Distribution Of Observed Data Research Articles

Linear Deconfounded Score Method: Scoring DAGs With Dense Unobserved Confounding.

This article deals with the discovery of causal relations from a combination of observational data and qualitative assumptions about the nature of causality in the presence of unmeasured confounding. We focus on applications where unobserved variables are known to have a widespread effect on many of the observed ones, which makes the problem particularly difficult for constraint-based methods, because most pairs of variables are conditionally dependent given any other subset, rendering the causal effect unidentifiable. In this article, we show that under the principle of independent mechanisms, unobserved confounding in this setting leaves a statistical footprint in the observed data distribution that allows for disentangling spurious and causal effects. Using this insight, we demonstrate that a sparse linear Gaussian directed acyclic graph (DAG) among observed variables may be recovered approximately and propose a simple adjusted score-based causal discovery algorithm that may be implemented with general-purpose solvers and scales to high-dimensional problems. We find, in addition, that despite the conditions we pose to guarantee causal recovery, performance in practice is robust to large deviations in model assumptions, and extensions to nonlinear structural models are possible.

Multiply robust estimators in longitudinal studies with missing data under control-based imputation.

Longitudinal studies are often subject to missing data. The recent guidance from regulatory agencies, such as the ICH E9(R1) addendum addresses the importance of defining a treatment effect estimand with the consideration of intercurrent events. Jump-to-reference (J2R) is one classical control-based scenario for the treatment effect evaluation, where the participants in the treatment group after intercurrent events are assumed to have the same disease progress as those with identical covariates in the control group. We establish new estimators to assess the average treatment effect based on a proposed potential outcomes framework under J2R. Various identification formulas are constructed, motivating estimators that rely on different parts of the observed data distribution. Moreover, we obtain a novel estimator inspired by the efficient influence function, with multiple robustness in the sense that it achieves n1/2-consistency if any pairs of multiple nuisance functions are correctly specified, or if the nuisance functions converge at a rate not slower than n-1/4 when using flexible modeling approaches. The finite-sample performance of the proposed estimators is validated in simulation studies and an antidepressant clinical trial.

Bounding the probabilities of benefit and harm through sensitivity parameters and proxies

Abstract We present two methods for bounding the probabilities of benefit (a.k.a. the probability of necessity and sufficiency, i.e., the desired effect occurs if and only if exposed) and harm (i.e., the undesired effect occurs if and only if exposed) under unmeasured confounding. The first method computes the upper or lower bound of either probability as a function of the observed data distribution and two intuitive sensitivity parameters, which can then be presented to the analyst as a 2-D plot to assist in decision-making. The second method assumes the existence of a measured nondifferential proxy for the unmeasured confounder. Using this proxy, tighter bounds than the existing ones can be derived from just the observed data distribution.

Deep Direct Discriminative Decoders for High-dimensional Time-series Data Analysis

The state-space models (SSMs) are widely utilized in the analysis of time-series data. SSMs rely on an explicit definition of the state and observation processes. Characterizing these processes is not always easy and becomes a modeling challenge when the dimension of observed data grows or the observed data distribution deviates from the normal distribution. Here, we propose a new formulation of SSM for high-dimensional observation processes with a heavy-tailed distribution. We call this solution the deep direct discriminative process (D4). The D4 brings deep neural networks’ expressiveness and scalability to the SSM formulation letting us build a novel solution that efficiently estimates the underlying state processes through high-dimensional observation signal.We demonstrate the D4 solutions in simulated and real data such as Lorenz attractors, Langevin dynamics, random walk dynamics, and rat hippocampus spiking neural data and show that the D4’s performance precedes traditional SSMs and RNNs. The D4 can be applied to a broader class of time-series data where the connection between high-dimensional observation and the underlying latent process is hard to characterize.

