscience as they are related to cognitive processes such as learning and memory. We analyse the distribution of spine locations on six different dendrite trees from mouse neurons using point process theory for linear networks. Besides some possible small-scale repulsion, we find that two of the spine point pattern data sets may be described by inhomogeneous Poisson process models, while the other point pattern data sets exhibit clustering between spines at a larger scale. To model this we propose an inhomogeneous Cox process model constructed by thinning a Poisson process on a linear network with retention probabilities determined by a spatially correlated random field. For model checking we consider network analogues of the empirical F-, G-, and J-functions originally introduced for inhomogeneous point …

Journal

Spatial Statistics

Published On

2020/10/1

Volume

39

Page

100478

## Authors

#### Jesper Møller

##### Aalborg Universitet

Position

Professor in Statistics

H-Index(all)

46

H-Index(since 2020)

23

I-10 Index(all)

0

I-10 Index(since 2020)

0

Citation(all)

0

Citation(since 2020)

0

Cited By

0

Research Interests

Mathematical Statistics

Probability Theory

University Profile Page

### Other Articles from authors

Jesper Møller

Aalborg Universitet

arXiv preprint arXiv:2404.09525

##### Coupling results and Markovian structures for number representations of continuous random variables

A general setting for nested subdivisions of a bounded real set into intervals defining the digits of a random variable with a probability density function is considered. Under the weak condition that is almost everywhere lower semi-continuous, a coupling between and a non-negative integer-valued random variable is established so that have an interpretation as the ``sufficient digits'', since the distribution of conditioned on does not depend on . Adding a condition about a Markovian structure of the lengths of the intervals in the nested subdivisions, becomes a Markov chain of a certain order . If then are IID with a known distribution. When and the Markov chain is uniformly geometric ergodic, a coupling is established between and a random time so that the chain after time is stationary and follows a simple known distribution. The results are related to several examples of number representations generated by a dynamical system, including base- expansions, generalized L\"uroth series, -expansions, and continued fraction representations. The importance of the results and some suggestions and open problems for future research are discussed.

*2024/4/15*

Jesper Møller

Aalborg Universitet

arXiv preprint arXiv:2404.08387

##### The asymptotic distribution of the scaled remainder for pseudo golden ratio expansions of a continuous random variable

Let be the base- expansion of a continuous random variable on the unit interval where is the positive solution to for an integer (i.e., is a generalization of the golden mean for which ). We study the asymptotic distribution and convergence rate of the scaled remainder when tends to infinity.

*2024/4/12*

Jesper Møller

Aalborg Universitet

Methodology and Computing in Applied Probability

##### How many digits are needed?

Let be the digits in the base-q expansion of a random variable X defined on [0, 1) where is an integer. For , we study the probability distribution of the (scaled) remainder : If X has an absolutely continuous CDF then converges in the total variation metric to the Lebesgue measure on the unit interval. Under weak smoothness conditions we establish first a coupling between X and a non-negative integer valued random variable N so that follows and is independent of , and second exponentially fast convergence of and its PDF . We discuss how many digits are needed and show examples of our results.

*2024/3*

Jesper Møller

Aalborg Universitet

arXiv preprint arXiv:2312.09652

##### The asymptotic distribution of the remainder in a certain base- expansion

Let be the base- expansion of a continuous random variable on the unit interval where is the golden ratio. We study the asymptotic distribution and convergence rate of the scaled remainder when tends to infinity.

