Bayesian Analysis of Multi-Factorial Experimental Designs Using SEM.

Latent repeated measures ANOVA (L-RM-ANOVA) has recently been proposed as an alternative to traditional repeated measures ANOVA. L-RM-ANOVA builds upon structural equation modeling and enables researchers to investigate interindividual differences in main/interaction effects, examine custom contrasts, incorporate a measurement model, and account for missing data. However, L-RM-ANOVA uses maximum likelihood and thus cannot incorporate prior information and can have poor statistical properties in small samples. We show how L-RM-ANOVA can be used with Bayesian estimation to resolve the aforementioned issues. We demonstrate how to place informative priors on model parameters that constitute main and interaction effects. We further show how to place weakly informative priors on standardized parameters which can be used when no prior information is available. We conclude that Bayesian estimation can lower Type 1 error and bias, and increase power and efficiency when priors are chosen adequately. We demonstrate the approach using a real empirical example and guide the readers through specification of the model. We argue that ANOVA tables and incomplete descriptive statistics are not sufficient information to specify informative priors, and we identify which parameter estimates should be reported in future research; thereby promoting cumulative research.

Utilizing Bayesian inference in accelerated testing models under constant stress via ordered ranked set sampling and hybrid censoring with practical validation.

This research investigates the application of the ordered ranked set sampling (ORSSA) procedure in constant-stress partially accelerated life-testing (CSPALTE). The study adopts the assumption that the lifespan of a specific item under operational stress follows a half-logistic probability distribution. Through Bayesian estimation methods, it concentrates on estimating the parameters, utilizing both asymmetric loss function and symmetric loss function. Estimations are conducted using ORSSAs and simple random samples, incorporating hybrid censoring of type-I. Real-world data sets are utilized to offer practical context and validate the theoretical discoveries, providing concrete insights into the research findings. Furthermore, a rigorous simulation study, supported by precise numerical calculations, is meticulously conducted to gauge the Bayesian estimation performance across the two distinct sampling methodologies. This research ultimately sheds light on the efficacy of Bayesian estimation techniques under varying sampling strategies, contributing to the broader understanding of reliability analysis in CSPALTE scenarios.

Myocardial T1 mapping using an instantaneous signal loss simulation modeling and a Bayesian estimation method: A robust T1 extraction method free of tuning parameters.

The Instantaneous Signal Loss Simulation (InSiL) model is a promising alternative to the classical mono-exponential fitting of the Modified Look-Locker Inversion-recovery (MOLLI) sequence in cardiac T1 mapping applications, which achieves better accuracy and is less sensitive to heart rate (HR) variations. Classical non-linear least squares (NLLS) estimation methods require some parameters of the model to be fixed a priori in order to give reliable T1 estimations and avoid outliers. This introduces further bias in the estimation, reducing the advantages provided by the InSiL model. In this paper, a novel Bayesian estimation method using a hierarchical model is proposed to fit the parameters of the InSiL model. The hierarchical Bayesian modeling has a shrinkage effect that works as a regularizer for the estimated values, by pulling spurious estimated values toward the group-mean, hence reducing greatly the number of outliers. Simulations, physical phantoms, and in-vivo human cardiac data have been used to show that this approach estimates accurately all the InSiL parameters, and achieve high precision estimation of the T1 compared to the classical MOLLI model and NLLS InSiL estimation.

Multiscale Bayes Adaptive Threshold Wavelet Transform Geomagnetic Basemap Denoising Taking Residual Constraints into Account.

To achieve high-precision geomagnetic matching navigation, a reliable geomagnetic anomaly basemap is essential. However, the accuracy of the geomagnetic anomaly basemap is often compromised by noise data that are inherent in the process of data acquisition and integration of multiple data sources. In order to address this challenge, a denoising approach utilizing an improved multiscale wavelet transform is proposed. The denoising process involves the iterative multiscale wavelet transform, which leverages the structural characteristics of the geomagnetic anomaly basemap to extract statistical information on model residuals. This information serves as the a priori knowledge for determining the Bayes estimation threshold necessary for obtaining an optimal wavelet threshold. Additionally, the entropy method is employed to integrate three commonly used evaluation indexes-the signal-to-noise ratio, root mean square (RMS), and smoothing degree. A fusion model of soft and hard threshold functions is devised to mitigate the inherent drawbacks of a single threshold function. During denoising, the Elastic Net regular term is introduced to enhance the accuracy and stability of the denoising results. To validate the proposed method, denoising experiments are conducted using simulation data from a sphere magnetic anomaly model and measured data from a Pacific Ocean sea area. The denoising performance of the proposed method is compared with Gaussian filter, mean filter, and soft and hard threshold wavelet transform algorithms. The experimental results, both for the simulated and measured data, demonstrate that the proposed method excels in denoising effectiveness; maintaining high accuracy; preserving image details while effectively removing noise; and optimizing the signal-to-noise ratio, structural similarity, root mean square error, and smoothing degree of the denoised image.

