Nonparametric Approach Research Articles

A SIMPLE AND FLEXIBLE TEST OF SAMPLE EXCHANGEABILITY WITH APPLICATIONS TO STATISTICAL GENOMICS.

In scientific studies involving analyses of multivariate data, basic but important questions often arise for the researcher: Is the sample exchangeable, meaning that the joint distribution of the sample is invariant to the ordering of the units? Are the features independent of one another, or perhaps the features can be grouped so that the groups are mutually independent? In statistical genomics, these considerations are fundamental to downstream tasks such as demographic inference and the construction of polygenic risk scores. We propose a non-parametric approach, which we call the V test, to address these two questions, namely, a test of sample exchangeability given dependency structure of features, and a test of feature independence given sample exchangeability. Our test is conceptually simple, yet fast and flexible. It controls the Type I error across realistic scenarios, and handles data of arbitrary dimensions by leveraging large-sample asymptotics. Through extensive simulations and a comparison against unsupervised tests of stratification based on random matrix theory, we find that our test compares favorably in various scenarios of interest. We apply the test to data from the 1000 Genomes Project, demonstrating how it can be employed to assess exchangeability of the genetic sample, or find optimal linkage disequilibrium (LD) splits for downstream analysis. For exchangeability assessment, we find that removing rare variants can substantially increase the -value of the test statistic. For optimal LD splitting, the V test reports different optimal splits than previous approaches not relying on hypothesis testing. Software for our methods is available in R (CRAN: flintyR) and Python (PyPI: flintyPy).

Magnetorheological Damper Force Prediction using Particle Swarm Optimization and Long Short-Term Memory Model

Smart materials, like magnetorheological (MR) fluid, are gaining attention for their ability to rapidly change properties under magnetic influence, making them useful in vibration control systems for vehicles, medical devices, and civil engineering structures. Common parametric models, such as Bouc-Wen and Bingham, are traditionally employed to model MR damper dynamics behavior. However, the manual tuning of numerous parameters in these models increases complexity and hinders the identification of inverse models, potentially leading to unpredictable optimum target forces. In response to these challenges, this study suggested a non-parametric approach using Long Short-Term Memory (LSTM) models to predict the optimum target force of MR dampers. Unlike parametric models, LSTM models capture dynamic behavior without the need for extensive manual tuning. To optimize the LSTM model, Particle Swarm Optimization (PSO) is employed to fine-tune hyperparameter values, ensuring robust performance. The proposed non-parametric method, specifically the PSO-LSTM model, demonstrates faster processing times compared to traditional parametric approaches. The proposed model produced an accurate damping force prediction with a root mean square error of less than 5%, This novel approach simplifies the modeling process and offers an efficient and precise alternative to traditional parametric methods.

Role of Crude Oil in Determining the Price of Corn in the United States: A Non-parametric Approach

Role of Crude Oil in Determining the Price of Corn in the United States: A Non-parametric Approach

An encoding approach for stable change point detection

Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis. We develop a structural subsampling procedure such that the observations are encoded into multiple sequences of Bernoulli variables. A maximum likelihood approach in conjunction with a newly developed searching algorithm is implemented to detect change points on each Bernoulli process separately. Then, aggregation statistics are proposed to collectively synthesize change-point results from all individual univariate time series into consistent and stable location estimations. We also study a weighting strategy to measure the degree of relevance for different subsampled groups. Simulation studies are conducted and shown that the proposed change-point methodology for multivariate time series has favorable performance comparing with currently available state-of-the-art nonparametric methods under various settings with different degrees of complexity. Real data analyses are finally performed on categorical, ordinal, and continuous time series taken from fields of genetics, climate, and finance.

Have countries accumulated enough capital? A non-parametric approach

ABSTRACT In this paper, we analyse the effect of capital accumulation on economic growth and verify whether countries have accumulated enough capital. We make use of panel data for 92 countries from 1965–2019, combined with intuitive robust non-parametric modelling based on linear programming. Our result indicates first that capital accumulation is important for economic growth. Second, we show that developing countries suffer from under-investment in capital, while developed countries have unexploited capacity. Therefore, to promote sustainable growth, developing countries need to implement policies to increase their capital stock. However, the situation of developed countries indicates that more capital accumulation is not the correct path for these countries, but better capital use is. Finally, we highlight the particular patterns of China and India and challenge our results by running three sensitivity tests. They confirm our early findings.

