Search Results (11)

Genome-wide association studies (GWAS) are commonly employed to study the genetic basis of complex traits/diseases, and a key question is how much heritability could be explained by all single nucleotide polymorphisms (SNPs) in GWAS. One widely used approach that relies on summary statistics only is linkage disequilibrium score regression (LDSC); however, this approach requires certain assumptions about the effects of SNPs (e.g., all SNPs contribute to heritability and each SNP contributes equal variance). More flexible modeling methods may be useful. We previously developed an approach recovering the “true” effect sizes from a set of observed z-statistics with an empirical Bayes approach, using only summary statistics. However, methods for standard error (SE) estimation are not available yet, limiting the interpretation of our results and the applicability of the approach. In this study, we developed several resampling-based approaches to estimate the SE of SNP-based heritability, including two jackknife and three parametric bootstrap methods. The resampling procedures are performed at the SNP level as it is most common to estimate heritability from GWAS summary statistics alone. Simulations showed that the delete-d-jackknife and parametric bootstrap approaches provide good estimates of the SE. In particular, the parametric bootstrap approaches yield the lowest root-mean-squared-error (RMSE) of the true SE. We also explored various methods for constructing confidence intervals (CIs). In addition, we applied our method to estimate the SNP-based heritability of 12 immune-related traits (levels of cytokines and growth factors) to shed light on their genetic architecture. We also implemented the methods to compute the sum of heritability explained and the corresponding SE in an R package SumVg. In conclusion, SumVg may provide a useful alternative tool for calculating SNP heritability and estimating SE/CI, which does not rely on distributional assumptions of SNP effects. Full article

In this investigation, a synthesis of Convolutional Neural Networks (CNNs) and Bayesian inference is presented, leading to a novel approach to the problem of Multiple Hypothesis Testing (MHT). Diverging from traditional paradigms, this study introduces a sequence-based uncalibrated Bayes factor approach to test many hypotheses using the same family of sampling parametric models. A two-step methodology is employed: initially, a learning phase is conducted utilizing simulated datasets encompassing a wide spectrum of null and alternative hypotheses, followed by a transfer phase applying this fitted model to real-world experimental sequences. The outcome is a CNN model capable of navigating the complex domain of MHT with improved precision over traditional methods, also demonstrating robustness under varying conditions, including the number of true nulls and dependencies between tests. Although indications of empirical evaluations are presented and show that the methodology will prove useful, more work is required to provide a full evaluation from a theoretical perspective. The potential of this innovative approach is further illustrated within the critical domain of genomics. Although formal proof of the consistency of the model remains elusive due to the inherent complexity of the algorithms, this paper also provides some theoretical insights and advocates for continued exploration of this methodology. Full article

In the fields of finance, insurance, system reliability, etc., it is often of interest to measure the dependence among variables by modeling a multivariate distribution using a copula. The copula models with parametric assumptions are easy to estimate but can be highly biased when such assumptions are false, while the empirical copulas are nonsmooth and often not genuine copulas, making the inference about dependence challenging in practice. As a compromise, the empirical Bernstein copula provides a smooth estimator, but the estimation of tuning parameters remains elusive. The proposed empirical checkerboard copula within a hierarchical empirical Bayes model alleviates the aforementioned issues and provides a smooth estimator based on multivariate Bernstein polynomials that itself is shown to be a genuine copula. Additionally, the proposed copula estimator is shown to provide a more accurate estimate of several multivariate dependence measures. Both theoretical asymptotic properties and finite-sample performances of the proposed estimator based on simulated data are presented and compared with some nonparametric estimators. An application to portfolio risk management is included based on stock prices data. Full article