*2023/12/15*

Jesper Møller

Aalborg Universitet

Proceedings of the London Mathematical Society

##### Realizability and tameness of fusion systems

A saturated fusion system over a finite p$p$‐group S$S$ is a category whose objects are the subgroups of S$S$ and whose morphisms are injective homomorphisms between the subgroups satisfying certain axioms. A fusion system over S$S$ is realized by a finite group G$G$ if S$S$ is a Sylow p$p$‐subgroup of G$G$ and morphisms in the category are those induced by conjugation in G$G$. One recurrent question in this subject is to find criteria as to whether a given saturated fusion system is realizable or not. One main result in this paper is that a saturated fusion system is realizable if all of its components (in the sense of Aschbacher) are realizable. Another result is that all realizable fusion systems are tame: a finer condition on realizable fusion systems that involves describing automorphisms of a fusion system in terms of those of some group that realizes it. Stated in this way, these results depend on the …

*2023/12*

Jesper Møller

Aalborg Universitet

ACM Transactions on Spatial Algorithms and Systems

##### Stochastic Routing with Arrival Windows

Arriving at a destination within a specific time window is important in many transportation settings. For example, trucks may be penalized for early or late arrivals at compact terminals, and early and late arrivals at general practitioners, dentists, and so on, are also discouraged, in part due to COVID. We propose foundations for routing with arrival-window constraints. In a setting where the travel time of a road segment is modeled by a probability distribution, we define two problems where the aim is to find a route from a source to a destination that optimizes or yields a high probability of arriving within a time window while departing as late as possible. In this setting, a core challenge is to enable comparison between paths that may potentially be part of a result path with the goal of determining whether a path is uninteresting and can be disregarded given the existence of another path. We show that existing solutions …

*2023/11/21*

Jesper Møller

Aalborg Universitet

Spatial Statistics

##### Fitting the grain orientation distribution of a polycrystalline material conditioned on a Laguerre tessellation

The description of distributions related to grain microstructure helps physicists to understand the processes in materials and their properties. This paper presents a general statistical methodology for the analysis of crystallographic orientations of grains in a 3D Laguerre tessellation dataset which represents the microstructure of a polycrystalline material. We introduce complex stochastic models which may substitute expensive laboratory experiments: conditional on the Laguerre tessellation, we suggest interaction models for the distribution of cubic crystal lattice orientations, where the interaction is between pairs of orientations for neighbouring grains in the tessellation. We discuss parameter estimation and model comparison methods based on maximum pseudolikelihood as well as graphical procedures for model checking using simulations. Our methodology is applied for analysing a dataset representing a nickel …

*2023/6/1*

Jesper Møller

Aalborg Universitet

Methodology and Computing in Applied Probability

##### Singular distribution functions for random variables with stationary digits

Let F be the cumulative distribution function (CDF) of the base-q expansion , where is an integer and is a stationary stochastic process with state space . In a previous paper we characterized the absolutely continuous and the discrete components of F. In this paper we study special cases of models, including stationary Markov chains of any order and stationary renewal point processes, where we establish a law of pure types: F is then either a uniform or a singular CDF on [0, 1]. Moreover, we study mixtures of such models. In most cases expressions and plots of F are given.

*2023/3*

Jesper Møller

Aalborg Universitet

arXiv preprint arXiv:2212.08402

##### Cox processes driven by transformed Gaussian processes on linear networks

There is a lack of point process models on linear networks. For an arbitrary linear network, we use isotropic covariance functions with respect to the geodesic metric or the resistance metric to construct new models for isotropic Gaussian processes and hence new models for various Cox processes with isotropic pair correlation functions. In particular we introduce three model classes given by log Gaussian, interrupted, and permanental Cox processes on linear networks, and consider for the first time statistical procedures and applications for parametric families of such models. Moreover, we construct new simulation algorithms for Gaussian processes on linear networks and discuss whether the geodesic metric or the resistance metric should be used for the kind of Cox processes studied in this paper.

*2022/12/16*

Jesper Møller

Aalborg Universitet

Stat

##### Determinantal shot noise Cox processes

We present a new class of cluster point process models, which we call determinantal shot noise Cox processes (DSNCP), with repulsion between cluster centres. They are the special case of generalized shot noise Cox processes where the cluster centres are determinantal point processes. We establish various moment results and describe how these can be used to easily estimate unknown parameters in two particularly tractable cases, namely, when the offspring density is isotropic Gaussian and the kernel of the determinantal point process of cluster centres is Gaussian or like in a scaled Ginibre point process. Through a simulation study and the analysis of a real point pattern data set, we see that when modelling clustered point patterns, a much lower intensity of cluster centres may be needed in DSNCP models as compared to shot noise Cox processes.

