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This research presents a procedure for determining the origin of marine pollution through the use of a time-direct trajectory modeling, associated with a Kriging metamodel technique and Monte Carlo random sampling. These methods were applied to a real case, specifically the oil spill that affected the Brazilian coast in the second half of 2019 and early 2020. A total of 140 trajectories, defined by the geographical coordinates of the origin and the spill date, were generated through Latin Hypercube Sampling and simulated using the PyGNOME model to construct the Kriging metamodel. The metamodel demonstrated cost-effectiveness by efficiently simulating numerous input data combinations which were compared and optimized based on available real data regarding temporal and spatial pollution distribution.

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In this paper, we propose a hierarchical Bayesian approach for modeling the evolution of the 7-day moving average for the number of deaths due to COVID-19 in a country, state or city. The proposed approach is based on a Gaussian process regression model. The main advantage of this model is that it assumes that a nonlinear function f used for modeling the observed data is an unknown random parameter in opposite to usual approaches that set up f as being a known mathematical function. This assumption allows the development of a Bayesian approach with a Gaussian process prior over f. In order to estimate the parameters of interest, we develop an MCMC algorithm based on the Metropolis-within-Gibbs sampling algorithm. We also present a procedure for making predictions. The proposed method is illustrated in a case study, in which, we model the 7-day moving average for the number of deaths recorded in the state of São Paulo, Brazil. Results obtained show that the proposed method is very effective in modeling and predicting the values of the 7-day moving average.

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Stochastic field reconstruction is a crucial technique to improve the accuracy of modern rock simulation. It allows explicit modelling of field conditions, often employed in uncertainty quantification analysis and upsampling and upscaling procedures. This paper presents a case-study of a framework for the stochastic reconstruction of rock's strain field using experimental data. The proposed framework is applied to a limestone outcrop in which the strain field is measured using Digital Image Correlation (DIC). Assuming that the strain fields of these rocks are well-represented by Gaussian random fields, we capitalize on the algorithms used for training Gaussian processes to estimate the correlation family and the parameters that best represent these fields. Although the spherical and exponential kernels often correspond to the best fit, our results depict that each field shall be analyzed separately and no general rule can be defined. We show that the method is versatile and can be employed in any measurable field reasonably represented by a Gaussian random field. Therefore, the present work aims to highlight the following topics:•A study-case of stochastic strain field reconstruction aims to contribute to uncertainty quantification of rock experimental procedures.•A stochastic minimization algorithm is presented to solve the maximum likelihood estimation to define the most suitable hyper-parameter: correlation length.•The calculated hyper-parameters of a set correlation functions are presented to best reproduce the strain fields of a rock sample.

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Reliable data are essential to obtain adequate simulations for forecasting the dynamics of epidemics. In this context, several political, economic, and social factors may cause inconsistencies in the reported data, which reflect the capacity for realistic simulations and predictions. In the case of COVID-19, for example, such uncertainties are mainly motivated by large-scale underreporting of cases due to reduced testing capacity in some locations. In order to mitigate the effects of noise in the data used to estimate parameters of models, we propose strategies capable of improving the ability to predict the spread of the diseases. Using a compartmental model in a COVID-19 study case, we show that the regularization of data by means of Gaussian process regression can reduce the variability of successive forecasts, improving predictive ability. We also present the advantages of adopting parameters of compartmental models that vary over time, in detriment to the usual approach with constant values.

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Tracking control of specific variables is key to achieve a proper fermentation. This paper analyzes a fed-batch bioethanol production process. For this system, a controller design based on linear algebra is proposed. Moreover, to achieve a reliable control, on-line monitoring of certain variables is needed. In this sense, for unmeasurable variables, state estimators based on Gaussian processes are designed. Cell, ethanol and glycerol concentrations are predicted with only substrates measurement. Simulation results when the controller and estimators are coupled, are shown. Furthermore, the algorithms were tested with parametric uncertainties and disturbances in the control action, and are compared, in all cases, with neural networks estimators (previous work). Bayesian estimators show a performance improvement, which is reflected in a decrease of the total error. Proposed techniques give reliable monitoring and control tools, with a low computational and economic cost, and less mathematical complexity than neural network estimators.

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Based on the application of the conditional mean rule, a sampling-recovery algorithm is studied for a Gaussian two-dimensional process. The components of such a process are the input and output processes of an arbitrary linear system, which are characterized by their statistical relationships. Realizations are sampled in both processes, and the number and location of samples in the general case are arbitrary for each component. As a result, general expressions are found that determine the optimal structure of the recovery devices, as well as evaluate the quality of recovery of each component of the two-dimensional process. The main feature of the obtained algorithm is that the realizations of both components or one of them is recovered based on two sets of samples related to the input and output processes. This means that the recovery involves not only its own samples of the restored realization, but also the samples of the realization of another component, statistically related to the first one. This type of general algorithm is characterized by a significantly improved recovery quality, as evidenced by the results of six non-trivial examples with different versions of the algorithms. The research method used and the proposed general algorithm for the reconstruction of multidimensional Gaussian processes have not been discussed in the literature.