Much effort has been devoted towards the identification of brain areas recruited during driving—as one of the most common motor skills of human beings. However, how driving experience impacts on the brain’s intrinsic functional architecture has not been fully investigated. Using resting-state fMRI data collected from 20 taxi drivers and 20 nondrivers, this paper asks whether there exists specific brain network integration encoding driving behavior. First, to address this, we proposed a general framework combining whole-brain functional connectivity analysis with effective connectivity analysis based on spectral Dynamic Causal Modeling. The validation results indicated that the application of this framework could effectively discover the brain network that best explained the observed BOLD fluctuations. Second, by segmenting supplementary motor area (SMA) into pre-SMA and SMA proper sub-regions, we used the above framework and discovered a hierarchical architecture with pre-SMA located at the higher level in both driver and control groups. Third, we further evaluated the possibility that driving behavior could be encoded by directed connections among the hierarchy, and found that the effective connectivity from pre-SMA to left superior frontal gyrus could distinguish drivers from nondrivers with a sensitivity of 80%. Our findings provide a new paradigm for analyzing the brain’s intrinsic functional integration, and may shed new light on the theory of neuroplasticity that training and experience can remodel the patterns of correlated spontaneous brain activity between specific processing regions. Meanwhile, from a methodological advantage perspective, our proposed framework takes the functional connectivity results as a prior, enabling subsequent spectral DCM to efficiently assess functional integration at a whole-brain scale, which is not available by only using other DCM methods, such as stochastic DCM or the State-of-the-Art multimodal DCM. Full article

The aim of this study is to obtain the Bayes estimators and the maximum likelihood estimators (MLEs) for the unknown parameters of the Rayleigh–Weibull (RW) distribution based on progressive type-II censored samples. The approximate Bayes estimators are calculated using the idea of Lindley, Tierney–Kadane approximations, and also the Markov Chain Monte Carlo (MCMC) method under the squared-error loss function when the Bayes estimators are not handed in explicit forms. In this study, the approximate Bayes estimates are compared with the maximum likelihood estimates in the aspect of the estimated risks (ERs) using Monte Carlo simulation. The asymptotic confidence intervals for the unknown parameters are obtained using the MLEs of parameters. In addition, the coverage probabilities the parametric bootstrap estimates are computed. Real lifetime datasets related to bladder cancer, head and neck cancer, and leukemia are used to illustrate the empirical results belonging to the approximate Bayes estimates, the maximum likelihood estimates, and the parametric bootstrap intervals. Full article

Cognitive diagnostic models (CDMs) are increasingly being used in various assessment contexts to identify cognitive processes and provide tailored feedback. However, the most commonly used estimation method for CDMs, marginal maximum likelihood estimation with Expectation–Maximization (MMLE-EM), can present difficulties when sample sizes are small. This study compares the results of different estimation methods for CDMs under varying sample sizes using simulated and empirical data. The methods compared include MMLE-EM, Bayes modal, Markov chain Monte Carlo, a non-parametric method, and a parsimonious parametric model such as Restricted DINA. We varied the sample size, and assessed the bias in the estimation of item parameters, the precision in attribute classification, the bias in the reliability estimate, and computational cost. The findings suggest that alternative estimation methods are preferred over MMLE-EM under low sample-size conditions, whereas comparable results are obtained under large sample-size conditions. Practitioners should consider using alternative estimation methods when working with small samples to obtain more accurate estimates of CDM parameters. This study aims to maximize the potential of CDMs by providing guidance on the estimation of the parameters. Full article

The univariate noncentral distributions can be derived by multiplying their central distributions with translation factors. When constructed in terms of translated uniform distributions on unit radius hyperspheres, these translation factors become generating functions for classical families of orthogonal polynomials. The ultraspherical noncentral t, normal N, F, and ${\chi }^2$ distributions are thus found to be associated with the Gegenbauer, Hermite, Jacobi, and Laguerre polynomial families, respectively, with the corresponding central distributions standing for the polynomial family-defining weights. Obtained through an unconstrained minimization of the Gibbs potential, Jaynes’ maximal entropy priors are formally expressed in terms of the empirical densities’ entropic convex duals. Expanding these duals on orthogonal polynomial bases allows for the expedient determination of the Jaynes–Gibbs priors. Invoking the moment problem and the duality principle, modelization can be reduced to the direct determination of the prior moments in parametric space in terms of the Bayes factor’s orthogonal polynomial expansion coefficients in random variable space. Genomics and geophysics examples are provided. Full article