*2022/12*

Jesper Møller

Aalborg Universitet

International Statistical Review

##### Should we condition on the number of points when modelling spatial point patterns?

We discuss the practice of directly or indirectly assuming a model for the number of points when modelling spatial point patterns even though it is rarely possible to validate such a model in practice because most point pattern data consist of only one pattern. We therefore explore the possibility to condition on the number of points instead when fitting and validating spatial point process models. In a simulation study with different popular spatial point process models, we consider model validation using global envelope tests based on functional summary statistics. We find that conditioning on the number of points will for some functional summary statistics lead to more narrow envelopes and thus stronger tests and that it can also be useful for correcting for some conservativeness in the tests when testing composite hypothesis. However, for other functional summary statistics, it makes little or no difference to condition …

*2022/12*

Jesper Møller

Aalborg Universitet

Journal of Applied Probability

##### Characterization of random variables with stationary digits

Let be an integer, a stochastic process with state space , and F the cumulative distribution function (CDF) of . We show that stationarity of is equivalent to a functional equation obeyed by F, and use this to characterize the characteristic function of X and the structure of F in terms of its Lebesgue decomposition. More precisely, while the absolutely continuous component of F can only be the uniform distribution on the unit interval, its discrete component can only be a countable convex combination of certain explicitly computable CDFs for probability distributions with finite support. We also show that is a Rajchman measure if and only if F is the uniform CDF on [0, 1].

*2022/12*

Jesper Møller

Aalborg Universitet

Spatial Statistics

##### Fitting three-dimensional Laguerre tessellations by hierarchical marked point process models

We present a general statistical methodology for analysing a Laguerre tessellation data set viewed as a realization of a marked point process model. In the first step, for the points, we use a nested sequence of multiscale processes which constitute a flexible parametric class of pairwise interaction point process models. In the second step, for the marks/radii conditioned on the points, we consider various exponential family models where the canonical sufficient statistic is based on tessellation characteristics. For each step, parameter estimation based on maximum pseudolikelihood methods is tractable. For model selection, we consider maximized log pseudolikelihood functions for models of the radii conditioned on the points. Model checking is performed using global envelopes and corresponding tests in both steps and moreover by comparing observed and simulated tessellation characteristics in the second step …

*2022/10/1*

Jesper Møller

Aalborg Universitet

Translational psychiatry

##### Layer III pyramidal cells in the prefrontal cortex reveal morphological changes in subjects with depression, schizophrenia, and suicide

Brodmann Area 46 (BA46) has long been regarded as a hotspot of disease pathology in individuals with schizophrenia (SCH) and major depressive disorder (MDD). Pyramidal neurons in layer III of the Brodmann Area 46 (BA46) project to other cortical regions and play a fundamental role in corticocortical and thalamocortical circuits. The AutoCUTS-LM pipeline was used to study the 3-dimensional structural morphology and spatial organization of pyramidal cells. Using quantitative light microscopy, we used stereology to calculate the entire volume of layer III in BA46 and the total number and density of pyramidal cells. Volume tensors estimated by the planar rotator quantified the volume, shape, and nucleus displacement of pyramidal cells. All of these assessments were carried out in four groups of subjects: controls (C, n = 10), SCH (n = 10), MDD (n = 8), and suicide subjects with a history of depression (SU …

*2022/9/5*

Jesper Møller

Aalborg Universitet

Graphs and Combinatorics

##### Equivariant Euler characteristics of symplectic buildings

We compute the equivariant Euler characteristics of the buildings for the symplectic groups over finite fields.

