David Bolin

• PhD
• Professor (Associate) at King Abdullah University of Science and Technology

The R software package rSPDE contains methods for approximating Gaussian random fields based on fractional-order stochastic partial differential equations (SPDEs). A common example of such fields are Whittle-Mat\'ern fields on bounded domains in $\mathbb{R}^d$, manifolds, or metric graphs. The package also implements various other models which are...

The modeling of spatial point processes has advanced considerably, yet extending these models to non-Euclidean domains, such as road networks, remains a challenging problem. We propose a novel framework for log-Gaussian Cox processes on general compact metric graphs by leveraging the Gaussian Whittle-Mat\'ern fields, which are solutions to fraction...

Spatial statistics is traditionally based on stationary models on $${\mathbb{R}}^{d}$$ like Matérn fields. The adaptation of traditional spatial statistical methods, originally designed for stationary models in Euclidean spaces, to effectively model phenomena on linear networks such as stream systems and urban road networks is challenging. The curr...

The increasing availability of network data has driven the development of advanced statistical models specifically designed for metric graphs, where Gaussian processes play a pivotal role. While models such as Whittle-Mat\'ern fields have been introduced, there remains a lack of practically applicable options that accommodate flexible non-stationar...

We derive an explicit link between Gaussian Markov random fields on metric graphs and graphical models, and in particular show that a Markov random field restricted to the vertices of the graph is, under mild regularity conditions, a Gaussian graphical model with a distribution which is faithful to its pairwise independence graph, which coincides w...

Model checking is essential to evaluate the adequacy of statistical models and the validity of inferences drawn from them. Particularly, hierarchical models such as latent Gaussian models (LGMs) pose unique challenges as it is difficult to check assumptions on the latent parameters. Diagnostic statistics are often used to quantify the degree to whi...

The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The cost can be reduced in certain special cases, but there are currently no generally applicable exact methods with...

Scoring rules are aimed at evaluation of the quality of predictions, but can also be used for estimation of parameters in statistical models. We propose estimating parameters of multivariate spatial models by maximising the average leave-one-out cross-validation score. This method, LOOS, thus optimises predictions instead of maximising the likeliho...

In econometrics, the Efficient Market Hypothesis posits that asset prices reflect all available information in the market. Several empirical investigations show that market efficiency drops when it undergoes extreme events. Many models for multivariate extremes focus on positive dependence, making them unsuitable for studying extremal dependence in...

Trees in agroforestry parklands influence crops both through competitive and facilitative mechanism, but the effects are challenging to disentangle due to the complexity of the system with high variability in tree cover structure and species diversity and crop combinations. Focusing on a landscape in central Burkina Faso dominated by Vitellaria par...

Moving average processes driven by exponential-tailed L\'evy noise are important extensions of their Gaussian counterparts in order to capture deviations from Gaussianity, more flexible dependence structures, and sample paths with jumps. Popular examples include non-Gaussian Ornstein--Uhlenbeck processes and type G Mat\'ern stochastic partial diffe...

Model checking is essential to evaluate the adequacy of statistical models and the validity of inferences drawn from them. Particularly, hierarchical models such as latent Gaussian models (LGMs) pose unique challenges as it is difficult to check assumptions about the distribution of the latent parameters. Discrepancy measures are often used to quan...

Statistical analysis of extremes can be used to predict the probability of future extreme events, such as large rainfalls or devastating windstorms. The quality of these forecasts can be measured through scoring rules. Locally scale invariant scoring rules put equal importance on the forecasts at different locations regardless of differences in the...

The Whittle-Mat\'ern fields are a recently introduced class of Gaussian processes on metric graphs, which are specified as solutions to a fractional-order stochastic differential equation on the metric graph. Contrary to earlier covariance-based approaches for specifying Gaussian fields on metric graphs, the Whittle-Mat\'ern fields are well-defined...

There has recently been much interest in Gaussian processes on linear networks and more generally on compact metric graphs. One proposed strategy for defining such processes on a metric graph $\Gamma$ is through a covariance function that is isotropic in a metric on the graph. Another is through a fractional order differential equation $L^\alpha (\...