Mapping the milky way’s stellar halo with 2D data

ABSTRACT We propose a new method for measuring the spatial density distribution of the stellar halo of the Milky Way. Our method is based on a pairwise statistic of the distribution of stars in the sky, the angular two-point correlation function (ATPCF). The ATPCF utilizes two-dimensional data of stars only and is therefore immune to the large uncertainties in the determination of distances to stars. We test our method using mock stellar data coming from various models including the single power-law (SPL) and the broken power-law (BPL) density profiles. We also test the influence of axisymmetric flattening factors using both constant and varying values. We find that the ATPCF is a powerful tool for recovering the spatial distributions of the stellar haloes in our models. We apply our method to observational data from the type ab RR Lyrae catalogue in the Catalina Survey Data Release 1. In the 3-parameter BPL model, we find that $s_{1}=2.46_{-0.20}^{+0.18}, s_{2}=3.99_{-1.33}^{+0.75}$, and $r_{0}=31.11_{-5.88}^{+7.61}$, which are in good agreement with previous results. We also find that introducing an extra parameter, the radially varying flattening factor, greatly improves our ability to model accurately the observed data distribution. This implies perhaps that the stellar halo of the Milky Way should be regarded as oblate.

Medical prediction from missing data with max-minus negative regularized dropout.

Missing data is a naturally common problem faced in medical research. Imputation is a widely used technique to alleviate this problem. Unfortunately, the inherent uncertainty of imputation would make the model overfit the observed data distribution, which has a negative impact on the model generalization performance. R-Drop is a powerful technique to regularize the training of deep neural networks. However, it fails to differentiate the positive and negative samples, which prevents the model from learning robust representations. To handle this problem, we propose a novel negative regularization enhanced R-Drop scheme to boost performance and generalization ability, particularly in the context of missing data. The negative regularization enhanced R-Drop additionally forces the output distributions of positive and negative samples to be inconsistent with each other. Especially, we design a new max-minus negative sampling technique that uses the maximum in-batch values to minus the mini-batch to yield the negative samples to provide sufficient diversity for the model. We test the resulting max-minus negative regularized dropout method on three real-world medical prediction datasets, including both missing and complete cases, to show the effectiveness of the proposed method.

Dirichlet process mixture models for the analysis of repeated attempt designs.

In longitudinal studies, it is not uncommon to make multiple attempts to collect a measurement after baseline. Recording whether these attempts are successful provides useful information for the purposes of assessing missing data assumptions. This is because measurements from subjects who provide the data after numerous failed attempts may differ from those who provide the measurement after fewer attempts. Previous models for these designs were parametric and/or did not allow sensitivity analysis. For the former, there are always concerns about model misspecification and for the latter, sensitivity analysis is essential when conducting inference in the presence of missing data. Here, we propose a new approach which minimizes issues with model misspecification by using Bayesian nonparametrics for the observed data distribution. We also introduce a novel approach for identification and sensitivity analysis. We re-analyze the repeated attempts data from a clinical trial involving patients with severe mental illness and conduct simulations to better understand the properties of ourapproach.

Fault Diagnosis for Complex Equipment Based on Belief Rule Base with Adaptive Nonlinear Membership Function

Fault diagnosis of complex equipment has become a hot field in recent years. Due to excellent uncertainty processing capability and small sample problem modeling capability, belief rule base (BRB) has been widely used in the fault diagnosis. However, previous BRB models almost did not consider the diverse distributions of observation data which may reduce diagnostic accuracy. In this paper, a new fault diagnosis model based on BRB is proposed. Considering that the previous triangular membership function cannot address the diverse distribution of observation data, a new nonlinear membership function is proposed to transform the input information. Then, since the model parameters initially determined by experts are inaccurate, a new parameter optimization model with the parameters of the nonlinear membership function is proposed and driven by the gradient descent method to prevent the expert knowledge from being destroyed. A fault diagnosis case of laser gyro is used to verify the validity of the proposed model. In the case study, the diagnosis accuracy of the new BRB-based fault diagnosis model reached 95.56%, which shows better fault diagnosis performance than other methods.