Nonparametric analysis of delayed treatment effects using single-crossing constraints.

Clinical trials involving novel immuno-oncology therapies frequently exhibit survival profiles which violate the proportional hazards assumption due to a delay in treatment effect, and, in such settings, the survival curves in the two treatment arms may have a crossing before the two curves eventually separate. To flexibly model such scenarios, we describe a nonparametric approach for estimating the treatment arm-specific survival functions which constrains these two survival functions to cross at most once without making any additional assumptions about how the survival curves are related. A main advantage of our approach is that it provides an estimate of a crossing time if such a crossing exists, and, moreover, our method generates interpretable measures of treatment benefit including crossing-conditional survival probabilities and crossing-conditional estimates of restricted residual mean life. Our estimates of these measures may be used together with efficacy measures from a primary analysis to provide further insight into differences in survival across treatment arms. We demonstrate the use and effectiveness of our approach with a large simulation study and an analysis of reconstructed outcomes from a recent combination therapytrial.

Item-Explanatory Mokken Scale Analysis: Using Nonparametric Item Response Theory to Explore Item Attributes

Researchers frequently examine the effects of item attributes (i.e., item properties, item covariates, item formats) as part of item analysis for cognitive and affective assessments. In this study, we propose and illustrate item-explanatory Mokken Scale Analysis (MSA) as an exploratory nonparametric approach to examining item attributes based on invariance principles. We used real data and an illustrative simulation to demonstrate the approach under various conditions. Our results suggest that item-explanatory MSA provides practical and theoretical insight to support measurement research in a variety of contexts. Because of the emphasis on invariance, our approach can help researchers explore the impact of item characteristics on examinee responses and evaluate the degree to which item characteristics have a consistent interpretation for all examinees. We consider the implications of our findings for research and practice, along with directions for further investigation.

Operating Efficiency in the Capital-Intensive Semiconductor Industry: A Nonparametric Frontier Approach

Abstract This article uses a nonparametric production frontier approach to investigate the operating efficiency differences by the impacts of capital expenditure and business model in the global semiconductor industry. Handling the impact of capital expenditure as a fixed input by the directional distance estimator, this study compares the operating efficiencies in the global semiconductor industry between the integrated device manufacturers and the fabless and foundry firms over 1999–2018. The estimation results indicate that the operating efficiencies do vary in the semiconductor by the business model. The vertically integrated manufacturers dominate the semiconductor industry, and the capital-intensive manufacturers operate more efficiently than the asset-light fabless firms on average.

Utilizing machine learning and vegetation indices for spring wheat yield forecasting

The results of research on the development and assessment of the accuracy of predictive models of spring wheat yield based on the use of remote sensing data and machine learning methods are presented. Yield data of spring wheat variety Novosibirskaya 31 obtained in a field experiment in the central forest-steppe of the Novosibirsk region in 2019–2022 were used in this work. Both qualitative predictors (the level of agrotechnologies intensification) and quantitative predictors (atmospheric precipitation in critical phases of wheat plant development and indicators of vegetation indices characterizing the condition of crops) were taken into account when creating the models. The use of various methods of intellectual data analysis, as well as the combination of parametric and non-parametric approaches in the study provided a sufficiently high accuracy of spring wheat yield forecasting. The methods used to predict spring wheat yield included linear regression, nonlinear Regression Splines based model, decision tree (CART), Random Forest, Adaptive Boosting (AdaBoost) and Gradient boosting. It was found that the models based on random forest, gradient and adaptive boosting algorithms were characterized by the highest predictive capabilities of crop yield depending on the emerging conditions of vegetation and controlling influence (R2 = 0.74–0.80). The development of predictive yield models using remote sensing and machine learning represent a certain scientific novelty and practical significance for effective management of crop productivity in changing soil-climatic and economic conditions. Predictive modeling is faced with multilevel environmental uncertainty and high variability of the resulting indicators on a particular land plot. In this regard, the multilevel approach may represent a promising solution for effective forecasting of spring wheat yield.