The fractional differential equation $L^\beta u = f$ posed on a compact metric graph is considered, where $\beta>\frac14$ and $L = \kappa - \frac{\mathrm{d}}{\mathrm{d} x}(H\frac{\mathrm{d}}{\mathrm{d} x})$ is a second-order elliptic operator equipped with certain vertex conditions and sufficiently smooth and positive coefficients $\kappa,H$. We de...

Spatial fields, aka random fields, are important models for analyzing data collected at different spatial locations. This article provides a short introduction to spatial fields for continuously indexed data, focusing on how to construct flexible Gaussian and non‐Gaussian fields. A brief introduction to spatial prediction of random fields is given,...

Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that contain inherently non-Gaussian features, such as sudden jumps or spikes, that adversely affect the inferences and...

Task functional magnetic resonance imaging (fMRI) is a type of neuroimaging data used to identify areas of the brain that activate during specific tasks or stimuli. These data are conventionally modeled using a massive univariate approach across all data locations, which ignores spatial dependence at the cost of model power. We previously developed...

The stochastic partial differential equation (SPDE) approach is widely used for modeling large spatial datasets. It is based on representing a Gaussian random field $u$ on $\mathbb{R}^d$ as the solution of an elliptic SPDE $L^\beta u = \mathcal{W}$ where $L$ is a second-order differential operator, $2\beta$ (belongs to natural number starting from...

Independent component analysis is commonly applied to functional magnetic resonance imaging (fMRI) data to extract independent components (ICs) representing functional brain networks. While ICA produces reliable group-level estimates, single-subject ICA often produces noisy results. Template ICA is a hierarchical ICA model using empirical populatio...

We define a new class of Gaussian processes on compact metric graphs such as street or river networks. The proposed models, the Whittle-Matérn fields, are defined via a fractional stochastic partial differential equation on the compact metric graph and are a natural extension of Gaussian fields with Matérn covariance functions on Euclidean domains...

The normal inverse Gaussian (NIG) and generalized asymmetric Laplace (GAL) distributions can be seen as skewed and heavy-tailed extensions of the Gaussian distribution. Models driven by these more flexible noise distributions are then regarded as generalizations of simpler Gaussian models. Inferential procedures tend to overestimate the degree of n...

Analysis of brain imaging scans is critical to understanding the way the human brain functions, which can be leveraged to treat injuries and conditions that affect the quality of life for a significant portion of the human population. In particular, functional magnetic resonance imaging (fMRI) scans give detailed data on a living subject at high sp...

The ocean wave distribution in a specific region of space and time is described by its sea state. Knowledge about the sea states a ship encounters on a journey can be used to assess various parameters of risk and wear associated with this journey. Two important characteristics of the sea state are significant wave height and mean wave period. We pr...

Gaussian processes and random fields have a long history, covering multiple approaches to representing spatial and spatio-temporal dependence structures, such as covariance functions, spectral representations, reproducing kernel Hilbert spaces, and graph based models. This article describes how the stochastic partial differential equation approach...

The general linear model (GLM) is a widely popular and convenient tool for estimating the functional brain response and identifying areas of significant activation during a task or stimulus. However, the classical GLM is based on a massive univariate approach that does not explicitly leverage the similarity of activation patterns among neighboring...

Various natural phenomena exhibit spatial extremal dependence at short distances only, while it usually vanishes as the distance between sites increases arbitrarily. However, models proposed in the literature for spatial extremes, which are based on max-stable or Pareto processes or comparatively less computationally demanding ``sub-asymptotic'' mo...

Gaussian processes and random fields have a long history, covering multiple approaches to representing spatial and spatio-temporal dependence structures, such as covariance functions, spectral representations, reproducing kernel Hilbert spaces, and graph based models. This article describes how the stochastic partial differential equation approach...

Both intensities of individual extreme rainfall events and the frequency of such events are important for infrastructure planning. We develop a new statistical extreme value model, the PGEV model, which makes it possible to use high quality annual maximum series data instead of lesswell checked daily data to estimate trends in intensity and frequen...

The general linear model (GLM) is a popular and convenient tool for estimating the functional brain response and identifying areas of significant activation during a task or stimulus. However, the classical GLM is based on a massive univariate approach that does not leverage the similarity of activation patterns among neighboring brain locations. A...

Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be unfeasible. We propose a new class of methods to overcome these challenges in the common case of sparse constraints, w...