*2022/6*

Jesper Møller

Aalborg Universitet

Journal of Computational and Graphical Statistics

##### MCMC computations for Bayesian mixture models using repulsive point processes

Repulsive mixture models have recently gained popularity for Bayesian cluster detection. Compared to more traditional mixture models, repulsive mixture models produce a smaller number of well-separated clusters. The most commonly used methods for posterior inference either require to fix a priori the number of components or are based on reversible jump MCMC computation. We present a general framework for mixture models, when the prior of the “cluster centers” is a finite repulsive point process depending on a hyperparameter, specified by a density which may depend on an intractable normalizing constant. By investigating the posterior characterization of this class of mixture models, we derive a MCMC algorithm which avoids the well-known difficulties associated to reversible jump MCMC computation. In particular, we use an ancillary variable method, which eliminates the problem of having intractable …

*2022/4/3*

Jesper Møller

Aalborg Universitet

Scandinavian Journal of Statistics

##### Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation

In this article, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not expressible in closed form but it is easy to simulate realizations under the model. We therefore explain how to use approximate Bayesian computation (ABC) to carry out statistical inference for this model. We suggest a method for model validation based on posterior predictions and global envelopes. We illustrate the ABC procedure and model validation approach using both simulated point patterns and a real data example.

*2022/3*

Jesper Møller

Aalborg Universitet

Communications Biology

##### Cellular 3D-reconstruction and analysis in the human cerebral cortex using automatic serial sections

Techniques involving three-dimensional (3D) tissue structure reconstruction and analysis provide a better understanding of changes in molecules and function. We have developed AutoCUTS-LM, an automated system that allows the latest advances in 3D tissue reconstruction and cellular analysis developments using light microscopy on various tissues, including archived tissue. The workflow in this paper involved advanced tissue sampling methods of the human cerebral cortex, an automated serial section collection system, digital tissue library, cell detection using convolution neural network, 3D cell reconstruction, and advanced analysis. Our results demonstrated the detailed structure of pyramidal cells (number, volume, diameter, sphericity and orientation) and their 3D spatial organization are arranged in a columnar structure. The pipeline of these combined techniques provides a detailed analysis of tissues …

*2021/9/2*

Jesper Møller

Aalborg Universitet

AMERICAN MATHEMATICAL SOCIETY

##### THE NUMBER OF p-ELEMENTS IN FINITE GROUPS OF LIE TYPE OF CHARACTERISTIC p

The combinatorics of the poset of p-radical p-subgroups of a finite group is used to count the number of p-elements.

*2021/7/1*

### Other articles from Spatial Statistics journal

Peng Wu

Curtin University

Spatial Statistics

##### Robust interaction detector: A case of road life expectancy analysis

Spatial stratified heterogeneity, revealing the disparity mechanisms across spatial strata, can be effectively quantified using the geographical detector (GD). GD requires reasonable spatial discretization strategies to investigate the spatial association between the target variable and numerical independent variables. In previous studies, the Robust Geographical Detector (RGD) optimized spatial strata for examining the power of determinants (PD) of individual variables, which demonstrate more robust spatial discretization than other models. However, the GD's interaction detector that explores PD of the interaction of two variables still needs to be enhanced by the robust spatial discretization. This study develops a Robust Interaction Detector (RID), an improved interaction detector, using change detection algorithms for the robust spatial stratified heterogeneity analysis with multiple explanatory variables. RID is …

*2024/3/1*

Vinicius Diniz Mayrink

Universidade Federal de Minas Gerais

Spatial Statistics

##### Spatial Functional Data analysis: Irregular spacing and Bernstein polynomials

Spatial Functional Data (SFD) analysis is an emerging statistical framework that combines Functional Data Analysis (FDA) and spatial dependency modeling. Unlike traditional statistical methods, which treat data as scalar values or vectors, SFD considers data as continuous functions, allowing for a more comprehensive understanding of their behavior and variability. This approach is well-suited for analyzing data collected over time, space, or any other continuous domain. SFD has found applications in various fields, including economics, finance, medicine, environmental science, and engineering. This study proposes new functional Gaussian models incorporating spatial dependence structures, focusing on irregularly spaced data and reflecting spatially correlated curves. The model is based on Bernstein polynomial (BP) basis functions and utilizes a Bayesian approach for estimating unknown quantities and …