A novel estimator for the two-way partial AUC

BackgroundThe two-way partial AUC has been recently proposed as a way to directly quantify partial area under the ROC curve with simultaneous restrictions on the sensitivity and specificity ranges of diagnostic tests or classifiers. The metric, as originally implemented in the tpAUC R package, is estimated using a nonparametric estimator based on a trimmed Mann-Whitney U-statistic, which becomes computationally expensive in large sample sizes. (Its computational complexity is of order O(nxny)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n_x n_y)$$\\end{document}, where nx\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_x$$\\end{document} and ny\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_y$$\\end{document} represent the number of positive and negative cases, respectively). This is problematic since the statistical methodology for comparing estimates generated from alternative diagnostic tests/classifiers relies on bootstrapping resampling and requires repeated computations of the estimator on a large number of bootstrap samples.MethodsBy leveraging the graphical and probabilistic representations of the AUC, partial AUCs, and two-way partial AUC, we derive a novel estimator for the two-way partial AUC, which can be directly computed from the output of any software able to compute AUC and partial AUCs. We implemented our estimator using the computationally efficient pROC R package, which leverages a nonparametric approach using the trapezoidal rule for the computation of AUC and partial AUC scores. (Its computational complexity is of order O(nlogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n \\log n)$$\\end{document}, where n=nx+ny\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n = n_x + n_y$$\\end{document}.). We compare the empirical bias and computation time of the proposed estimator against the original estimator provided in the tpAUC package in a series of simulation studies and on two real datasets.ResultsOur estimator tended to be less biased than the original estimator based on the trimmed Mann-Whitney U-statistic across all experiments (and showed considerably less bias in the experiments based on small sample sizes). But, most importantly, because the computational complexity of the proposed estimator is of order O(nlogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n \\log n)$$\\end{document}, rather than O(nxny)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n_x n_y)$$\\end{document}, it is much faster to compute when sample sizes are large.ConclusionsThe proposed estimator provides an improvement for the computation of two-way partial AUC, and allows the comparison of diagnostic tests/machine learning classifiers in large datasets where repeated computations of the original estimator on bootstrap samples become too expensive to compute.

Nonparametric efficiency measurement of undergraduate teaching by university size

Conventional data envelopment analysis (DEA) models assume that all decision-making units (DMUs) are homogenous. While higher education institutions (HEIs) of very different sizes challenge the homogeneity of DMUs, DEA studies have paid relatively little attention to university size when assessing the performance of HEIs. This article proposes novel, effective methods for evaluating university performance and identifying useful benchmarks for improving the operations of inefficient performers. Specifically, DEA and cluster analysis (CA) are applied for the evaluation of the performance of traditional Spanish public universities. DEA is utilized to examine the relative performance of these universities in terms of undergraduate teaching output. CA is applied to find similar-in-scale universities prior to the DEA to facilitate peer-groupings. The advantage of this method is that when DMUs are clustered based on their size, one can obtain homogenous groups of units with comparable operating environments. Furthermore, using the meta-frontier framework, this research finds significant evidence that there is an efficiency advantage for medium- and large-sized universities over small ones in providing undergraduate teaching. A bootstrapped, non-parametric meta-frontier approach also verifies this latter result. Some of the factors that contribute to the differences in the relative efficiencies are identified as well.

Nonparametric Kernel Smoothing Item Response Theory Analysis of Likert Items

Likert scales are the most common psychometric response scales in the social and behavioral sciences. Likert items are typically used to measure individuals’ attitudes, perceptions, knowledge, and behavioral changes. To analyze the psychometric properties of individual Likert-type items and overall Likert scales, mostly methods based on classical test theory (CTT) are used, including corrected item–total correlations and reliability indices. CTT methods heavily rely on the total scale scores, making it challenging to directly examine the performance of items and response options across varying levels of the trait. In this study, Kernel Smoothing Item Response Theory (KS-IRT) is introduced as a graphical nonparametric IRT approach for the evaluation of Likert items. Unlike parametric IRT models, nonparametric IRT models do not involve strong assumptions regarding the form of item response functions (IRFs). KS-IRT provides graphics for detecting peculiar patterns in items across different levels of a latent trait. Differential item functioning (DIF) can also be examined by applying KS-IRT. Using empirical data, we illustrate the application of KS-IRT to the examination of Likert items on a psychological scale.