Recent research indicates prolonged disorders of consciousness (PDOC) result from structural and functional impairments to key cortical and subcortical networks, including the default mode network (DMN) and the anterior forebrain mesocircuit (AFM). However, the specific mechanisms which underpin such impairments remain unknown. It is known that disruptions in the striatal-pallidal pathway can result in the over inhibition of the thalamus and lack of excitation to the cortex that characterizes PDOC. Here, we used spectral dynamic causal modelling and parametric empirical Bayes on rs-fMRI data to assess whether DMN changes in PDOC are caused by disruptions in the AFM. PDOC patients displayed overall reduced coupling within the AFM, and specifically, decreased self-inhibition of the striatum, paired with reduced coupling from striatum to thalamus. This led to loss of inhibition from AFM to DMN, mostly driven by posterior areas including the precuneus and inferior parietal cortex. In turn, the DMN showed disruptions in self-inhibition of the precuneus and medial prefrontal cortex. Our results provide support for the anterior mesocircuit model at the subcortical level but highlight an inhibitory role for the AFM over the DMN, which is disrupted in PDOC. Full article

Functional Electrical Stimulation (FES) has demonstrated to improve walking ability and to induce the carryover effect, long-lasting persisting improvement. Functional magnetic resonance imaging has been used to investigate effective connectivity differences and longitudinal changes in a group of chronic stroke patients that attended a FES-based rehabilitation program for foot-drop correction, distinguishing between carryover effect responders and non-responders, and in comparison with a healthy control group. Bayesian hierarchical procedures were employed, involving nonlinear models at within-subject level—dynamic causal models—and linear models at between-subjects level. Selected regions of interest were primary sensorimotor cortices (M1, S1), supplementary motor area (SMA), and angular gyrus. Our results suggest the following: (i) The ability to correctly plan the movement and integrate proprioception information might be the features to update the motor control loop, towards the carryover effect, as indicated by the reduced sensitivity to proprioception input to S1 of FES non-responders; (ii) FES-related neural plasticity supports the active inference account for motor control, as indicated by the modulation of SMA and M1 connections to S1 area; (iii) SMA has a dual role of higher order motor processing unit responsible for complex movements, and a superintendence role in suppressing standard motor plans as external conditions changes. Full article

The variable selection problem in general, and specifically for the ordinary linear regression model, is considered in the setup in which the number of covariates is large enough to prevent the exploration of all possible models. In this context, Gibbs-sampling is needed to perform stochastic model exploration to estimate, for instance, the model inclusion probability. We show that under a Bayesian non-parametric prior model for analyzing Gibbs-sampling output, the usual empirical estimator is just the asymptotic version of the expected posterior inclusion probability given the simulation output from Gibbs-sampling. Other posterior conditional estimators of inclusion probabilities can also be considered as related to the latent probabilities distributions on the model space which can be sampled given the observed Gibbs-sampling output. This paper will also compare, in this large model space setup the conventional prior approach against the non-local prior approach used to define the Bayes Factors for model selection. The approach is exposed along with simulation samples and also an application of modeling the Travel and Tourism factors all over the world. Full article

Recent work has focused on the problem of nonparametric estimation of information divergence functionals between two continuous random variables. Many existing approaches require either restrictive assumptions about the density support set or difficult calculations at the support set boundary which must be known a priori. The mean squared error (MSE) convergence rate of a leave-one-out kernel density plug-in divergence functional estimator for general bounded density support sets is derived where knowledge of the support boundary, and therefore, the boundary correction is not required. The theory of optimally weighted ensemble estimation is generalized to derive a divergence estimator that achieves the parametric rate when the densities are sufficiently smooth. Guidelines for the tuning parameter selection and the asymptotic distribution of this estimator are provided. Based on the theory, an empirical estimator of Rényi-$\alpha$ divergence is proposed that greatly outperforms the standard kernel density plug-in estimator in terms of mean squared error, especially in high dimensions. The estimator is shown to be robust to the choice of tuning parameters. We show extensive simulation results that verify the theoretical results of our paper. Finally, we apply the proposed estimator to estimate the bounds on the Bayes error rate of a cell classification problem. Full article