Spatio-temporal modeling of traffic accidents incidence on urban road networks based on an explicit network triangulation.

Traffic deaths and injuries are one of the major global public health concerns. The present study considers accident records in an urban environment to explore and analyze spatial and temporal in the incidence of road traffic accidents. We propose a spatio-temporal model to provide predictions of the number of traffic collisions on any given road segment, to further generate a risk map of the entire road network. A Bayesian methodology using Integrated nested Laplace approximations with stochastic partial differential equations (SPDE) has been applied in the modeling process. As a novelty, we have introduced SPDE network triangulation to estimate the spatial autocorrelation restricted to the linear network. The resulting risk maps provide information to identify safe routes between source and destination points, and can be useful for accident prevention and multi-disciplinary road safety measures.

A spatio-temporal Dirichlet process mixture model for coronavirus disease-19.

Understanding the spatio-temporal patterns of the coronavirus disease 2019 (COVID-19) is essential to construct public health interventions. Spatially referenced data can provide richer opportunities to understand the mechanism of the disease spread compared to the more often encountered aggregated count data. We propose a spatio-temporal Dirichlet process mixture model to analyze confirmed cases of COVID-19 in an urban environment. Our method can detect unobserved cluster centers of the epidemics, and estimate the space-time range of the clusters that are useful to construct a warning system. Furthermore, our model can measure the impact of different types of landmarks in the city, which provides an intuitive explanation of disease spreading sources from different time points. To efficiently capture the temporal dynamics of the disease patterns, we employ a sequential approach that uses the posterior distribution of the parameters for the previous time step as the prior information for the current time step. This approach enables us to incorporate time dependence into our model in a computationally efficient manner without complicating the model structure. We also develop a model assessment by comparing the data with theoretical densities, and outline the goodness-of-fit of our fitted model.

COVID-19 transmission risk in Surabaya and Sidoarjo: an inhomogeneous marked Poisson point process approach.

Understanding the spatio-temporal dynamics of COVID-19 transmission is necessary to plan better strategies for controlling the spread of the disease. However, only a few studies explore the COVID-19 transmission risk over a fine spatial resolution while considering relevant spatial and temporal factors. To this aim, we consider an inhomogeneous marked Poisson point process model to assess COVID-19 transmission risk using data of home addresses of confirmed cases, in relation to locations of sources of crowd (enterprise, market, and place of worship) and population density in Surabaya and Sidoarjo, Indonesia. Our marked model is able to analyze how the spatial covariates are varying with time, helping authorities to evaluate the information of covariates depending on the period in which restrictions are taking place. Our results show that enterprise, place of worship, and population densities have significant impact to the transmission risk in Surabaya and Sidoarjo. We finally provide predicted risk maps which provide additional information based on the demographic-based risk analysis to help conduct more efficient testing, tracing, and vaccination programs.

Spatio-temporal stochastic differential equations for crime incidence modeling.

We propose a methodology for the quantitative fitting and forecasting of real spatio-temporal crime data, based on stochastic differential equations. The analysis is focused on the city of Valencia, Spain, for which 90247 robberies and thefts with their latitude-longitude positions are available for a span of eleven years (2010-2020) from records of the 112-emergency phone. The incidents are placed in the 26 zip codes of the city (46001-46026), and monthly time series of crime are built for each of the zip codes. Their annual-trend components are modeled by Itô diffusion, with jointly correlated noises to account for district-level relations. In practice, this study may help simulate spatio-temporal situations and identify risky areas and periods from present and past data.

Spatially informed Bayesian neural network for neurodegenerative diseases classification.

Magnetic resonance imaging (MRI) plays an increasingly important role in the diagnosis and prognosis of neurodegenerative diseases. One field of extensive clinical use of MRI is the accurate and automated classification of degenerative disorders. Most of current classification studies either do not mirror medical practice where patients may exhibit early stages of the disease, comorbidities, or atypical variants, or they are not able to produce probabilistic predictions nor account for uncertainty. Also, the spatial heterogeneity of the brain alterations caused by neurodegenerative processes is not usually considered, despite the spatial configuration of the neuronal loss is a characteristic hallmark for each disorder. In this article, we propose a classification technique that incorporates uncertainty and spatial information for distinguishing between healthy subjects and patients from four distinct neurodegenerative diseases: Alzheimer's disease, mild cognitive impairment, Parkinson's disease, and Multiple Sclerosis. We introduce a spatially informed Bayesian neural network (SBNN) that combines a three-dimensional neural network to extract neurodegeneration features from MRI, Bayesian inference to account for uncertainty in diagnosis, and a spatially informed MRI image using hidden Markov random fields to encode cerebral spatial information. The SBNN model demonstrates that classification accuracy increases up to 25% by including a spatially informed MRI scan. Furthermore, the SBNN provides a robust probabilistic diagnosis that resembles clinical decision-making and can account for the heterogeneous medical presentations of neurodegenerative disorders.

