An adaptive ensemble filter for heavy-tailed distributions: tuning-free inflation and localization

Heavy tails is a common feature of filtering distributions that results from the nonlinear dynamical and observation processes as well as the uncertainty from physical sensors. In these settings, the Kalman filter and its ensemble version - the ensemble Kalman filter (EnKF) - that have been designed under Gaussian assumptions result in degraded performance. t-distributions are a parametric family of distributions whose tail-heaviness is modulated by a degree of freedom $\nu$. Interestingly, Cauchy and Gaussian distributions correspond to the extreme cases of a t-distribution for $\nu = 1$ and $\nu = \infty$, respectively. Leveraging tools from measure transport (Spantini et al., SIAM Review, 2022), we present a generalization of the EnKF whose prior-to-posterior update leads to exact inference for t-distributions. We demonstrate that this filter is less sensitive to outlying synthetic observations generated by the observation model for small $\nu$. Moreover, it recovers the Kalman filter for $\nu = \infty$. For nonlinear state-space models with heavy-tailed noise, we propose an algorithm to estimate the prior-to-posterior update from samples of joint forecast distribution of the states and observations. We rely on a regularized expectation-maximization (EM) algorithm to estimate the mean, scale matrix, and degree of freedom of heavy-tailed \textit{t}-distributions from limited samples (Finegold and Drton, arXiv preprint, 2014). Leveraging the conditional independence of the joint forecast distribution, we regularize the scale matrix with an $l1$ sparsity-promoting penalization of the log-likelihood at each iteration of the EM algorithm. By sequentially estimating the degree of freedom at each analysis step, our filter can adapt its prior-to-posterior update to the tail-heaviness of the data. We demonstrate the benefits of this new ensemble filter on challenging filtering problems.Comment: 28 pages, 9 figure

Psychosocial health among immigrants in central and southern Europe.

Migration exposes people to a number of risks that threaten their health, including those related to psychosocial health. Self-perceived health is usually the main indicator used to assess psychosocial health. Electronic databases were used to examine the literature on the psychosocial health of immigrants in Europe and of North Africans living in their own countries. Immigrants of various ethnic groups show a similar risk of psychosocial disorders but generally present a higher risk than the local population. This risk is related to gender (being higher in women), poor socio-economic status and acculturation, discrimination, time elapsed since migration and age on arrival in the new country. Although the stressors and situations the different ethnic groups experience in the host country may be shared, the way they deal with them may differ according to cultural factors. There is a need to collect detailed data on psychosocial health among the various immigrant groups in Europe, as well as to monitor this aspect in North African residents who lack access to specific services

Asymmetric Autocorrelation Function To Resolve Directional Ambiguity In PIV Images

ABSTRACT Autocorrelation of a double-exposed image, unlike cross-correlation between two images, produces a correlation function that i

Discovery of 6.035GHz Hydroxyl Maser Flares in IRAS18566+0408

We report the discovery of 6.035GHz hydroxyl (OH) maser flares toward the massive star forming region IRAS18566+0408 (G37.55+0.20), which is the only region known to show periodic formaldehyde (4.8 GHz H2CO) and methanol (6.7 GHz CH3OH) maser flares. The observations were conducted between October 2008 and January 2010 with the 305m Arecibo Telescope in Puerto Rico. We detected two flare events, one in March 2009, and one in September to November 2009. The OH maser flares are not simultaneous with the H2CO flares, but may be correlated with CH3OH flares from a component at corresponding velocities. A possible correlated variability of OH and CH3OH masers in IRAS18566+0408 is consistent with a common excitation mechanism (IR pumping) as predicted by theory.Comment: Accepted for publication in the Astrophysical Journa

Chemical and isotopic fractionation of lead in the surface soils of Egypt

Chemical fractionation via sequential extraction (SEP) combined with isotopic analysis of Pb was used to investigate the origins and reactivity of Pb in 66 topsoil samples collected from 12 different locations in Egypt. The total soil Pb concentrations (TPb) covered a wide range (∼80–16,000 mg kg−1), but were only elevated in four industrial and urban locations within Cairo and Alexandria. In all the other locations values of TPb were generally low and were close to the average crustal Pb concentration of 14 mg kg−1. The largest Pb fraction in all soils, with the exception of two industrial locations, was the ‘residual’ fraction (38–63% of TPb) followed by Pb bound to ‘organic’ and ‘metal oxide’ phases. The Pb isotopic signatures (206Pb/207Pb vs 208Pb/207Pb) of all samples in all SEP fractions were highly variable, suggesting a heterogeneous mix of Pb contamination sources; however, they aligned closely to a binary mixing line between geogenic and petrol Pb sources. There were similar Pb isotopic patterns across all of the non-residual fractions with measureable data (F2 – F4) suggesting that the non-residual anthropogenic-Pb and geogenic-Pb have been assimilated into common pools within the soil. Binary and ternary source-apportionment models based on Pb isotopic ratios and abundances showed that the relative contribution of petrol-Pb and geogenic-Pb can be ascribed with reasonable certainty. However, the contribution of further sources can only be accounted for if the isotopic abundance of all end-members are known and are at the periphery of the soils dataset