A Comparison of the Rank-based and Slope-based Nonparametric Tests for Trend Detection in Climate Time Series

Trend detection in climate time series data is crucial for understanding climate change, predicting future climate patterns, assessing impacts, managing resources, and formulating policies. Several trend detection methods have been introduced in the literature, including parametric and non-parametric approaches. Nonparametric trend detection methods are often considered more preferable than parametric methods in certain situations due to their flexibility and robustness. Comparing various nonparametric methods of trend detection is vital in data analysis because different techniques can yield divergent results based on the same dataset. In this study, three nonparametric trend tests which were the MannKendall (MK), Sen’s Innovative Trend Analysis (ITA) and Modified Mann-Kendall by Sen’s Innovative Trend Analysis (MMK_ITA) were compared based on their power. The MK test is a rank-based test and the ITA is a slope-based test. Meanwhile, the combination of rank-based and slope-based methods is known as the MMK_ITA test. The power analysis was conducted through Monte Carlo simulation on normal, non-normal and autocorrelated time series. The simulation results indicated that test power relied on magnitude of linear trend slope, sample sizes, distribution type and variation in time series. These tests were then applied to monthly maximum temperature from 2002 until 2021 for Selangor, Malaysia. This study found that the slope-based test performed better compared to the rank-based test and their combined methods from the simulation studies and real data application based on the calculated power.

Measuring the carbon shadow price of agricultural production: a regional-level nonparametric approach.

Climate change poses an urgent threat, necessitating the implementation of measures to actively reduce carbon emissions. The development of effective carbon emission reduction policies requires accurate estimation of the costs involved. In situations where actual prices of commodities are not available in the market, shadow pricing provides a useful method to calculate relative prices between commodities with and without price information. However, most studies focus on the industry, with few contributions on agricultural sector. This paper estimates the shadow price of carbon emissions in the agricultural sector from a provincial perspective, incorporating the impact of livestock into the calculation of carbon emissions and shadow pricing. Our findings indicate that ignoring livestock may overestimate CSP values. On the whole, the level of carbon shadow price is rising, indicating good green development in China's agricultural sector. The two types of convergence results show that there is sigma convergence and beta convergence in the western and central regions, demonstrating a significant improvement in environmental performance.

A Bayesian nonparametric approach for multiple mediators with applications in mental health studies.

Mediation analysis with contemporaneously observed multiple mediators is a significant area of causal inference. Recent approaches for multiple mediators are often based on parametric models and thus may suffer from model misspecification. Also, much of the existing literature either only allow estimation of the joint mediation effect or estimate the joint mediation effect just as the sum of individual mediator effects, ignoring the interaction among the mediators. In this article, we propose a novel Bayesian nonparametric method that overcomes the two aforementioned drawbacks. We model the joint distribution of the observed data (outcome, mediators, treatment, and confounders) flexibly using an enriched Dirichlet process mixture with three levels. We use standardization (g-computation) to compute all possible mediation effects, including pairwise and all other possible interaction among the mediators. We thoroughly explore our method via simulations and apply our method to a mental health data from Wisconsin Longitudinal Study, where we estimate how the effect of births from unintended pregnancies on later life mental depression (CES-D) among the mothers is mediated through lack of self-acceptance and autonomy, employment instability, lack of social participation, and increased family stress. Our method identified significant individual mediators, along with some significant pairwise effects.