A mechanistic spatio-temporal modeling of COVID-19 data.

Understanding the evolution of an epidemic is essential to implement timely and efficient preventive measures. The availability of epidemiological data at a fine spatio-temporal scale is both novel and highly useful in this regard. Indeed, having geocoded data at the case level opens the door to analyze the spread of the disease on an individual basis, allowing the detection of specific outbreaks or, in general, of some interactions between cases that are not observable if aggregated data are used. Point processes are the natural tool to perform such analyses. We analyze a spatio-temporal point pattern of Coronavirus disease 2019 (COVID-19) cases detected in Valencia (Spain) during the first 11 months (February 2020 to January 2021) of the pandemic. In particular, we propose a mechanistic spatio-temporal model for the first-order intensity function of the point process. This model includes separate estimates of the overall temporal and spatial intensities of the model and a spatio-temporal interaction term. For the latter, while similar studies have considered different forms of this term solely based on the physical distances between the events, we have also incorporated mobility data to better capture the characteristics of human populations. The results suggest that there has only been a mild level of spatio-temporal interaction between cases in the study area, which to a large extent corresponds to people living in the same residential location. Extending our proposed model to larger areas could help us gain knowledge on the propagation of COVID-19 across cities with high mobility levels.

Modeling noisy time-series data of crime with stochastic differential equations.

We develop and calibrate stochastic continuous models that capture crime dynamics in the city of Valencia, Spain. From the emergency phone, data corresponding to three crime events, aggressions, stealing and women alarms, are available from the year 2010 until 2020. As the resulting time series, with monthly counts, are highly noisy, we decompose them into trend and seasonality parts. The former is modeled by geometric Brownian motions, both uncorrelated and correlated, and the latter is accommodated by randomly perturbed sine-cosine waves. Albeit simple, the models exhibit high ability to simulate the real data and show promising for crimes-interaction identification and short-term predictive policing.

A phenomenological model for COVID-19 data taking into account neighboring-provinces effect and random noise.

We model the incidence of the COVID-19 disease during the first wave of the epidemic in Castilla-Leon (Spain). Within-province dynamics may be governed by a generalized logistic map, but this lacks of spatial structure. To couple the provinces, we relate the daily new infections through a density-independent parameter that entails positive spatial correlation. Pointwise values of the input parameters are fitted by an optimization procedure. To accommodate the significant variability in the daily data, with abruptly increasing and decreasing magnitudes, a random noise is incorporated into the model, whose parameters are calibrated by maximum likelihood estimation. The calculated paths of the stochastic response and the probabilistic regions are in good agreement with the data.

Modeling infectious disease dynamics: Integrating contact tracing-based stochastic compartment and spatio-temporal risk models.

Major infectious diseases such as COVID-19 have a significant impact on population lives and put enormous pressure on healthcare systems globally. Strong interventions, such as lockdowns and social distancing measures, imposed to prevent these diseases from spreading, may also negatively impact society, leading to jobs losses, mental health problems, and increased inequalities, making crucial the prioritization of riskier areas when applying these protocols. The modeling of mobility data derived from contact-tracing data can be used to forecast infectious trajectories and help design strategies for prevention and control. In this work, we propose a new spatial-stochastic model that allows us to characterize the temporally varying spatial risk better than existing methods. We demonstrate the use of the proposed model by simulating an epidemic in the city of Valencia, Spain, and comparing it with a contact tracing-based stochastic compartment reference model. The results show that, by accounting for the spatial risk values in the model, the peak of infected individuals, as well as the overall number of infected cases, are reduced. Therefore, adding a spatial risk component into compartment models may give finer control over the epidemic dynamics, which might help the people in charge to make better decisions.

Multivariate Kalman filtering for spatio-temporal processes.