Interplay of turbulence and proton-microinstability growth in space plasmas

Numerous prior studies have shown that as proton beta increases, a narrower range of proton temperature anisotropy values is observed. This effect has often been ascribed to the actions of kinetic microinstabilities because the distribution of observational data aligns with contours of constant instability growth rates in the beta-anisotropy plane. However, the linear Vlasov theory of instabilities assumes a uniform background in which perturbations grow. The established success of linear-microinstability theories suggests that the conditions in regions of extreme temperature anisotropy may remain uniform for a long enough time so that the instabilities have the chance to grow to sufficient amplitude. Turbulence, on the other hand, is intrinsically nonuniform and nonlinear. Thin current sheets and other coherent structures generated in a turbulent plasma may quickly destroy the uniformity. It is, therefore, not a-priori obvious whether the presence of intermittency and coherent structures favors or disfavors instabilities. To address this question, we examined the statistical distribution of growth rates associated with proton temperature-anisotropy driven microinstabilities and local nonlinear time scales in turbulent plasmas. Linear growth rates are, on average, substantially less than the local nonlinear rates. However, at the regions of extreme values of temperature anisotropy, near the “edges” of the populated part of the proton temperature anisotropy-parallel beta plane, the instability growth rates are comparable or faster than the turbulence time scales. These results provide a possible answer to the question as to why the linear theory appears to work in limiting plasma excursions in anisotropy and plasma beta.

Constraining the Hubble constant and its lower limit from the proper motion of extragalactic radio jets

ABSTRACT The Hubble constant (H0) is a measurement to describe the expansion rate of the Universe in the current era. However, there is a 4.4σ discrepancy between the measurements from the early Universe and the late Universe. In this research, we propose a model-free and distance-free method to constrain H0. Combining Friedman–Lemaître–Robertson–Walker cosmology with geometrical relation of the proper motion of extragalactic jets, the lower limit (H0,min) of H0 can be determined using only three cosmology-free observables: the redshifts of the host galaxies, and the approaching and receding angular velocities of radio jets. Using these, we propose to use the Kolmogorov–Smirnov test (K–S test) between cumulative distribution functions of H0,min to differentiate cosmology. We simulate 100, 200, and 500 extragalactic jets with three levels of accuracy of the proper motion (μa and μr), at 10, 5, and 1 per cent, corresponding to the accuracies of the current and future radio interferometers. We perform K–S tests between the simulated samples as theoretical distributions with different H0 and power-law index of velocity distribution of jets and mock observational data. Our result suggests increasing sample sizes leads to tighter constraints on both power-law index and the Hubble constant at moderate accuracy (i.e. $10$ and $5{{\ \rm per\ cent}}$), while at $1{{\ \rm per\ cent}}$ accuracy, increasing sample sizes leads to tighter constraints on power-law index more. Improving accuracy results in better constraints in the Hubble constant compared with the power-law index in all cases, but it alleviates the degeneracy.

Use of expert elicitation in the field of occupational hygiene: Comparison of expert and observed data distributions.

The concept of professional judgement underpins the way in which an occupational hygienist assesses an exposure problem. Despite the importance placed on professional judgement in the discipline, a method of assessment to characterise accuracy has not been available. In this paper, we assess the professional judgement of four occupational hygienists (‘experts’) when completing exposure assessments on a range of airborne contaminants across a number of job roles within a surface mining environment in the Pilbara region of Western Australia. The job roles assessed were project driller, mobile equipment operator, fixed plant maintainer, and drill and blast operator. The contaminants of interest were respirable crystalline silica, respirable dust, and inhalable dust. The novel approach of eliciting exposure estimates focusing on contaminant concentration and attribution of an exposure standard estimate was used. The majority of the elicited values were highly skewed; therefore, a scaled Beta distribution were fitted. These elicited fitted distributions were then compared to measured data distributions, the results of which had been collected as part of an occupational hygiene program assessing full-shift exposures to the same contaminants and job roles assessed by the experts. Our findings suggest that the participating experts within this study tended to overestimate exposures. In addition, the participating experts were more accurate at estimating percentage of an exposure standard than contaminant concentration. We demonstrate that this elicitation approach and the encoding methodology contained within can be applied to assess accuracy of exposure judgements which will impact on worker protection and occupational health outcomes.