*2024/4/1*

Gyuwon Lee

Kyungpook National University

Spatial Statistics

##### Spatial classification in the presence of measurement error

In recent decades, spatial classification has received considerable attention in a wide array of disciplines. In practice, binary response variable is often subject to measurement error, misclassification. To account for the misclassified response in spatial classification, we proposed validation data-based adjustment methods that use interval validation data to rectify misclassified responses. Regression calibration and multiple imputation methods are utilized to correct the misclassified outcomes at the locations where the gold-standard device is not available. Generalized linear mixed model and indicator Kriging are applied for spatial classification at unsampled locations. Simulation studies are performed to compare the proposed methods with naive methods that ignore the misclassification. It was found that the proposed models significantly improve prediction accuracy. Additionally, the proposed models are applied …

*2024/3/1*

Fernando A. López-Hernández

Universidad Politécnica de Cartagena

Spatial Statistics

##### Searching for correct specification in spatial probit models. Classical approaches versus Gradient Boosting algorithm

Selecting correct specification in spatial model frameworks is a relevant research topic in spatial econometrics. The purpose of this paper is to examine and contrast two well-known model selection strategies, Specific-to-General, Stge, and General-to-Specific, Gets, in the context of spatial probit models. The results obtained from these classical methods are juxtaposed with those generated through the utilization of a powefull machine learning algorithm: Gradient Boosting. The paper includes an extensive Monte Carlo experiment to compare the performance of these three strategies with small and medium sample sizes. The results show that under ideal conditions, both classical strategies obtain similar results for medium-sized samples, but for small samples, Stge performs slightly better than Gets. The Gradient Boosting algorithm obtains slightly higher success rates than the classical strategies, especially with …

*2024/4/6*

Hiroshi Yamada

Hiroshima University

Spatial Statistics

##### Spatial Smoothing Using Graph Laplacian Penalized Filter

This paper considers a filter for smoothing spatial data. It can be used to smooth data on the vertices of arbitrary undirected graphs with arbitrary non-negative spatial weights. It consists of a quantity analogous to Geary’s c, which is one of the most prominent measures of spatial autocorrelation. In addition, the quantity can be represented by a matrix called the graph Laplacian in spectral graph theory. We show mathematically how spatial data becomes smoother as a parameter, called the smoothing parameter, increases from 0 and is fully smoothed as the parameter goes to infinity, except for the case where the spatial data is originally fully smoothed. We also illustrate the results numerically and apply the spatial filter to climatological/meteorological data. In addition, as supplementary investigations, we examine how the sum of squared residuals and the effective degrees of freedom vary with the smoothing …

*2024/1/17*

A.Erhan Tercan

Hacettepe Üniversitesi

Spatial Statistics

##### Copula-Based Data-Driven Multiple-Point Simulation Method

Multiple-point simulation is a commonly used method in modeling complex curvilinear structures. The method is based on the application of training images that are open to manipulation. The present study introduces a new data-driven multiple-point simulation method that derives multiple point statistics directly from sparse data using copulas and applies them in simulation of complex mineral deposits. This method is based on simplification of N-dimensional copulas by its underlying two-dimensional copulas and taking advantage of conditional independence assumption to integrate information from different sources. The method was compared to Filtersim, a conventional multiple-point geostatistical method, through two synthetic data sets. Reproduction of cumulative distribution function, variogram, N-point connectivity, and visual patterns were considered in comparison. The copula-based multiple-point …

*2024/3/1*

Duncan Lee

University of Glasgow

Spatial Statistics

##### Computationally efficient localised spatial smoothing of disease rates using anisotropic basis functions and penalised regression fitting