An increasing interest in models for multivariate spatio-temporal processes has been noted in the last years. Some of these models are very flexible and can capture both marginal and cross spatial associations amongst the components of the multivariate process. In order to contribute to the statistical analysis of these models, this paper deals with the estimation and prediction of multivariate spatio-temporal processes by using multivariate state-space models. In this context, a multivariate spatio-temporal process is represented through the well-known Wold decomposition. Such an approach allows for an easy implementation of the Kalman filter to estimate linear temporal processes exhibiting both short and long range dependencies, together with a spatial correlation structure. We illustrate, through simulation experiments, that our method offers a good balance between statistical efficiency and computational complexity. Finally, we apply the method for the analysis of a bivariate dataset on average daily temperatures and maximum daily solar radiations from 21 meteorological stations located in a portion of south-central Chile. Supplementary Information: The online version contains supplementary material available at 10.1007/s00477-022-02266-3.

A Spatially Correlated Model with Generalized Autoregressive Conditionally Heteroskedastic Structure for Counts of Crimes.

Crime is a negative phenomenon that affects the daily life of the population and its development. When modeling crime data, assumptions on either the spatial or the temporal relationship between observations are necessary if any statistical analysis is to be performed. In this paper, we structure space-time dependency for count data by considering a stochastic difference equation for the intensity of the space-time process rather than placing structure on a latent space-time process, as Cox processes would do. We introduce a class of spatially correlated self-exciting spatio-temporal models for count data that capture both dependence due to self-excitation, as well as dependence in an underlying spatial process. We follow the principles in Clark and Dixon (2021) but considering a generalized additive structure on spatio-temporal varying covariates. A Bayesian framework is proposed for inference of model parameters. We analyze three distinct crime datasets in the city of Riobamba (Ecuador). Our model fits the data well and provides better predictions than other alternatives.

A Bayesian machine learning approach for spatio-temporal prediction of COVID-19 cases.

Modeling the spread of infectious diseases in space and time needs to take care of complex dependencies and uncertainties. Machine learning methods, and neural networks, in particular, are useful in modeling this sort of complex problems, although they generally lack of probabilistic interpretations. We propose a neural network method embedded in a Bayesian framework for modeling and predicting the number of cases of infectious diseases in areal units. A key feature is that our combined model considers the impact of human movement on the spread of the infectious disease, as an additional random factor to the also considered spatial neighborhood and temporal correlation components. Our model is evaluated over a COVID-19 dataset for 245 health zones of Castilla-Leon (Spain). The results show that a Bayesian model informed by a neural network method is generally able to predict the number of cases of COVID-19 in both space and time, with the human mobility factor having a strong influence on the model, together with the number of infections and deaths in nearby areas.

A stochastic Bayesian bootstrapping model for COVID-19 data.

We provide a stochastic modeling framework for the incidence of COVID-19 in Castilla-Leon (Spain) for the period March 1, 2020 to February 12, 2021, which encompasses four waves. Each wave is appropriately described by a generalized logistic growth curve. Accordingly, the four waves are modeled through a sum of four generalized logistic growth curves. Pointwise values of the twenty input parameters are fitted by a least-squares optimization procedure. Taking into account the significant variability in the daily reported cases, the input parameters and the errors are regarded as random variables on an abstract probability space. Their probability distributions are inferred from a Bayesian bootstrap procedure. This framework is shown to offer a more accurate estimation of the COVID-19 reported cases than the deterministic formulation.

A spatial randomness test based on the box-counting dimension.

Statistical modelling of a spatial point pattern often begins by testing the hypothesis of spatial randomness. Classical tests are based on quadrat counts and distance-based methods. Alternatively, we propose a new statistical test of spatial randomness based on the fractal dimension, calculated through the box-counting method providing an inferential perspective contrary to the more often descriptive use of this method. We also develop a graphical test based on the log-log plot to calculate the box-counting dimension. We evaluate the performance of our methodology by conducting a simulation study and analysing a COVID-19 dataset. The results reinforce the good performance of the method that arises as an alternative to the more classical distances-based strategies.

Capturing spatial dependence of COVID-19 case counts with cellphone mobility data.

Spatial dependence is usually introduced into spatial models using some measure of physical proximity. When analysing COVID-19 case counts, this makes sense as regions that are close together are more likely to have more people moving between them, spreading the disease. However, using the actual number of trips between each region may explain COVID-19 case counts better than physical proximity. In this paper, we investigate the efficacy of using telecommunications-derived mobility data to induce spatial dependence in spatial models applied to two Spanish communities' COVID-19 case counts. We do this by extending Besag York Mollié (BYM) models to include both a physical adjacency effect, alongside a mobility effect. The mobility effect is given a Gaussian Markov random field prior, with the number of trips between regions as edge weights. We leverage modern parametrizations of BYM models to conclude that the number of people moving between regions better explains variation in COVID-19 case counts than physical proximity data. We suggest that this data should be used in conjunction with physical proximity data when developing spatial models for COVID-19 case counts.

