Approximation of Bayesian inverse problems for PDEs

Inverse problems are often ill posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is based on an approach to regularization, employing a Bayesian formulation of the problem, which leads to a notion of well posedness for inverse problems, at the level of probability measures. The stability which results from this well posedness may be used as the basis for quantifying the approximation, in finite dimensional spaces, of inverse problems for functions. This paper contains a theory which utilizes this stability property to estimate the distance between the true and approximate posterior distributions, in the Hellinger metric, in terms of error estimates for approximation of the underlying forward problem. This is potentially useful as it allows for the transfer of estimates from the numerical analysis of forward problems into estimates for the solution of the related inverse problem. It is noteworthy that, when the prior is a Gaussian random field model, controlling differences in the Hellinger metric leads to control on the differences between expected values of polynomially bounded functions and operators, including the mean and covariance operator. The ideas are applied to some non-Gaussian inverse problems where the goal is determination of the initial condition for the Stokes or Navier–Stokes equation from Lagrangian and Eulerian observations, respectively

Variational data assimilation using targetted random walks

The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis (offline hindcasting). In either of these scenarios it can be important to assess uncertainties in the assimilated state. Ideally it would be desirable to have complete information concerning the Bayesian posterior distribution for unknown state, given data. The purpose of this paper is to show that complete computational probing of this posterior distribution is now within reach in the offline situation. In this paper we will introduce an MCMC method which enables us to directly sample from the Bayesian\ud posterior distribution on the unknown functions of interest, given observations. Since we are aware that these\ud methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however more sophisticated MCMC methods are available\ud which do exploit derivative information. For simplicity of exposition we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number (Stokes flow) scenario in a two dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces

Bone mineral density in Iranian patients: Effects of age, sex, and body mass index

Introduction: Osteoporosis is a multifactorial skeletal disease that is characterized by reduced bone mineral density (BMD). BMD values de-pend on several factors such as age, sex and age at menopause. The purpose of this study was to determine the prevalence and changes in bone mineral density in Iranian patients. Meth-ods: Three hundred patients were selected through random sampling technique in 2009. BMD was assessed by Norland (Excell) technique at the lumbar and femoral neck. Weight and height were measured through standard methods. A thorough history was taken from each patient. The data was analyzed using SPSS software version 13.0. P-values less than 0.05 were con-sidered statistically significant. Results: From among the 300 studied patients, 86.6% were fe-male. their mean age was 52.7 years. Their av-erage body mass index (BMI) was 28.14 kg/m2. Mean T-Score at lumbar spine and femoral neck was −1.07 ± 1.19 and −1.75 ± 1.33 respectively. Mean BMD value at lumbar spine and femoral neck was 0.92 ± 0.19 and 0.77 ± 0.16 respectively. The prevalence of osteoporosis at lumbar spine and femoral neck was 33.7% and 16.7, respec-tively. There was a significant correlation be-tween age, BMI and BMD values (P-Value < 0.01). Correlation between gender and BMD value at the lumbar spine and femoral neck was not sig-nificant. Conclusion: This study shows that age- ing and low BMI are risk factors associated with bone loss. it is recommended to measure BMD and implement prevention programs for high- risk people. Keywords: Bone Mineral Density; Body Mass Index;Age; Gende

Roles and Routines in Investigative Journalism in Collaborative Environments

&nbsp;A global network of journalistic networks has transformed investigative journalism over the past two decades, adding layers of collaboration to what was previously an individual pursuit. A recent case&nbsp;of collaborative investigative reporting at its best was a worldwide effort to reveal breaches of tax haven information, through&nbsp;the Panama Papers (2016). As a result of these remarkable accomplishments, study&nbsp;on multi countries partnership&nbsp;is rising. However, it's still unclear how this combining&nbsp;of facilities, connections and time&nbsp;has influenced day-to-day operation. Newsrooms in developing and heritage newsrooms are navigating their patterns and duties while creating new investigative journalistic practices. The Guardian, a mainstream media firm that has worked at both the domestic&nbsp;and international&nbsp;levels, and Bureau Local, a society/neighborhood&nbsp;journalism co-op, are all given as examples. These actors use a language of justification to explain the differences between the old and the new. While "new" ideas become more common with time, notions like cooperation are also becoming&nbsp;element of decision making&nbsp;process, and information and information&nbsp;development take place within the conventional&nbsp;context of reporting

Pulmonary tuberculosis and some underlying conditions in Golestan Province of Iran, during 2001-2005

Context: Pulmonary tuberculosis has been a major health problem in Golestan province of Iran. Aims: This descriptive cross-sectional study was performed to evaluate the frequency of coexisting medical conditions and their effects on some epidemiologic factors in patients with pulmonary tuberculosis. Setting and Design: This was a descriptive cross-sectional study. Methods and Material: Demographic information, time of admission in the hospital and coexisting medical conditions (diabetes, chronic renal failure/hemodyalysis, corticosteroids consumption and malignancies) were extracted from the patient's file. Statistical analysis used: Chi-square test was used to assess the relationship between variables. Results: Two hundred forty three patients with pulmonary tuberculosis during 5 years were studied. Out of all, 162 cases (66.7%) did not have any co-morbidities. Diabetes mellitus was found to be the most prevalent condition (23.05%) followed by chronic renal failure, corticosteroid consumption and malignancy ranking second, third and forth in the list (5.8%, 2.5% and 2 respectively). The mean age of the patients was 50.15±19 years old. In the group without co morbidities, male/ female ratio was 1.41/1, but co morbidity with diabetes was significantly more prevalent in females (p<0.05). Conclusions: We suggest screening of tuberculosis in patients with chronic renal failure and diabetes mellitus in our area. Also for patients with pulmonary tuberculosis, diabetes screening should be considered essential