The spatial variation in population-level disease rates can be estimated from aggregated disease data relating to N areal units using Bayesian hierarchical models. Spatial autocorrelation in these data is captured by random effects that are assigned a Conditional autoregressive (CAR) prior, which assumes that neighbouring areal units exhibit similar disease rates. This approach ignores boundaries in the disease rate surface, which are locations where neighbouring units exhibit a step-change in their rates. CAR type models have been extended to account for this localised spatial smoothness, but they are computationally prohibitive for big data sets. Therefore this paper proposes a novel computationally efficient approach for localised spatial smoothing, which is motivated by a new study of mental ill health across N= 32,754 Lower Super Output Areas in England. The approach is based on a computationally …

*2024/3/1*

Joon Jin Song

Baylor University

Spatial Statistics

##### Spatial classification in the presence of measurement error

In recent decades, spatial classification has received considerable attention in a wide array of disciplines. In practice, binary response variable is often subject to measurement error, misclassification. To account for the misclassified response in spatial classification, we proposed validation data-based adjustment methods that use interval validation data to rectify misclassified responses. Regression calibration and multiple imputation methods are utilized to correct the misclassified outcomes at the locations where the gold-standard device is not available. Generalized linear mixed model and indicator Kriging are applied for spatial classification at unsampled locations. Simulation studies are performed to compare the proposed methods with naive methods that ignore the misclassification. It was found that the proposed models significantly improve prediction accuracy. Additionally, the proposed models are applied …

*2024/3/1*

Asrat Mekonnen Belachew

Universidade de São Paulo

Spatial Statistics

##### Bayesian spatio-temporal statistical modeling of violent-related fatality in western and central Africa

Fatality arising from violent events is a critical public health problem in Africa. Although numerous studies on crime and violent events have been conducted, adequate attention has not been given to the distribution of fatalities arising from these events. This study unraveled the spatio-temporal pattern of fatality from violent events in Western and Central Africa. A two-component spatio-temporal zero-inflated model on a continuous spatial domain within a Bayesian framework was adopted. The stochastic partial differential equation was used to quantify the continuous pattern and make projections in unsampled regions. Fatality data from 1997 to 2021 was obtained from the Armed Conflict Location and Event Data Project (ACLED). Findings from the result revealed a spatial and temporal divide in the prevalence of fatality in the study region. Between the years 1997 and 2010, fatality from violence was most prevalent …

*2024/4/1*

Thomas Kneib

Georg-August-Universität Göttingen

Spatial Statistics

##### A simplified spatial+ approach to mitigate spatial confounding in multivariate spatial areal models

Spatial areal models encounter the well-known and challenging problem of spatial confounding. This issue makes it arduous to distinguish between the impacts of observed covariates and spatial random effects. Despite previous research and various proposed methods to tackle this problem, finding a definitive solution remains elusive. In this paper, we propose a simplified version of the spatial+ approach that involves dividing the covariate into two components. One component captures large-scale spatial dependence, while the other accounts for short-scale dependence. This approach eliminates the need to separately fit spatial models for the covariates. We apply this method to analyse two forms of crimes against women, namely rapes and dowry deaths, in Uttar Pradesh, India, exploring their relationship with socio-demographic covariates. To evaluate the performance of the new approach, we conduct …

*2024/3/1*

Patrick E Brown

University of Toronto

Spatial Statistics

##### Profile likelihoods for parameters in trans-Gaussian geostatistical models

Profile likelihoods are rarely used in geostatistical models due to the computational burden imposed by repeated decompositions of large variance matrices. Accounting for uncertainty in covariance parameters can be highly consequential in geostatistical models as some covariance parameters are poorly identified, the problem is severe enough that the differentiability parameter of the Matern correlation function is typically treated as fixed. The problem is compounded with anisotropic spatial models as there are two additional parameters to consider. In this paper, we make the following contributions: Firstly, a methodology is created for profile likelihoods for Gaussian spatial models with Matérn family of correlation functions, including anisotropic models. This methodology adopts a novel reparameterization for generation of representative points, and uses GPUs for parallel profile likelihoods computation in software …