Contextual contact tracing based on stochastic compartment modeling and spatial risk assessment.

The current situation of COVID-19 highlights the paramount importance of infectious disease surveillance, which necessitates early monitoring for effective response. Policymakers are interested in data insights identifying high-risk areas as well as individuals to be quarantined, especially as the public gets back to their normal routine. We investigate both requirements by the implementation of disease outbreak modeling and exploring its induced dynamic spatial risk in form of risk assessment, along with its real-time integration back into the disease model. This paper implements a contact tracing-based stochastic compartment model as a baseline, to further modify the existing setup to include the spatial risk. This modification of each individual-level contact's intensity to be dependent on its spatial location has been termed as Contextual Contact Tracing. The results highlight that the inclusion of spatial context tends to send more individuals into quarantine which reduces the overall spread of infection. With a simulated example of an induced spatial high-risk, it is highlighted that the new spatio-SIR model can act as a tool to empower the analyst with a capability to explore disease dynamics from a spatial perspective. We conclude that the proposed spatio-SIR tool can be of great help for policymakers to know the consequences of their decision prior to their implementation.

Spatio-temporal small area surveillance of the COVID-19 pandemic.

The emergence of COVID-19 requires new effective tools for epidemiological surveillance. Spatio-temporal disease mapping models, which allow dealing with small units of analysis, are a priority in this context. These models provide geographically detailed and temporally updated overviews of the current state of the pandemic, making public health interventions more effective. These models also allow estimating epidemiological indicators highly demanded for COVID-19 surveillance, such as the instantaneous reproduction number R t , even for small areas. In this paper, we propose a new spatio-temporal spline model particularly suited for COVID-19 surveillance, which allows estimating and monitoring R t for small areas. We illustrate our proposal on the study of the disease pandemic in two Spanish regions. As a result, we show how tourism flows have shaped the spatial distribution of the disease in these regions. In these case studies, we also develop new epidemiological tools to be used by regional public health services for small area surveillance.

Structural Complexity and Informational Transfer in Spatial Log-Gaussian Cox Processes.

The doubly stochastic mechanism generating the realizations of spatial log-Gaussian Cox processes is empirically assessed in terms of generalized entropy, divergence and complexity measures. The aim is to characterize the contribution to stochasticity from the two phases involved, in relation to the transfer of information from the intensity field to the resulting point pattern, as well as regarding their marginal random structure. A number of scenarios are explored regarding the Matérn model for the covariance of the underlying log-intensity random field. Sensitivity with respect to varying values of the model parameters, as well as of the deformation parameters involved in the generalized informational measures, is analyzed on the basis of regular lattice partitionings. Both a marginal global assessment based on entropy and complexity measures, and a joint local assessment based on divergence and relative complexity measures, are addressed. A Poisson process and a log-Gaussian Cox process with white noise intensity, the first providing an upper bound for entropy, are considered as reference cases. Differences regarding the transfer of structural information from the intensity field to the subsequently generated point patterns, reflected by entropy, divergence and complexity estimates, are discussed according to the specifications considered. In particular, the magnitude of the decrease in marginal entropy estimates between the intensity random fields and the corresponding point patterns quantitatively discriminates the global effect of the additional source of variability involved in the second phase of the double stochasticity.

A hierarchical spatio-temporal model to analyze relative risk variations of COVID-19: a focus on Spain, Italy and Germany.

The novel coronavirus disease (COVID-19) has spread rapidly across the world in a short period of time and with a heterogeneous pattern. Understanding the underlying temporal and spatial dynamics in the spread of COVID-19 can result in informed and timely public health policies. In this paper, we use a spatio-temporal stochastic model to explain the temporal and spatial variations in the daily number of new confirmed cases in Spain, Italy and Germany from late February 2020 to mid January 2021. Using a hierarchical Bayesian framework, we found that the temporal trends of the epidemic in the three countries rapidly reached their peaks and slowly started to decline at the beginning of April and then increased and reached their second maximum in the middle of November. However decline and increase of the temporal trend seems to show different patterns in Spain, Italy and Germany.

Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields.

The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282-288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Rényi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2 ) self-similar processes.