Reservoir porosity assessment and anomaly identification from seismic attributes using Gaussian process machine learning

AbstractPorosity, as one of the reservoir properties, is an important parameter to numerous studies, i.e., the reservoir’s oil/gas volume estimation or even the storage capacity measurement in the Carbon Capture Storage (CCS) project. However, an approach to estimate porosity using elastic property from the inversion propagates its error, affecting the result’s accuracy. On the other hand, direct estimation from seismic data is another approach to estimating porosity, but it poses a high non-linear problem. Thus, we propose the non-parametric machine learning approach, Gaussian Process (GP), which draws distribution over the function to solve the high non-linear problem between seismic data with porosity and quantify the prediction uncertainty simultaneously. With the help of Random Forest (RF) as the feature selection method, the GP predictions show excellent results in the blind test, a well that is completely removed from the training data, and comparison with other machine learning models. The uncertainty, standard deviation from GP prediction, can act as a quantitative evaluation of the prediction result. Moreover, we generate a new attribute based on the quartile of the standard deviation to delineate the anomaly zones. High anomaly zones are highlighted and associated with high porosity from GP and low inverted P-impedance from inversion results. Thus, applying the GP using seismic data shows its potential to characterize the reservoir property spatially, and the uncertainty offers insights into quantitative and qualitative evaluation for hydrocarbon exploration and development.

Non-contrast free-breathing 2D CINE compressed SENSE T1-TFE cardiovascular MRI at 3T in sedated young children for assessment of congenital heart disease.

Cardiac MRI is a crucial tool for assessing congenital heart disease (CHD). However, its application remains challenging in young children when performed at 3T. The aim of this retrospective single center study was to compare a non-contrast free-breathing 2D CINE T1-weighted TFE-sequence with compressed sensing (FB 2D CINE CS T1-TFE) with 3D imaging for diagnostic accuracy of CHD, image quality, and vessel diameter measurements in sedated young children. FB 2D CINE CS T1-TFE was compared with a 3D non-contrast whole-heart sequence (3D WH) and 3D contrast-enhanced MR angiography (3D CE-MRA) at 3T in 37 CHD patients (20♂, 1.5±1.4 years). Two radiologists independently assessed image quality, type of CHD, and diagnostic confidence. Diameters and measures of contrast and sharpness of the aorta and pulmonary vessels were determined. A non-parametric multi-factorial approach was used to estimate diagnostic accuracy for the diagnosis of CHD. Linear mixed models were calculated to compare contrast and vessel sharpness. Krippendorff's alpha was determined to quantify vessel diameter agreement. FB 2D CINE CS T1-TFE was rated superior regarding image quality, diagnostic confidence, and diagnostic sensitivity for both intra- and extracardiac pathologies compared to 3D WH and 3D CE-MRA (all p<0.05). FB 2D CINE CS T1-TFE showed superior contrast and vessel sharpness (p<0.001) resulting in the highest proportion of measurable vessels (740/740; 100%), compared to 3D WH (530/620; 85.5%) and 3D CE-MRA (540/560; 96.4%). Regarding vessel diameter measurements, FB 2D CINE CS T1-TFE revealed the closest inter-reader agreement (Krippendorff's alpha: 0.94-0.96; 3D WH: 0.78-0.94; 3D CE-MRA: 0.76-0.93). FB 2D CINE CS T1-TFE demonstrates robustness at 3T and delivers high-quality diagnostic results to assess CHD in sedated young children. Its ability to function without contrast injection and respiratory compensation enhances ease of use and could encourage widespread adoption in clinical practice.

Strategies for optimal sky subtraction in the low surface brightness regime

ABSTRACT The low surface brightness (LSB) regime (μg ≳ 26 mag arcsec−2) comprises a vast, mostly unexplored discovery space, from dwarf galaxies to the diffuse interstellar medium. Accessing this regime requires precisely removing instrumental signatures and light contamination, including, most critically, night sky emission. This is not trivial, as faint astrophysical and instrumental contamination can bias sky models at the precision needed to characterize LSB structures. Using idealized synthetic images, we assess how this bias impacts two common LSB-oriented sky-estimation algorithms: (1) masking and parametric modelling, and (2) stacking and smoothing dithered exposures. Undetected flux limits both methods by imposing a pedestal offset to all derived sky models. Careful, deep masking of fixed sources can mitigate this, but source density always imposes a fundamental limit. Stellar scattered light can contribute ∼28–29 mag arcsec−2 of background flux even in low-density fields; its removal is critical prior to sky estimation. For complex skies, image combining is an effective non-parametric approach, although it strongly depends on observing strategy and adds noise to images on the smoothing kernel scale. Preemptive subtraction of fixed sources may be the only practical approach for robust sky estimation. We thus tested a third algorithm, subtracting a preliminary sky-subtracted coadd from exposures to isolate sky emission. Unfortunately, initial errors in sky estimation propagate through all subsequent sky models, making the method impractical. For large-scale surveys like Legacy Survey of Space and Time, where key science goals constrain observing strategy, masking and modelling remain the optimal sky estimation approach, assuming stellar scattered light is removed first.