Pore geometry characterization-methods are important tools for understanding how pore structure influences properties such as transport through a porous material. Bottlenecks can have a large influence on transport and related properties. However, existing methods only catch certain types of bottleneck effects caused by variations in pore size. We...

We consider Gaussian measures $\mu, \tilde{\mu}$ on a separable Hilbert space, with fractional-order covariance operators $A^{-2\beta}$ resp. $\tilde{A}^{-2\tilde{\beta}}$, and derive necessary and sufficient conditions on $A, \tilde{A}$ and $\beta, \tilde{\beta} > 0$ for I. equivalence of the measures $\mu$ and $\tilde{\mu}$, and II. uniform asymp...

The relation between pedestrian flows, the structure of the city and the street network is of central interest in urban research. However, studies of this have traditionally been based on small data sets and simplistic statistical methods. Because of a recent large‐scale cross‐country pedestrian survey, there is now enough data available to study t...

We consider the analysis of continuous repeated measurement outcomes that are collected longitudinally. A standard framework for analysing data of this kind is a linear Gaussian mixed effects model within which the outcome variable can be decomposed into fixed effects, time invariant and time-varying random effects, and measurement noise. We develop...

The Mat\' ern field is the most well known family of covariance functions used for Gaussian processes in spatial models. We build upon the original research of Whittle (1953, 1964) and develop the diffusion-based extension of the Mat\' ern field to space-time (DEMF). We argue that this diffusion-based extension is the natural extension of these pro...

ICA is commonly applied to fMRI data to extract independent components (ICs) representing functional brain networks. While ICA produces highly reliable results at the group level, single-subject ICA often produces inaccurate results due to high noise levels. Previously, we proposed template ICA (tICA), a hierarchical ICA model using empirical popul...

Optimal linear prediction (also known as kriging) of a random field $\{Z(x)\}_{x\in\mathcal{X}}$ indexed by a compact metric space $(\mathcal{X},d_{\mathcal{X}})$ can be obtained if the mean value function $m\colon\mathcal{X}\to\mathbb{R}$ and the covariance function $\varrho\colon\mathcal{X}\times\mathcal{X}\to\mathbb{R}$ of $Z$ are known. We cons...

A non-stationary Gaussian random field model is developed based on a combination of the stochastic partial differential equation (SPDE) approach and the classical deformation method. With the deformation method, a stationary field is defined on a domain which is deformed so that the field becomes non-stationary. We show that if the stationary field...

Vehicle-to-vehicle (V2V) wireless communications can improve traffic safety at road intersections and enable congestion avoidance. However, detailed knowledge about the wireless propagation channel is needed for the development and realistic assessment of V2V communication systems. In this paper, we present a novel geometry-based stochastic MIMO ch...

For many applications with multivariate data, random‐field models capturing departures from Gaussianity within realizations are appropriate. For this reason, we formulate a new class of multivariate non‐Gaussian models based on systems of stochastic partial differential equations with additive type G noise whose marginal covariance functions are of...

Averages of proper scoring rules are often used to rank probabilistic forecasts. In many cases, the individual observations and their predictive distributions in these averages have variable scale (variance). We show that some of the most popular proper scoring rules, such as the continuous ranked probability score (CRPS), up-weight observations wi...

Plot systems (also referred to as "property", "parcel", or "lot") are generally recognised as the organisational framework of urban form that contributes to the economic performance of cities. However, studies that link the spatial form of plots to economic data are limited. The paper builds on the theory of Webster and Lai, which argues that the p...

This work follows a long line of studies and empirical investigations in Space Syntax research, that, in general, try to conceptualise, describe and quantify the relation between physical space and human agency. How many people share public space is known to affect many socioeconomic processes in cities, such as segregation, vitality and local comm...

Bayesian whole-brain functional magnetic resonance imaging (fMRI) analysis with three-dimensional spatial smoothing priors have been shown to produce state-of-the-art activity maps without pre-smoothing the data. The proposed inference algorithms are computationally demanding however, and the proposed spatial priors have several less appealing prop...

The ocean wave distribution in a specific region of space and time is described by its sea state. Knowledge about the sea states a ship encounters on a journey can be used to assess various parameters of risk and wear associated with the journey. Two important characteristics of the sea state are the significant wave height and mean wave period. We...