Projection of Extreme Temperature Events over the Mediterranean and Sahara Using Bias-Corrected CMIP6 Models

Climate change continues to increase the intensity, frequency and impacts of weather and climate extremes. This work uses bias-adjusted Coupled Model Intercomparison Project Phase six (CMIP6) model datasets to investigate the future changes in temperature extremes over Mediterranean (MED) and Sahara (SAH) regions. The mid- (2041–2070) and far-future (2071–2100) are studied under two Shared Socioeconomic Pathways: SSP2-4.5 and SSP5-8.5 scenarios. Quantile mapping function greatly improved the performance of CMIP6 by reducing the notable biases to match the distribution of observation data, the Climate Prediction Center (CPC). Results show persistent significant warming throughout the 21st century, increasing with the increase in radiative forcing. The MED will record a higher increase in temperature extremes as compared to SAH. The warming is supported by the projected reduction in cold days (TX10p) and cold nights (TN10p), with the reduction in the number of cold nights exceeding cold days. Notably, warm spell duration index (WSDI) and summer days (SU) have a positive trend in both timelines over the entire study area. There is a need to simulate how climate sensitive sectors, such as water and agriculture, are likely to be affected by projected changes under different scenarios for informed decision making in the choice and implementation of adaptation and mitigation effective measures.

A spatially constrained skew Student’s-t mixture model for brain MR image segmentation and bias field correction

Accurate segmentation of brain magnetic resonance images is a key step in quantitative analysis of brain images. Finite mixture model is one of the most widely used methods in brain magnetic resonance image segmentation. However, due to the presence of intensity inhomogeneity artifact and noise, the image histogram distribution of brain MR images may follow a heavy tailed distribution or asymmetric distribution, which makes traditional finite mixture model, such as Gaussian mixture model, hard to achieve accurate segmentation results. To alleviate these problems, a novel spatially constrained finite skew student’s-t mixture model is proposed in this paper. Firstly, we propose anisotropic two-level spatial information, which combines the prior and posterior probabilities, to reduce the impact of noise. The proposed spatial information can preserve rich details, such as edges and corners. Secondly, we couple the anisotropic spatial information into the skew student’s-t distribution to fit the intensity distribution of observation data with heavy tail distribution or asymmetric distribution. Thirdly, we use a linear combination of a set of orthogonal basis functions to model the intensity inhomogeneities. Finally, the objective function integrates both tissue segmentation and the bias field estimation. In the implementation, we used an improved expectation maximization (EM) algorithm to estimate the model parameters. The experimental results of our model on synthetic data and brain magnetic resonance images are better than other state-of-the-art segmentation methods.

Immunohematological Parameters of Male and Female Blood Donors at Kenyatta National Hospital

Background: Immunohaematological reference intervals are critical in making accurate decisions in research, diagnosis and monitoring therapeutic outcomes. Consequently any gender – based disparities in the intervals need to be determined and so reflected when utilizing the ranges. This cross-section study to determine male and female immunohaematological reference intervals was conducted on suitable blood donors attended to at Kenyatta National Hospital blood donor Unit between 2018 and 2019.
 Objectives: To determine gender-based means, medians, 2.5 th and 97.5 th interquartile ranges of: CD4+ lymphocytes, red cell values, white cells absolute and differential counts and thrombocyte counts in suitable blood donors.
 Methods: A total of 108 (53.5%) female and 94 (46.5%) male volunteer blood donors aged between 18 and 60 years were recruited consecutively as they consented. Bootstrap methods were used to calculate means, medians and confidence intervals. The enrollees’ social demographic characteristics including: level of education, occupation, alcohol - drinking and smoking habits were captured using a questionnaire form. Immediately after blood donation five milliliters of blood samples for CD4+ analysis and haemogram were drawn from the pilot tube of the blood bag by injecting the cap of ethylene diamine tetra acetate (EDTA)-containing vacutaners with the donation needle. Analyses were done within 8 hours of sample collection using standard laboratory methods. The fit of the observed data distribution was determined using Shapiro – Wilk test with P > 0.05 indicating Gaussian distribution. Statistical analyses were done using SPSS version 21. Means, medians and 2.5 th and 97.5 th interquartiles were determined. Gender – based differences were compared using Mann Whitney U test with P < 0.05 being considered significant.
 Results: The male enrollees had a mean age of 31.91 years, while females’ mean age was 31.85 years. The majority of enrollees had tertially education with most males being in business and in formal employment; while most females were in business. Males demonstrated significantly higher mean values than females in: red blood cells (RBCs), haemoglobin (HB) and eosinophils (E). Significantly lower mean values in males than in females were demonstrated in: white blood cells (WBC), neutrophils (N), Lymphocytes (L), monocytes (M), CD4+ cells and Platelets (P).
 Conclusion: There exists significant gender-based differences in immunohaematological reference ranges that may lead to biased conclusions in laboratory diagnosis and research.

