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Classical statistical methods prove advantageous for small datasets, whereas machine learning algorithms can excel with larger datasets. Our paper challenges this conventional wisdom by addressing a highly significant problem: the identification of burned areas through satellite imagery, that is a clear example of imbalanced data. The methods are illustrated in the North-Central Portugal and the North-West of Spain in October 2017 within a multi-temporal setting of satellite imagery. Daily satellite images are taken from Moderate Resolution Imaging Spectroradiometer (MODIS) products. Our analysis shows that a classical Logistic regression (LR) model competes on par, if not surpasses, a widely employed machine learning algorithm called the extreme gradient boosting algorithm (XGBoost) within this particular domain. [ABSTRACT FROM AUTHOR]

We propose an adaptive-sliding-window approach (LACPD) for the problem of change-point detection in a set of time-ordered observations. The proposed method is combined with sub-sampling techniques to compensate for the lack of enough data near the time series' tails. Through a simulation study, we analyse its behaviour in the presence of an early/middle/late change-point in the mean, and compare its performance with some of the frequently used and recently developed change-point detection methods in terms of power, type I error probability, area under the ROC curves (AUC), absolute bias, variance, and root-mean-square error (RMSE). We conclude that LACPD outperforms other methods by maintaining a low type I error probability. Unlike some other methods, the performance of LACPD does not depend on the time index of change-points, and it generally has lower bias than other alternative methods. Moreover, in terms of variance and RMSE, it outperforms other methods when change-points are close to the time series' tails, whereas it shows a similar (sometimes slightly poorer) performance as other methods when change-points are close to the middle of time series. Finally, we apply our proposal to two sets of real data: the well-known example of annual flow of the Nile river in Awsan, Egypt, from 1871 to 1970, and a novel remote sensing data application consisting of a 34-year time-series of satellite images of the Normalised Difference Vegetation Index in Wadi As-Sirham valley, Saudi Arabia, from 1986 to 2019. We conclude that LACPD shows a good performance in detecting the presence of a change as well as the time and magnitude of change in real conditions. [ABSTRACT FROM AUTHOR]

Outliers and missing data are commonly found in satellite imagery. These are usually caused by atmospheric or electronic failures, hampering the correct monitoring of remote-sensing data. To avoid distorted data, we propose a procedure called "spatial functional prediction" (SFP). The SFP procedure consists of the following: (1) aggregating remote-sensing data for reducing the number of missing data and/or outliers; (2) additively decomposing the time series of images into a trend, a seasonal, and an error component; (3) defining the spatial functional data and predicting the trend component using an ordinary kriging; and (4) adding back the seasonal and error components to the predicted trend. The benefits of the SFP procedure are illustrated in the following scenarios: introducing random outliers, random missing data, mixtures of both, and artificial clouds in an extensive simulation study of composite images, and using daily images with real clouds. The following two derived variables are considered: land surface temperature (LST day) and normalized vegetation index (NDVI), which are obtained as remote-sensing data in a region in northern Spain during 2003–2016. The performance of SFP was checked using the root mean squared error (RMSE). A comparison with a procedure based on predicting with thin-plate splines (TpsP) is also made. We conclude that SFP is simpler and faster than TpsP, and provides smaller values of RMSE. [ABSTRACT FROM AUTHOR]

In some diseases it is well-known that a unimodal mortality pattern exists. A clear example in developed countries is breast cancer, where mortality increased sharply until the nineties and then decreased. This clear unimodal pattern is not necessarily applicable to all regions within a country. In this paper, we develop statistical tools to check if the unimodality pattern persists within regions using order restricted inference. Break points as well as confidence intervals are also provided. In addition, a new test for checking monotonicity against unimodality is derived allowing to discriminate between a simple increasing pattern and an up-then-down response pattern. A comparison with the widely used joinpoint regression technique under unimodality is provided. We show that the joinpoint technique could fail when the underlying function is not piecewise linear. Results will be illustrated using age-specific breast cancer mortality data from Spain in the period 1975-2005. [ABSTRACT FROM AUTHOR]

Spatio-temporal statistical models have been proposed for the analysis of the temporal evolution of the geographical pattern of mortality (or incidence) risks in disease mapping. However, as far as we know, functional approaches based on Hilbert-valued processes have not been used so far in this area. In this paper, the autoregressive Hilbertian process framework is adopted to estimate the functional temporal evolution of mortality relative risk maps. Specifically, the penalized functional estimation of log-relative risk maps is considered to smooth the classical standardized mortality ratio. The reproducing kernel Hilbert space (RKHS) norm is selected for definition of the penalty term. This RKHS-based approach is combined with the Kalman filtering algorithm for the spatio-temporal estimation of risk. Functional confidence intervals are also derived for detecting high risk areas. The proposed methodology is illustrated analyzing breast cancer mortality data in the provinces of Spain during the period 1975-2005. A simulation study is performed to compare the ARH(1) based estimation with the classical spatio-temporal conditional autoregressive approach. [ABSTRACT FROM AUTHOR]