The general condition of the ocean surface at a certain location in space and time is described by the sea state. Knowing the distribution of the sea state is, for example, important when estimating the wear and risks associated with a planned journey of a ship. One important characteristic of the sea state is the significant wave height. We propos...

Vehicle-to-vehicle (V2V) wireless communications can improve traffic safety at road intersections and enable congestion avoidance. However, detailed knowledge about the wireless propagation channel is needed for the development and realistic assessment of V2V communication systems. In this paper, we present a novel geometry-based stochastic MIMO ch...

The numerical approximation of solutions to stochastic partial differential equations with additive spatial white noise on bounded domains in $\mathbb{R}^d$ is considered. The differential operator is given by the fractional power $L^\beta$, $\beta\in(0,1)$, of an integer order elliptic differential operator $L$ and is therefore non-local. Its inve...

Diffusive transport through porous materials is to a large extent determined by the microstructure of the material. To design materials with controlled transport properties, it is hence important to connect properties of the pore geometry to diffusive transport rates. Different kinds of microstructures from a stochastic model are generated and mult...

The R software package excursions contains methods for calculating probabilistic excursion sets, contour credible regions, and simultaneous confidence bands for latent Gaussian stochastic processes and fields. It also contains methods for uncertainty quantification of contour maps and computation of Gaussian integrals. This article describes the th...

For many problems in geostatistics, land cover classification, and brain imaging the classical Gaussian process models are unsuitable due to sudden, discontinuous, changes in the data. To handle data of this type, we introduce a new model class that combines discrete Markov random fields (MRFs) with Gaussian Markov random fields. The model is defin...

There is an interest to replace computed tomography (CT) images with magnetic resonance (MR) images for a number of diagnostic and therapeutic workflows. In this article, predicting CT images from a number of magnetic resonance imaging (MRI) sequences using regression approach is explored. Two principal areas of application for estimated CT images...

Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realistically‐sized datasets from scratch is time‐consuming, and if changes are made to the model, there is little guarantee that the code performs well. The key advantages of R...

The performance of Markov chain Monte Carlo (MCMC) algorithms like the Metropolis Hastings Random Walk (MHRW) is highly dependent on the choice of scaling matrix for the proposal distributions. A popular choice of scaling matrix in adaptive MCMC methods is to use the empirical covariance matrix (ECM) of previous samples. However, this choice is pro...

We consider the analysis of continuous repeated measurement outcomes that are collected through time, also known as longitudinal data. A standard framework for analysing data of this kind is a linear Gaussian mixed-effects model within which the outcome variable can be decomposed into fixed-effects, time-invariant and time-varying random-effects, a...

Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realistically-sized datasets from scratch is time-consuming, and if changes are made to the model, there is little guarantee that the code performs well. The key advantages of R...

The numerical approximation of the solution $u$ to a stochastic partial differential equation with additive spatial white noise on a bounded domain in $\mathbb{R}^d$ is considered. The differential operator is assumed to be a fractional power $L^\beta$ of an integer order elliptic differential operator $L$, where $\beta\in(0,1)$. The solution $u$ i...

The numerical approximation of the solution to a stochastic partial differential equation with additive spatial white noise on a bounded domain is considered. The differential operator is assumed to be a fractional power of an integer order elliptic differential operator. The solution is approximated by means of a finite element discretization in s...

A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form Lβu=W, where W is Gaussian white noise, L is a second-order differential operator, and β>0 is a parameter that determines the smoothness of u. However, this approach...

A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form $L^{\beta}u = \mathcal{W}$, where $\mathcal{W}$ is Gaussian white noise, $L$ is a second-order differential operator, and $\beta>0$ is a parameter that determines th...

The log-Gaussian Cox process (LGCP) is a popular point process for modeling non interacting spatial point patterns. This paper extends the LGCP model to data exhibiting a finite number of fundamentally different behaviors partitioned on the spatial domain into an unknown set of subregions. The aim of the analyst might be either to identify and clas...

The log-Gaussian Cox process (LGCP) is a popular point process for modeling non-interacting spatial point patterns. This paper extends the LGCP model to handle data exhibiting fundamentally different behaviors in different subregions of the spatial domain. The aim of the analyst might be either to identify and classify these regions, to perform kri...