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The present study proposes a Gaussian process regression (GPR) approach to develop a model to predict true metabolizable energy corrected for nitrogen (TMEn) content of corn samples (as model output) for poultry given levels of feed chemical compositions of crude protein, ether extract, crude fiber, and ash (as model inputs). A 30 corn samples obtained from 5 origins [Brazil (n = 9), China (n = 5), Iran (n = 7), and Ukraine (n = 9)] were assayed to determine chemical composition and TMEn content using chemical analyses and bioassay technique. In addition to GPR model, data were also analyzed by multiple linear regression (MLR) model. Results revealed that corn samples of different origins differ in their gross energy and chemical composition of crude protein, crude fiber, and ash, but no differences were observed for their ether extract and TMEn contents. Based on model evaluation criteria of R2 and root mean square error (RMSE), the GPR model showed satisfactory performance (R2 = 0.92 and RMSE = 33.68 kcal/kg DM) in predicting TMEn and produced relatively better prediction values than those produce by MLR (R2 = 0.23 and RMSE = 104.85 kcal/kg DM). The GPR model may be capable of improving our aptitude and capacity to precisely predict energy contents of feed ingredients to formulate optimal diets for poultry.

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Aims: Assessment of minimum lumen areas in intravascular ultrasound (IVUS) pullbacks is time-consuming and demands adequately trained personnel. In this work, we introduce a novel and fully automated pipeline to segment the lumen boundary in IVUS datasets. Methods and results: First, an automated gating is applied to select end-diastolic frames and bypass saw-tooth artefacts. Second, within a machine learning (ML) environment, we automatically segment the lumen boundary using a multi-frame (MF) convolutional neural network (MFCNN). Finally, we use the theory of Gaussian processes (GPs) to regress the final lumen boundary. The dataset consisted of 85 IVUS pullbacks (52 patients). The dataset was partitioned at the pullback-level using 73 pullbacks for training (20 586 frames), 6 pullbacks for validation (1692 frames), and 6 for testing (1692 frames). The degree of overlapping, between the ground truth and ML contours, median (interquartile range, IQR) systematically increased from 0.896 (0.874-0.933) for MF1 to 0.925 (0.911-0.948) for MF11. The median (IQR) of the distance error was also reduced from 3.83 (2.94-4.98)% for MF1 to 3.02 (2.25-3.95)% for MF11-GP. The corresponding median (IQR) in the lumen area error remained between 5.49 (2.50-10.50)% for MF1 and 5.12 (2.15-9.00)% for MF11-GP. The dispersion in the relative distance and area errors consistently decreased as we increased the number of frames, and also when the GP regressor was coupled to the MFCNN output. Conclusion: These results demonstrate that the proposed ML approach is suitable to effectively segment the lumen boundary in IVUS scans, reducing the burden of costly and time-consuming manual delineation.

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OBJECTIVE: An obsessive-compulsive disorder (OCD) subtype has been associated with streptococcal infections and is called pediatric autoimmune neuropsychiatric disorders associated with streptococci (PANDAS). The neuroanatomical characterization of subjects with this disorder is crucial for the better understanding of its pathophysiology; also, evaluation of these features as classifiers between patients and controls is relevant to determine potential biomarkers and useful in clinical diagnosis. This was the first multivariate pattern analysis (MVPA) study on an early-onset OCD subtype. METHODS: Fourteen pediatric patients with PANDAS were paired with 14 healthy subjects and were scanned to obtain structural magnetic resonance images (MRI). We identified neuroanatomical differences between subjects with PANDAS and healthy controls using voxel-based morphometry, diffusion tensor imaging (DTI), and surface analysis. We investigated the usefulness of these neuroanatomical differences to classify patients with PANDAS using MVPA. RESULTS: The pattern for the gray and white matter was significantly different between subjects with PANDAS and controls. Alterations emerged in the cortex, subcortex, and cerebellum. There were no significant group differences in DTI measures (fractional anisotropy, mean diffusivity, radial diffusivity, and axial diffusivity) or cortical features (thickness, sulci, volume, curvature, and gyrification). The overall accuracy of 75% was achieved using the gray matter features to classify patients with PANDAS and healthy controls. CONCLUSION: The results of this integrative study allow a better understanding of the neural substrates in this OCD subtype, suggesting that the anatomical gray matter characteristics could have an immune origin that might be helpful in patient classification.

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Marginal structural models (MSMs) are a general class of causal models for specifying the average effect of treatment on an outcome. These models can accommodate discrete or continuous treatments, as well as treatment effect heterogeneity (causal effect modification). The literature on estimation of MSM parameters has been dominated by semiparametric estimation methods, such as inverse probability of treatment weighted (IPTW). Likelihood-based methods have received little development, probably in part due to the need to integrate out confounders from the likelihood and due to reluctance to make parametric modeling assumptions. In this article we develop a fully Bayesian MSM for continuous and survival outcomes. In particular, we take a Bayesian nonparametric (BNP) approach, using a combination of a dependent Dirichlet process and Gaussian process to model the observed data. The BNP approach, like semiparametric methods such as IPTW, does not require specifying a parametric outcome distribution. Moreover, by using a likelihood-based method, there are potential gains in efficiency over semiparametric methods. An additional advantage of taking a fully Bayesian approach is the ability to account for uncertainty in our (uncheckable) identifying assumption. To this end, we propose informative prior distributions that can be used to capture uncertainty about the identifying "no unmeasured confounders" assumption. Thus, posterior inference about the causal effect parameters can reflect the degree of uncertainty about this assumption. The performance of the methodology is evaluated in several simulation studies. The results show substantial efficiency gains over semiparametric methods, and very little efficiency loss over correctly specified maximum likelihood estimates. The method is also applied to data from a study on neurocognitive performance in HIV-infected women and a study of the comparative effectiveness of antihypertensive drug classes.

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