Associations of Circadian Rest-Activity Rhythms With Affect and Cognition in Community-Dwelling Stroke Survivors: An Ambulatory Assessment Study

Background Rest-activity rhythm (RAR) is a modifiable behavioral factor associated with affect and cognition. Identifying RAR characteristics associated with affect and cognition among stroke survivors provides insight into preventing poststroke affective and cognitive impairment. Objective To examine the associations of RAR characteristics with affect and cognition among community-dwelling stroke survivors. Methods Forty participants with mild stroke (mean age = 52.8; 42.5% female; 55% White) reported their affect and cognitive complaints using ecological momentary assessment and wore an accelerometer for 7 consecutive days and completed the National Institutes of Health Toolbox Cognition Battery. RAR characteristics were extracted using parametric and non-parametric approaches. Multivariable linear regressions were used to identify RAR characteristics associated with affect and cognition. Results Later onset of rest (B = 0.45; P = .008) and activity (B = 0.36; P = .041) were positively associated with depressed affect. These associations were reversed for cheerful effect (rest onset: B = −0.42; P = .017; activity onset: B = −0.39; P = .033). Cheerful affect was also positively associated with relative amplitude (ie, distinctions in activity levels between rest and activity; B = .39; P = .030). Intra-daily variability (ie, RAR fragmentation; B = 0.35; P = .042) and later onset of activity (B = .36; P = .048) were positively associated with cognitive complaints. Less erratic RAR was positively associated with fluid cognition (B = 0.29; P = .036); RAR fragmentation was positively associated with crystallized cognition (B = 0.39; P = .015). Conclusions We identified RAR correlates of affect and cognition among stroke survivors, highlighting the value of managing RAR and sleep in stroke rehabilitation. Future studies should test whether advancing the onset of rest and activity, promoting a regular active lifestyle, and improving rest and sleep in the nighttime protect stroke survivors from affective and cognitive impairment.

NPB-REC: A non-parametric Bayesian deep-learning approach for undersampled MRI reconstruction with uncertainty estimation

The ability to reconstruct high-quality images from undersampled MRI data is vital in improving MRI temporal resolution and reducing acquisition times. Deep learning methods have been proposed for this task, but the lack of verified methods to quantify the uncertainty in the reconstructed images hampered clinical applicability. We introduce “NPB-REC”, a non-parametric fully Bayesian framework, for MRI reconstruction from undersampled data with uncertainty estimation. We use Stochastic Gradient Langevin Dynamics during training to characterize the posterior distribution of the network parameters. This enables us to both improve the quality of the reconstructed images and quantify the uncertainty in the reconstructed images. We demonstrate the efficacy of our approach on a multi-coil MRI dataset from the fastMRI challenge and compare it to the baseline End-to-End Variational Network (E2E-VarNet). Our approach outperforms the baseline in terms of reconstruction accuracy by means of PSNR and SSIM (34.55, 0.908 vs. 33.08, 0.897, p<0.01, acceleration rate R=8) and provides uncertainty measures that correlate better with the reconstruction error (Pearson correlation, R=0.94 vs. R=0.91). Additionally, our approach exhibits better generalization capabilities against anatomical distribution shifts (PSNR and SSIM of 32.38, 0.849 vs. 31.63, 0.836, p<0.01, training on brain data, inference on knee data, acceleration rate R=8). NPB-REC has the potential to facilitate the safe utilization of deep learning-based methods for MRI reconstruction from undersampled data. Code and trained models are available at https://github.com/samahkh/NPB-REC.