Nowadays, GPS receivers are very reliable because of their good accuracy and precision; however, uncertainty is also inherent in geospatial data. Quality of GPS measurements can be influenced by atmospheric disturbances, multipathing, synchronization of clocks, satellite geometry, geographical features of the observed region, low broadcasting coverage, inadequate transmitting formats, or human or instrumental unknown errors. Assuming that the scenario and technical conditions that can influence the quality of GPS measurements are optimal, that functional and stochastic models that process the signals to a geodetic measurement are correct, and that all the GPS observables are taken in the same conditions, it is still possible to estimate the positional errors as the difference between the real coordinates and those measured by the GPS. In this paper, three spatial linear mixed models, one for each axis, are used for modelling real-time kinematic GPS accuracy and precision, of a multiple-reference-station network in dual-frequency with carrier phase measurements. Along the paper, the proposed models provide an estimate of the 'accuracy' in terms of bias defined as the difference between real coordinates and measured coordinates after being processed and 'precision' through the standard errors of the estimated differences. This is done using ten different transmitting formats. Mapping and quantifying these differences can be interesting for users and GPS professionals. The performance of these models is illustrated by mapping positional error estimates within the whole region of Navarre, Spain. Sampled data have been taken in 54 out of the 211 geodetic vertex points of this region. Maps show interesting error patterns depending on transmitting formats, the different axes, and the geographical characteristics of the region. Higher differences are found in regions with bad broadcasting coverage, due to the presence of mountains and high degree of humidity. [ABSTRACT FROM AUTHOR]

Smoothing risks is one of the main goals in disease mapping as classical measures, such as standardized mortality ratios, can be extremely variable. However, smoothing risks might hinder the detection of high risk areas, since these two objectives are somewhat contradictory. Most of the work on smoothing risks and detection of high risk areas has been derived using conditional autoregressive (CAR) models. In this work, penalized splines (P-splines) models are also investigated. Confidence intervals for the log-relative risk predictor will be derived as a tool to detect high-risk areas. The performance of P-spline and CAR models will be compared in terms of smoothing (relative bias), sensitivity (ability to detect high risk areas), and specificity (ability to discard false patterns created by noise) through a simulation study based on the well-known Scottish lip cancer data. [ABSTRACT FROM AUTHOR]

One of the main objectives in disease mapping is the identification of temporal trends and the production of a series of smoothed maps from which spatial patterns of mortality risks can be monitored over time. When studying rare diseases, conditional autoregressive models have been commonly used for smoothing risks. In this work, a P-spline ANOVA type model is used instead. The model is anisotropic and explicitly considers different smooth terms for space, time, and space-time interaction avoiding, in addition, model identifiability problems. The mean squared error of the log-risk predictor is derived accounting for the variability associated to the estimation of the smoothing parameters. The procedure is illustrated analyzing Spanish prostate cancer mortality data in the period 1975-2008. [ABSTRACT FROM AUTHOR]

Measuring forest tree biomass is becoming a very important issue due to the general environmental awareness motivated by global warming and climate change. However, weighing a tree is a very complicated, expensive, and destructive process. The tree is divided into several parts, and the total weight is obtained by adding the weight of the different components. The biomass information of a forest is obtained using statistical models, but one of the main difficulties is that the additivity property is not generally satisfied, i.e., when adding the predicted weights for the different tree components, the result does not match up with the total weight predicted for the tree. In this work, alternative methods for obtaining biomass predictions satisfying the additivity property are analyzed. In particular, segmented regression models with a common break point and penalized splines with the same smoothing parameter achieve the additivity property without any further adjustments. Some classical models will be also used for comparison purposes. Results are illustrated with real data from a beech forest (European project FORSEE-020) in the province of Navarre, Spain. [ABSTRACT FROM AUTHOR]

Nowadays, the detection of areas with high nitrate concentration in groundwater is of public concern because an excess of these nitrogen compounds in any area represents serious environmental pollution. Hence, governmental agencies require geostatistical researchers to develop methods for assessing nitrate concentration. In this paper, we propose a linear mixed model which incorporates both spatial as well as longitudinal information with the particular objective of detecting areas with excess of nitrate in groundwater. The model extends in a natural way the traditional kriging approach, incorporating the longitudinal dimension. We illustrate the results using real data taken from wells pouring into the Ebro river and its tributaries in the province of Navarra, Spain. [ABSTRACT FROM AUTHOR]

This article aims to estimate the total area occupied by olive trees in a region called Comarca IV, located in a central region of Navarra, Spain. Traditionally, small area linear mixed models have been used for similar purposes using regular quadrats (also called segments) as sampling units, and assuming that the majority of segments are fully included in the study domain. When this does not happen, the sampling units are of different size, and there exists an extra variability that can be very different within areas. In this case it is advisable to include model weights in the model. In this article, we propose a weighted unit level linear mixed model where both the variance components and the coefficients of the model are estimated using these weights. We also discuss, the model performance and compare it with alternatives. [ABSTRACT FROM AUTHOR]

In this paper we derive score tests for spatial independence in mortality or incidence risk in the framework of hierarchical spatial models where different Gaussian Markov random field (MRF) priors are given for modelling the area random effects (specifically, two non-intrinsic Gaussian priors and a convolution Gaussian prior). The techniques used to test the practically relevant and important simplifying hypotheses of an absence of spatial variation in risk will provide a guidance for practitioners to select an adequate model (i.e., a model with an exchangeable-independent-prior, an intrinsic prior, a convolution prior or a non-intrinsic prior, for the area-specific random effects distribution). The proposed methodology is illustrated by analyzing the well-known data set of lip cancer in Scotland and female mortality due to cerebrovascular disease in Navarra, Spain. [ABSTRACT FROM AUTHOR]

This article presents alternative models for describing spatial dependence among dwelling selling prices. Often housing selling market prices are spatially autocorrelated meaning that dwellings located in a nearby area have similar prices. Moreover, the autocorrelation decays with distance. There are several reasons why dwelling selling prices depend strongly upon location. First, households in a neighborhood area have similar structural characteristics, such as building materials, total living area, age of construction, garages and storage rooms. Second, they share common social services, such as schools, health centers, libraries or malls. Finally, they share the same distances to administrative and commercial nerve-centers.