Spatial prediction of categorical variables in environmental sciences : a minimum divergence and Bayesian data fusion approach

Categorical variables have always played an important role in a wide variety of statistical applications in several scientific fields, including environmental sciences. In a spatial environmental context, such data naturally arise in geography, geology or remote sensing classification, although they might be used with quite different goals in mind. Due to sampling limitations, these data often are not spatially exhaustive (i.e., values are not known everywhere in the spatial domain of interest); therefore, modeling and spatial prediction steps are required at some stage of the study. Although dealing with spatial continuous data based on a statistical framework has generated considerable literature for a long time and has led to well-established methods, modeling and predicting spatial categorical data have proved to be much more complex. Elegant approaches have been advocated, such as the Bayesian maximum Entropy (BME) methodology that originates from the concepts of entropy maximization and posterior conditioning. Among its advantages, this methodology is distribution-free, allows us to integrate both hard and soft data, does not rely on restrictive assumptions and provides a complete posterior distribution while classical methods are often limited in providing only few statistical moments. Although the BME approach for categorical data is very general and is a real outsider compared to more traditional approaches, this method also suffers from some drawbacks. This work aims at generalizing further the theoretical results of the BME framework in order to (i) account for qualitative data, such as experts’ opinions or frugal information, through a minimum divergence approach, and (ii) ease the integration multiple information sources through a Bayesian data fusion methodology suitable for categorical data. The first part of this work sets the theoretical background while the second part is dedicated to applications that illustrate the benefits of the suggested methodology in the field of land cover mapping, where accounting for qualitative data (e.g., crowdsourced information) and integrating multiple data sources (e.g., combining several land cover products) are of prime interest.(AGRO - Sciences agronomiques et ingénierie biologique) -- UCL, 201

Estimates of genetic parameters among body condition score and calving traits in first parity Canadian Ayrshire cows

The objective of this study was to estimate genetic correlations between body condition score (BCS) and calving traits using random regression animal models. Calving traits were a) calving ease (CE) scored from 1=unassisted to 4=surgery and b) calf survival (CS) scored from 0=dead to 1=alive. The data analyzed included first parity Ayrshire BCS records collected between 2001 and 2008 by field staff in herds from Québec. BCS observations were available from 100 days before the calving to 335 after the calving. Calving records were extracted for herds with at least one BCS record. Data included 9,944 BCS observations; 12,011 CE records and 11,600 CS records. (Co)variances were estimated by REML using 2 two-traits models. For BCS, regression curve of genetic and permanent environmental effect were modelled using Legendre polynomials of order 3. For calving traits, no covariance between maternal and direct effects was assumed. The genetic correlation between the maternal effect of CE and the BCS during the 100 days before and after calving ranged between -0.40 and -0.25; a low BCS seemed to increase the chance of the cow to calf with difficulty. For direct CE and maternal and direct CS, the highest correlations with BCS occurred in mid and late lactation. The genetic correlations between BCS and direct and maternal CS ranged from 0.2 to 0.4 and the genetic correlation between BCS and direct CE was around 0.6 at 200 days in milk. It indicated that the ability of the cow to recover its body reserves after the postpartum period would increase the chance of the calf to born easily and to surviv

Integrating Crowdsourced Data with a Land Cover Product: A Bayesian Data Fusion Approach

For many environmental applications, an accurate spatial mapping of land cover is a major concern. Currently, land cover products derived from satellite data are expected to offer a fast and inexpensive way of mapping large areas. However, the quality of these products may also largely depend on the area under study. As a result, it is common that various products disagree with each other, and the assessment of their respective quality still relies on ground validation datasets. Recently, crowdsourced data have been suggested as an alternate source of information that might help overcome this problem. However, crowdsourced data still remain largely discarded in scientific studies due to their inherent poor quality assurance. The aim of this paper is to present an efficient methodology that allows the user to code information brought by crowdsourced data even if no prior quality estimation is at hand and possibly to fuse this information with existing land cover products in order to improve their accuracy. It is first suggested that information brought by volunteers can be coded as a set of inequality constraints about the probabilities of the various land use classes at the visited places. This in turn allows estimating optimal probabilities based on a maximum entropy principle and to proceed afterwards with a spatial interpolation of these volunteers’ information. Finally, a Bayesian data fusion approach can be used for fusing multiple volunteers’ contributions with a remotely-sensed land cover product. This methodology is illustrated in this paper by focusing on the mapping of croplands in Ethiopia, where the aim is to improve the mapping of cropland as coming out from a land cover product with mitigated performances. It is shown how crowdsourced information can seriously improve the quality of the final product. The corresponding results also suggest that a prior assessing of remotely-sensed data quality can seriously improve the benefit of crowdsourcing campaigns, so that both sources of information need to be accounted together in order to optimize the sampling efforts

Bayesian maximum entropy and data fusion for processing qualitative data: theory and application for crowdsourced cropland occurrences in Ethiopia