An approximate empirical Bayesian method for large-scale linear-Gaussian inverse problems

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often determined via an empirical Bayesian method that maximizes the marginal likelihood function, i.e., the probability density of the data conditional on the hyperparameters. Evaluating the marginal likelihood, however, is computationally challenging for large-scale problems. In this work, we present a method to approximately evaluate marginal likelihood functions, based on a low-rank approximation of the update from the prior covariance to the posterior covariance. We show that this approximation is optimal in a minimax sense. Moreover, we provide an efficient algorithm to implement the proposed method, based on a combination of the randomized SVD and a spectral approximation method to compute square roots of the prior covariance matrix. Several numerical examples demonstrate good performance of the proposed method

Meningococcal disease in children in Merseyside, England:a 31 year descriptive study

Meningococcal disease (MCD) is the leading infectious cause of death in early childhood in the United Kingdom, making it a public health priority. MCD most commonly presents as meningococcal meningitis (MM), septicaemia (MS), or as a combination of the two syndromes (MM/MS). We describe the changing epidemiology and clinical presentation of MCD, and explore associations with socioeconomic status and other risk factors. A hospital-based study of children admitted to a tertiary children's centre, Alder Hey Children's Foundation Trust, with MCD, was undertaken between 1977 to 2007 (n = 1157). Demographics, clinical presentations, microbiological confirmation and measures of deprivation were described. The majority of cases occurred in the 1-4 year age group and there was a dramatic fall in serogroup C cases observed with the introduction of the meningococcal C conjugate (MCC) vaccine. The proportion of MS cases increased over the study period, from 11% in the first quarter to 35% in the final quarter. Presentation with MS (compared to MM) and serogroup C disease (compared to serogroup B) were demonstrated to be independent risk factors for mortality, with odds ratios of 3.5 (95% CI 1.18 to 10.08) and 2.18 (95% CI 1.26 to 3.80) respectively. Cases admitted to Alder Hey were from a relatively more deprived population (mean Townsend score 1.25, 95% CI 1.09 to 1.41) than the Merseyside reference population. Our findings represent one of the largest single-centre studies of MCD. The presentation of MS is confirmed to be a risk factor of mortality from MCD. Our study supports the association between social deprivation and MCD

Bariatric surgery tourism in the COVID-19 era

Background: Since the start of the Covid-19 pandemic primary and secondary health care services in Northern Ireland have observed an increase in the number of patients who have had bariatric surgery outside of the UK. This study sought to estimate the frequency of bariatric surgery tourism and to audit indications, blood monitoring and medical complications.Methods: All primary care centres within the Western Health Social Care Trust (WHSCT) were invited to document the number of patients undergoing bariatric surgery between January 1, 2017 and December 31, 2022. For one primary care centre, patients who underwent bariatric surgery were assessed against the National Institute of Health and Clinical Excellence (NICE) guideline indications for bariatric surgery. In addition, the blood monitoring of these patients was audited against the British Obesity and Metabolic Surgery Society (BOMSS) guidelines for up to two years following surgery. Medical contacts for surgical complications of bariatric surgery were recorded.Results: Thirty-five of 47 (74.5%) GP surgeries replied to the survey, representing 239,961 patients among 325,126 registrations (73.8%). In the six year study period 463 patients had reported having bariatric surgery to their GP. Women were more likely to have had bariatric surgery than men (85.1% versus 14.9%). There was a marked increase in the number of patients undergoing bariatric surgery with each year of the study (p&lt;0.0001 chi square for trend). Twenty-one of 47 patients (44.7%) evaluated in one primary care centre fulfilled NICE criteria for bariatric surgery. The level of three-month monitoring ranged from 23% (for vitamin D) to 89% (electrolytes), but decreased at two years to 9% (vitamin D) and 64% (electrolytes and liver function tests). Surgical complication prevalence from wound infections was 19% (9 of 44). Antidepressant medications were prescribed for 23 of 47 patients (48.9%).Conclusions: The WHSCT has experienced a growing population of patients availing of bariatric surgery outside of the National Health Service. In view of this and the projected increase in obesity prevalence, a specialist obesity management service is urgently required in Northern Ireland.</p

Robust Online Hamiltonian Learning

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance.Comment: 24 pages, 12 figures; to appear in New Journal of Physic