*2024/4/1*

Yongze Song

Curtin University

Spatial Statistics

##### Robust interaction detector: A case of road life expectancy analysis

Spatial stratified heterogeneity, revealing the disparity mechanisms across spatial strata, can be effectively quantified using the geographical detector (GD). GD requires reasonable spatial discretization strategies to investigate the spatial association between the target variable and numerical independent variables. In previous studies, the Robust Geographical Detector (RGD) optimized spatial strata for examining the power of determinants (PD) of individual variables, which demonstrate more robust spatial discretization than other models. However, the GD's interaction detector that explores PD of the interaction of two variables still needs to be enhanced by the robust spatial discretization. This study develops a Robust Interaction Detector (RID), an improved interaction detector, using change detection algorithms for the robust spatial stratified heterogeneity analysis with multiple explanatory variables. RID is …

*2024/3/1*

Francisco Louzada

Universidade de São Paulo

Spatial Statistics

##### Bayesian spatio-temporal statistical modeling of violent-related fatality in western and central Africa

Fatality arising from violent events is a critical public health problem in Africa. Although numerous studies on crime and violent events have been conducted, adequate attention has not been given to the distribution of fatalities arising from these events. This study unraveled the spatio-temporal pattern of fatality from violent events in Western and Central Africa. A two-component spatio-temporal zero-inflated model on a continuous spatial domain within a Bayesian framework was adopted. The stochastic partial differential equation was used to quantify the continuous pattern and make projections in unsampled regions. Fatality data from 1997 to 2021 was obtained from the Armed Conflict Location and Event Data Project (ACLED). Findings from the result revealed a spatial and temporal divide in the prevalence of fatality in the study region. Between the years 1997 and 2010, fatality from violence was most prevalent …

*2024/4/1*

Werner G. Müller

Johannes Kepler Universität Linz

Spatial Statistics

##### A criterion and incremental design construction for simultaneous kriging predictions

In this paper, we further investigate the problem of selecting a set of design points for universal kriging, which is a widely used technique for spatial data analysis. Our goal is to select the design points in order to make simultaneous predictions of the random variable of interest at a finite number of unsampled locations with maximum precision. Specifically, we consider as response a correlated random field given by a linear model with an unknown parameter vector and a spatial error correlation structure. We propose a new design criterion that aims at simultaneously minimizing the variation of the prediction errors at various points. We also present various efficient techniques for incrementally building designs for that criterion scaling well for high dimensions. Thus the method is particularly suitable for big data applications in areas of spatial data analysis such as mining, hydrogeology, natural resource monitoring …

*2024/3/1*

Philipp Otto

Leibniz Universität Hannover

Spatial Statistics

##### A multivariate spatial and spatiotemporal arch model

This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects, as they are usually present in geo-referenced data. Furthermore, spatial and temporal cross-variable effects in the conditional variance are explicitly modelled. We transform the model to a multivariate spatiotemporal autoregressive model using a log-squared transformation and derive a consistent quasi-maximum-likelihood estimator (QMLE). For finite samples and different error distributions, the performance of the QMLE is analysed in a series of Monte-Carlo simulations. In addition, we illustrate the practical usage of the new model with a real-world example. We analyse the monthly real-estate price returns for three different property types in Berlin from 2002 to 2014. We find weak (instantaneous …