Cortical surface fMRI (cs-fMRI) has recently grown in popularity versus traditional volumetric fMRI, as it allows for more meaningful spatial smoothing and is more compatible with the common assumptions of isotropy and stationarity in Bayesian spatial models. However, as no Bayesian spatial model has been proposed for cs-fMRI data, most analyses co...

Cortical surface fMRI (cs-fMRI) has recently grown in popularity versus traditional volumetric fMRI, as it allows for more meaningful spatial smoothing and is more compatible with the common assumptions of isotropy and stationarity in Bayesian spatial models. However, as no Bayesian spatial model has been proposed for cs-fMRI data, most analyses co...

The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the covariance matrix, such as the marginal variances, which may be non-trivial to obtain when the dimension is larg...

The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the covariance matrix, such as the marginal variances, which may be non-trivial to obtain when the dimension is larg...

The numerical approximation of solutions to stochastic partial differential equations with additive spatial white noise on bounded domains in $\mathbb{R}^d$ is considered. The differential operator is given by the fractional power $L^\beta$, $\beta\in(0,1)$, of an integer order elliptic differential operator $L$ and is therefore non-local. Its inve...

A thresholded Gaussian random field model is developed for the microstructure of porous materials. Defining the random field as a solution to a stochastic partial differential equation allows for flexible modelling of non-stationarities in the material and facilitates computationally efficient methods for simulation and model fitting. A Markov Chai...

A thresholded Gaussian random field model is developed for the microstructure of porous materials. Defining the random field as a solution to stochastic partial differential equation allows for flexible modelling of non-stationarities in the material and facilitates computationally efficient methods for simulation and model fitting. A Markov Chain...

There is an interest to replace computed tomography (CT) images with magnetic resonance (MR) images for a number of diagnostic and therapeutic workflows. In this article, predicting CT images from a number of magnetic resonance imaging (MRI) sequences using regression approach is explored. Two principal areas of application for estimated CT images...

There is an interest to replace computed tomography (CT) images with magnetic resonance (MR) images for a number of diagnostic and therapeutic workflows. In this article, predicting CT images from a number of magnetic resonance imaging (MRI) sequences using regression approach is explored. Two principal areas of application for estimated CT images...

Spatial whole-brain Bayesian modeling of task-related functional magnetic resonance imaging (fMRI) is a serious computational challenge. Most of the currently proposed methods therefore do inference in subregions of the brain separately or do approximate inference without comparison to the true posterior distribution. A popular such method, which i...

Computed tomography (CT) equivalent information is needed for attenuation correction in PET imaging and for dose planning in radiotherapy. Prior work has shown that Gaussian mixture models can be used to generate a substitute CT (s-CT) image from a specific set of MRI modalities. This work introduces a more flexible class of mixture models for s-CT...

For many applications with multivariate data, random field models capturing departures from Gaussianity within realisations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of stochastic partial differential equations with additive type G noise whose marginal covariance functions are of...

Dynamical downscaling of earth system models is intended to produce high-resolution climate information at regional to local scales. Current models, while adequate for describing temperature distributions at relatively small scales, struggle when it comes to describing precipitation distributions. In order to better match the distribution of observ...

Spatial whole-brain Bayesian modeling of task-related functional magnetic resonance imaging (fMRI) is a great computational challenge. Most of the currently proposed methods therefore do inference in subregions of the brain separately or do approximate inference without comparison to the true posterior distribution. A popular such method, which is...

Contour maps are widely used to display estimates of spatial fields. Instead of showing the estimated field, a contour map only shows a fixed number of contour lines for different levels. However, despite the ubiquitous use these maps, the uncertainty associated with them has been given a surprisingly small amount of attention. We derive measures o...

Covariance tapering is a popular approach for reducing the computational cost of spatial prediction and parameter estimation for Gaussian process models. However, previous work has shown that tapering can have poor performance for example when the data is sampled at spatially irregular locations. In this work we introduce a computationally convenie...

The pathloss exponent and the variance of the large-scale fading are two parameters that are of great importance when modeling and characterizing wireless propagation channels. The pathloss is typically modeled using a log-distance power law with a large-scale fading term that is log-normal. In practice, the received signal is affected by the dynam...