C-Reactive Protein Levels in Male and Female Blood Donors at Kenyatta National Hospital, Kenya

Background: C-reactive protein is an inflammatory marker and has found a wide clinical application in monitoring disease progress, effectiveness of treatment and post-operative complications. Determination of gender – based reference intervals of this protein would be of great value in eliminating any biases in results interpretation. It was in this endeavor that this cross-section study was conducted at Kenyatta National Hospital, blood donor unit, between 2018 and 2019. Objectives: To determine gender-based means, medians and 2.5 th and 97.5 th interquartile ranges of C-reactive protein (CRP) in suitable blood donors attended to at the blood donor unit of Kenyatta National Hospital, Kenya. Methods: A total of 108 (53.5%) female and 94 (46.5%) male volunteer blood donors aged between 18 and 60 years were recruited consecutively as they consented. Their social demographic characteristics were captured using a questionnaire form. Immediately after blood donation five milliliters of blood samples for CRP determination were drawn from the pilot tube of the blood bag by injecting the cap of an Ethylene dopamine tetra acetic acid (EDTA) vacutainer with the donation needle. Extracted plasma samples were stored frozen at -70 0 C till analysis. Analysis was done using standard laboratory methods. Statistical analyses were done using SPSS version 21. Bootstrap methods were used to calculate means, medians and confidence intervals. The fit of the observed data distribution was determined using Shapiro – Wilk tests with P > 0.05 indicating Gaussian distribution. Means, medians and 2.5 th and 97.5 th interquartiles were determined. Gender – based comparison of the medians were done using Wilcoxon rank-sum test with, p< 0.05, considered significant. Results: The male enrollees had a mean age of 31.91 years, while females’ mean age was 31.85 years. C-reactive protein demonstrated non-parametric distribution. Females’ medians were higher than males’ (11.7 mg/l vs. 4.4 mg/l, p< 0.01) Conclusion: The females have significantly higher CRP median values than males in health.

Assessment of professional judgement in the field of occupational hygiene: comparison of expert and observed data distributions

Assessment of professional judgement in the field of occupational hygiene: comparison of expert and observed data distributions

Robust Assessing the Lifetime Performance of Products with Inverse Gaussian Distribution in Bayesian and Classical Setup

The inverse Gaussian (Wald) distribution belongs to the two-parameter family of continuous distributions having a range from 0 to ∞ and is considered as a potential candidate to model diffusion processes and lifetime datasets. Bayesian analysis is a modern inferential technique in which we estimate the parameters of the posterior distribution obtained by formally combining a prior distribution with an observed data distribution. In this article, we have attempted to perform the Bayesian and classical analyses of the Wald distribution and compare the results. Jeffreys' and uniform priors are used as noninformative priors, while the exponential distribution is used as an informative prior. The analysis comprises finding joint posterior distributions, the posterior means, predictive distributions, and credible intervals. To illustrate the entire estimation procedure, we have used real and simulated datasets, and the results thus obtained are discussed and compared. We have used the Bayesian specialized Open BUGS software to perform Markov Chain Monte Carlo (MCMC) simulations using a real dataset.