*2024/4/2*

Dominic Schuhmacher

Georg-August-Universität Göttingen

Spatial Statistics

##### Graph convolutional networks for spatial interpolation of correlated data

Several deep learning methods for spatial data have been developed that report good performance in a big data setting. These methods typically require the choice of an appropriate kernel and some tuning of hyperparameters, which are contributing reasons for poor performance on smaller data sets. In this paper, we propose a mathematical construction of a graph-based neural network for spatial prediction that substantially generalizes the KCN model in [Appleby, Liu and Liu (2020). Kriging convolutional networks. In Proc. AAAI Conf. AI 34, pp. 3187–3194]. In particular, our model, referred to as SPONGE, allows for integrated learning of the convolutional kernel, admits higher order neighborhood structures and can make use of the distance between locations in the neighborhood and between labels of neighboring nodes. All of this yields higher flexibility in capturing spatial correlations. We investigate in …

*2024/4/1*

Mahmoud Torabi

University of Manitoba

Spatial Statistics

##### Analyzing COVID-19 data in the Canadian province of Manitoba: A new approach

The basic homogeneous SEIR (susceptible–exposed–infected–removed) model is a commonly used compartmental model for analysing infectious diseases such as influenza and COVID-19. However, in the homogeneous SEIR model, it is assumed that the population of study is homogeneous and, one cannot incorporate individual-level information (e.g., location of infected people, distance between susceptible and infected individuals, vaccination status) which may be important in predicting new disease cases. Recently, a geographically-dependent individual-level model (GD-ILM) within an SEIR framework was developed for when both regional and individual-level spatial data are available. In this paper, we propose to use an SEIR GD-ILM for each health region of Manitoba (central Canadian province) population to analyse the COVID-19 data. As different health regions of the population under study may act …

*2023/6/1*

Fabrizio Durante

Università del Salento

Spatial Statistics

##### Correlation-based hierarchical clustering of time series with spatial constraints

Correlation-based hierarchical clustering methods for time series typically are based on a suitable dissimilarity matrix derived from pairwise measures of association. Here, this dissimilarity is modified in order to take into account the presence of spatial constraints. This modification exploits the geometric structure of the space of correlation matrices, i.e. their Riemannian manifold. Specifically, the temporal correlation matrix (based on van der Waerden coefficient) is aggregated to the spatial correlation matrix (obtained from a suitable Matérn correlation function) via a geodesic in the Riemannian manifold. Our approach is presented and discussed using simulated and real data, highlighting its main advantages and computational aspects.

*2023/11/30*

Stephen Jun Villejo

University of the Philippines Los Baños

Spatial Statistics

##### Data fusion in a two-stage spatio-temporal model using the INLA-SPDE approach

This paper proposes a two-stage estimation approach for a spatial misalignment scenario that is motivated by the epidemiological problem of linking pollutant exposures and health outcomes. We use the integrated nested Laplace approximation method to estimate the parameters of a two-stage spatio-temporal model—the first stage models the exposures using data fusion while the second stage links the health outcomes to exposures. The first stage is based on the Bayesian melding model, which assumes a common latent field for the different data sources for the pollutants. The second stage fits a generalized linear mixed model using the spatial averages of the estimated latent field, and additional spatial and temporal random effects. Uncertainty from the first stage is accounted for by simulating repeatedly from the posterior predictive distribution of the latent field. A simulation study was carried out to assess the …

*2023/4/1*

Anang Kurnia

Institut Pertanian Bogor

Spatial Statistics

##### Geo-additive mixed model with variable selection using the adaptive elastic net to handle nonresponse in official rice productivity survey

This study is motivated by the nonresponse problem in the official rice productivity survey conducted by Statistics Indonesia. Handling nonresponse is essential to support the vision as a quality statistical data provider for advanced Indonesia. This study aimed to improve the quality of official rice productivity data by imputing nonresponse data using the geo-additive mixed model with variable selection. Then we simulated three nonresponse data scenarios to determine whether the imputation technique is better than the listwise deletion. The results showed that the proposed imputation model was the best-imputed model for estimating rice productivity compared to the linear regression, SVM, and geo-additive mixed models without variable selection. The proposed model outperforms other models when the data conditions experience spatial autocorrelation and multicollinearity. The proposed model had two …

*2023/8/1*