Scaled unscented transform Gaussian sum filter: theory and application

In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf ... This work is on the construction of the Gaussian sum filter based on the scaled unscented transform

Optimal projection of observations in a Bayesian setting

Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on information theory: the projection that minimizes the Kullback-Leibler divergence between the posterior distributions of the original and the projected models, the one that minimizes the expected Kullback-Leibler divergence between the same distributions, and the one that maximizes the mutual information between the parameter of interest and the projected observations. The first two optimization problems are formulated as the determination of an optimal subspace and therefore the solution is computed using Riemannian optimization algorithms on the Grassmann manifold. Regarding the maximization of the mutual information, it is shown that there exists an optimal subspace that minimizes the entropy of the posterior distribution of the reduced model; a basis of the subspace can be computed as the solution to a generalized eigenvalue problem; an a priori error estimate on the mutual information is available for this particular solution; and that the dimensionality of the subspace to exactly conserve the mutual information between the input and the output of the models is less than the number of parameters to be inferred. Numerical applications to linear and nonlinear models are used to assess the efficiency of the proposed approaches, and to highlight their advantages compared to standard approaches based on the principal component analysis of the observations

Coordinate Transformation and Polynomial Chaos for the Bayesian Inference of a Gaussian Process with Parametrized Prior Covariance Function

This paper addresses model dimensionality reduction for Bayesian inference based on prior Gaussian fields with uncertainty in the covariance function hyper-parameters. The dimensionality reduction is traditionally achieved using the Karhunen-\Loeve expansion of a prior Gaussian process assuming covariance function with fixed hyper-parameters, despite the fact that these are uncertain in nature. The posterior distribution of the Karhunen-Lo\`{e}ve coordinates is then inferred using available observations. The resulting inferred field is therefore dependent on the assumed hyper-parameters. Here, we seek to efficiently estimate both the field and covariance hyper-parameters using Bayesian inference. To this end, a generalized Karhunen-Lo\`{e}ve expansion is derived using a coordinate transformation to account for the dependence with respect to the covariance hyper-parameters. Polynomial Chaos expansions are employed for the acceleration of the Bayesian inference using similar coordinate transformations, enabling us to avoid expanding explicitly the solution dependence on the uncertain hyper-parameters. We demonstrate the feasibility of the proposed method on a transient diffusion equation by inferring spatially-varying log-diffusivity fields from noisy data. The inferred profiles were found closer to the true profiles when including the hyper-parameters' uncertainty in the inference formulation.Comment: 34 pages, 17 figure

Data assimilation using bayesian filters and B-spline geological models

This paper proposes a new approach to problems of data assimilation, also known as history matching, of oilfield production data by adjustment of the location and sharpness of patterns of geological facies. Traditionally, this problem has been addressed using gradient based approaches with a level set parameterization of the geology. Gradient-based methods are robust, but computationally demanding with real-world reservoir problems and insufficient for reservoir management uncertainty assessment. Recently, the ensemble filter approach has been used to tackle this problem because of its high efficiency from the standpoint of implementation, computational cost, and performance. Incorporation of level set parameterization in this approach could further deal with the lack of differentiability with respect to facies type, but its practical implementation is based on some assumptions that are not easily satisfied in real problems. In this work, we propose to describe the geometry of the permeability field using B-spline curves. This transforms history matching of the discrete facies type to the estimation of continuous B-spline control points. As filtering scheme, we use the ensemble square-root filter (EnSRF). The efficacy of the EnSRF with the B-spline parameterization is investigated through three numerical experiments, in which the reservoir contains a curved channel, a disconnected channel or a 2-dimensional closed feature. It is found that the application of the proposed method to the problem of adjusting facies edges to match production data is relatively straightforward and provides statistical estimates of the distribution of geological facies and of the state of the reservoir

Physical Activity and Obesity Indicators: National Cross Sectional Study on Lebanese Adults

Association between higher levels of physical activity and lower rates of obesity has been shown. The aim is to assess the relation between the prevalence of physical activity and the Physical Activity Index (PAI) of 300 Lebanese healthy adults, with age, gender, occupation, body mass indices and waist circumferences (WC). The cutoff points of WC for both genders were determined using the values of Body Mass Index (BMI). A cross-sectional study using self-reported valid questionnaire was conducted randomly on 150 men and 150 women, between 18 and 74 years, from Beirut region. Association between variables was performed using chi2, T-Test and ANOVA. Linear regression determined the WC cutoffs based on BMI. 22% of the population was obese with WC mean level of 92.47±14.4cm (87.71±14.4 cm for women and 97.24±12.96 cm for men). The prevalence of physical activity was 34% in overall population (27% in women and 40% in men).There was no significant association between BMI values and PAI (p< 0.085 for men and p< 0.300 for women). However there was an inverse association between WC values and PAI in both genders (p<0.043 in men and p< 0.036 in women). Linear regression showed WC cut-off point in Lebanese women with BMI ≥25 kg/m2 and ≥30 kg/m2 of 86 cm and 100 cm respectively, whereas for men it was 92.12 cm and 105 cm respectively. The prevalence of physical activity in Beirut is low with differences among genders. The highest physical activity index is associated with the decreased values of waist circumference

Biological Properties of SARS-CoV-2 Variants: Epidemiological Impact and Clinical Consequences

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a virus that belongs to the coronavirus family and is the cause of coronavirus disease 2019 (COVID-19). As of May 2022, it had caused more than 500 million infections and more than 6 million deaths worldwide. Several vaccines have been produced and tested over the last two years. The SARS-CoV-2 virus, on the other hand, has mutated over time, resulting in genetic variation in the population of circulating variants during the COVID-19 pandemic. It has also shown immune-evading characteristics, suggesting that vaccinations against these variants could be potentially ineffective. The purpose of this review article is to investigate the key variants of concern (VOCs) and mutations of the virus driving the current pandemic, as well as to explore the transmission rates of SARS-CoV-2 VOCs in relation to epidemiological factors and to compare the virus’s transmission rate to that of prior coronaviruses. We examined and provided key information on SARS-CoV-2 VOCs in this study, including their transmissibility, infectivity rate, disease severity, affinity for angiotensin-converting enzyme 2 (ACE2) receptors, viral load, reproduction number, vaccination effectiveness, and vaccine breakthrough

Evaluating tropical phytoplankton phenology metrics using contemporary tools

The timing of phytoplankton growth (phenology) in tropical oceans is a crucial factor influencing the survival rates of higher trophic levels, food web structure and the functioning of coral reef ecosystems. Phytoplankton phenology is thus categorised as an ‘ecosystem indicator’, which can be utilised to assess ecosystem health in response to environmental and climatic perturbations. Ocean-colour remote sensing is currently the only technique providing global, long-term, synoptic estimates of phenology. However, due to limited available in situ datasets, studies dedicated to the validation of satellite-derived phenology metrics are sparse. The recent development of autonomous oceanographic observation platforms provides an opportunity to bridge this gap. Here, we use satellite-derived surface chlorophyll-a (Chl-a) observations, in conjunction with a Biogeochemical-Argo dataset, to assess the capability of remote sensing to estimate phytoplankton phenology metrics in the northern Red Sea – a typical tropical marine ecosystem. We find that phenology metrics derived from both contemporary platforms match with a high degree of precision (within the same 5-day period). The remotely-sensed surface signatures reflect the overall water column dynamics and successfully capture Chl-a variability related to convective mixing. Our findings offer important insights into the capability of remote sensing for monitoring food availability in tropical marine ecosystems, and support the use of satellite-derived phenology as an ecosystem indicator for marine management strategies in regions with limited data availability