Categorical data play an important role in a wide variety of spatial applications, while modeling and predicting this type of statistical variable has proved to be complex in many cases. Among other possible approaches, the Bayesian maximum entropy methodology has been developed and advocated for this goal and has been successfully applied in various spatial prediction problems. This approach aims at building a multivariate probability table from bivariate probability functions used as constraints that need to be fulfilled, in order to compute a posterior conditional distribution that accounts for hard or soft information sources. In this paper, our goal is to generalize further the theoretical results in order to account for a much wider type of information source, such as probability inequalities. We first show how the maximum entropy principle can be implemented efficiently using a linear iterative approximation based on a minimum norm criterion, where the minimum norm solution is obtained at each step from simple matrix operations that converges to the requested maximum entropy solution. Based on this result, we show then how the maximum entropy problem can be related to the more general minimum divergence problem, which might involve equality and inequality constraints and which can be solved based on iterated minimum norm solutions. This allows us to account for a much larger panel of information types, where more qualitative information, such as probability inequalities can be used. When combined with a Bayesian data fusion approach, this approach deals with the case of potentially conflicting information that is available. Although the theoretical results presented in this paper can be applied to any study (spatial or non-spatial) involving categorical data in general, the results are illustrated in a spatial context where the goal is to predict at best the occurrence of cultivated land in Ethiopia based on crowdsourced information. The results emphasize the benefit of the methodology, which integrates conflicting information and provides a spatially exhaustive map of these occurrence classes over the whole country

Bayesian Data Fusion Applied to Soil Drainage Classes Spatial Mapping

Soil drainage classes spatial mapping is of great interest since drainage has direct effects on crop productivity and hydrological modelling. However, the prediction of this categorical variable often requires a laborious and expensive sampling over large areas. There is thus a need for a methodology that is able to combine several sources of information to improve the prediction. Bayesian maximum entropy (BME) has become a complete framework in the context of space–time prediction. This method proposes solutions to combine several sources of data no matter what the nature of information is. However, the various attempts that were made for adapting the BME methodology to categorical variables and mixed random fields faced some limitations, as a high computational burden. The main objective of this paper is to overcome this limitation by generalizing the Bayesian data fusion (BDF) theoretical framework to categorical variables, which is a simplification of the BME method through the conditional independence hypothesis. The BDF methodology for categorical variables is first described and then applied to a practical case study: the estimation of soil drainage classes using a soil map and point observations around Mechelen (Belgium). The BDF approach is compared to BME along with more classical approaches, as indicator cokriging (ICK) and logistic regression. Estimators are compared using various indicators, namely the percentage of correctly classified locations and the average highest probability. Although BDF methodology for categorical variables is a simplification of BME approach, both methods lead to very close results and have strong advantages compared to ICK and logistic regression

Case report of osteomyelitis of the mandible in osteopetrosis and management considerations

WOS:000636326200101International audienceINTRODUCTION AND IMPORTANCE: Osteopetrosis is a poorly known and probably underdiagnosed pathology. It is caused by various genetic abnormalities resulting in osteoclast dysfunction. Functional and aesthetic consequences have a major impact on the patient's quality of life. Ten percent of osteopetrosis cases develop osteomyelitis that usually involves the mandible. Management of this complication remains complex and often unsatisfactory.CASE PRESENTATION: We report a case of a 62-year-old woman with osteopetrosis, complicated by mandibular osteomyelitis with intra-oral bone exposure and submental fistulas. Management was performed with antibiotic therapy and surgical necrotic resection. This cured the fistulas but the bone exposure persisted.DISCUSSION: This case report highlights the difficulty of achieving complete healing of osteomyelitis in osteopetrosis. Antibiotic therapy, surgical management, or even hyperbaric oxygen therapy are required, but must be adapted to the case. A free flap procedure is undesirable but, when it is necessary, a bone marrow transplant could be considered to restore osteoclast function.CONCLUSION: The management of mandibular osteomyelitis in patients with osteopetrosis must adapt to the situation and severity. To avoid most cases of osteomyelitic complications in patients suffering from osteopetrosis, we propose that a preventive strategy of better dental care should be considered. (C) 2021 The Authors. Published by Elsevier Ltd on behalf of IJS Publishing Group Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Emerging patterns in multi-sourced data modeling uncertainty

The abundance of spatial and space–time data in many research fields has led to an increasing interest in the analytics of spatial data information. This development has renewed the attention to predictive spatial methodologies and advancing geostatistical tools. In this context, the present work reviews a series of cross-discipline studies that utilize multiple monitoring sources,and promote applied approaches in spatial and spatiotemporal modeling to improve our understanding of uncertainty. As multisourced information gives birth to new aspects of uncertainty, we explore emerging patterns in dealing with uncertainty in sources across structured, unstructured, and incomplete spatial data. We also illustrate how additional forms of information, such as secondary data and physical models, can further support and benefit research in the characterization and modeling of natural attributes