Development of High-Resolution Regional Climatology in the East/Japan Sea With a Primary Focus on Meridional Temperature Gradient Correction

In this study, we developed a new high-resolution regional climatology (0.1° by 0.1° by 19 levels) in the East/Japan Sea. National Centers for Environmental Information and Korea Oceanic Data Center already released the regional climatology of East Asian seas including the East/Japan Sea with 0.1° by 0.1° resolution. It provides a reliable temperature and salinity structure compared to previous 1° or 0.25° climatologies. However, this study found an abnormal meridional temperature gradient problem when calculating geostrophic currents based on this new climatology. Geostrophic currents show a strong repetitive eastward flow along the 1° latitudinal band especially in the East/Japan Sea, which corresponds with abnormal meridional temperature gradients at the same areas. This problem could be related to the objective analysis procedure generating the high-resolution climatology. Here, we reproduced a high-resolution climatology without the abnormal meridional temperature gradient problem by using the optimal interpolation method. Results show that the meridional gradient problem can partly be attributed to both the use of the World Ocean Atlas background field on the 1° grid, and the spatial distribution of World Ocean database observation data; however, these are not the primary causes. We corrected the abnormal temperature gradient by increasing the meridional decorrelation length scale without losing the meso-scale feature in the East/Japan Sea, as shown by the wavelet analysis. Improvement of the new gridded field is also validated by using serial hydrographic data and the altimetry-derived surface current product.

Probabilistic Prediction of Scouring around Piers using Monte Carlo Simulation

Assessing local scour around a pier is important in terms of creating a good design for any bridge. Many equations are available to predict local scour around pier, though the reliability of these must be checked using statistical tools. A Monte Carlo simulation was thus used in this study to check the probabilistic accuracy of lab equations of local scour around a test pier so that the observation data and prediction equation were both tested probabilistically before use in simulation. The parameters of the prediction equation were specified based on the probabilistic and deterministic variables, with average velocity, critical velocity, water depth, median bed diameter, and Froude number being the unknown variables. The deterministic variables were the diameter of the pier and the spacing from the pier to the abutment. The optimum number of iterations utilised in the Monte Carlo simulation was also investigated based on standard deviation. The independent terms of the prediction equation for the simulation model were derived based on the original distribution of the equation of local scour and the relevant statistical values. The distribution of observation data of local scour was assumed to be normal, while the simulation model was lognormal. The input data was then used to check the probabilistic outcomes of the deterministic equation. The deterministic equation of local scour gave the results at the corresponding confidence level of about 20%, depending on the curve of a cumulative probability distribution. The probabilistic results were thus deemed preferable for the computation of local scour around the pier.

Self-Organizing Nebulous Growths for Robust and Incremental Data Visualization.

Nonparametric dimensionality reduction techniques, such as t-distributed Stochastic Neighbor Embedding (t-SNE) and uniform manifold approximation and projection (UMAP), are proficient in providing visualizations for data sets of fixed sizes. However, they cannot incrementally map and insert new data points into an already provided data visualization. We present self-organizing nebulous growths (SONG), a parametric nonlinear dimensionality reduction technique that supports incremental data visualization, i.e., incremental addition of new data while preserving the structure of the existing visualization. In addition, SONG is capable of handling new data increments, no matter whether they are similar or heterogeneous to the already observed data distribution. We test SONG on a variety of real and simulated data sets. The results show that SONG is superior to Parametric t-SNE, t-SNE, and UMAP in incremental data visualization. Especially, for heterogeneous increments, SONG improves over Parametric t-SNE by 14.98% on the Fashion MNIST data set and 49.73% on the MNIST data set regarding the cluster quality measured by the adjusted mutual information scores. On similar or homogeneous increments, the improvements are 8.36% and 42.26%, respectively. Furthermore, even when the abovementioned data sets are presented all at once, SONG performs better or comparable to UMAP and superior to t-SNE. We also demonstrate that the algorithmic foundations of SONG render it more tolerant to noise compared with UMAP and t-SNE, thus providing greater utility for data with high variance, high mixing of clusters, or noise.