Bayesian inverse problem for a fractional diffusion model of cell migration.

In the present work, both direct and inverse problems are considered for a Fisher-type fractional diffusion equation, which is proposed to describe the phenomenon of cell migration. For the direct problem, a solution is given via the Fourier method and the Laplace transform. On the other hand, we solved the inverse problem from a Bayesian statistical framework using a set of data that are the result of a cell migration experiment on a wound closure assay. We estimated the parameters of the mathematical model via Markov Chain Monte Carlo methods.

Improving Microstructural Estimation in Time-Dependent Diffusion MRI With a Bayesian Method.

BACKGROUND: Accurately fitting diffusion-time-dependent diffusion MRI (td-dMRI) models poses challenges due to complex and nonlinear formulas, signal noise, and limited clinical data acquisition. PURPOSE: Introduce a Bayesian methodology to refine microstructural fitting within the IMPULSED (Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion) model and optimize the prior distribution within the Bayesian framework. STUDY TYPE: Retrospective. POPULATION: Involving 69 pediatric patients (median age 6 years, interquartile range [IQR] 3-9 years, 61% male) with 41 low-grade and 28 high-grade gliomas, of which 76.8% were identified within the brainstem or cerebellum. FIELD STRENGTH/SEQUENCE: 3 T, oscillating gradient spin-echo (OGSE) and pulsed gradient spin-echo (PGSE). ASSESSMENT: The Bayesian method's performance in fitting cell diameter ( d $$ d $$ ), intracellular volume fraction ( f in $$ {f}_{in} $$ ), and extracellular diffusion coefficient ( D ex $$ {D}_{ex} $$ ) was compared against the NLLS method, considering simulated and experimental data. The tumor region-of-interest (ROI) were manually delineated on the b0 images. The diagnostic performance in distinguishing high- and low-grade gliomas was assessed, and fitting accuracy was validated against H&E-stained pathology. STATISTICAL TESTS: T-test, receiver operating curve (ROC), area under the curve (AUC) and DeLong's test were conducted. Significance considered at P < 0.05. RESULTS: Bayesian methodology manifested increased accuracy with robust estimates in simulation (RMSE decreased by 29.6%, 40.9%, 13.6%, and STD decreased by 29.2%, 43.5%, and 24.0%, respectively for d $$ d $$ , f in $$ {f}_{in} $$ , and D ex $$ {D}_{ex} $$ compared to NLLS), indicating fewer outliers and reduced error. Diagnostic performance for tumor grade was similar in both methods, however, Bayesian method generated smoother microstructural maps (outliers ratio decreased by 45.3% ± 19.4%) and a marginal enhancement in correlation with H&E staining result (r = 0.721 for f in $$ {f}_{in} $$ compared to r = 0.698 using NLLS, P = 0.5764). DATA CONCLUSION: The proposed Bayesian method substantially enhances the accuracy and robustness of IMPULSED model estimation, suggesting its potential clinical utility in characterizing cellular microstructure. EVIDENCE LEVEL: 3 TECHNICAL EFFICACY: Stage 1.

Sub-Nyquist SAR Imaging and Error Correction Via an Optimization-Based Algorithm.

Sub-Nyquist synthetic aperture radar (SAR) based on pseudo-random time-space modulation has been proposed to increase the swath width while preserving the azimuthal resolution. Due to the sub-Nyquist sampling, the scene can be recovered by an optimization-based algorithm. However, these methods suffer from some issues, e.g., manually tuning difficulty and the pre-definition of optimization parameters, and a low signal-noise ratio (SNR) resistance. To address these issues, a reweighted optimization algorithm, named pseudo-ℒ0-norm optimization algorithm, is proposed for the sub-Nyquist SAR system in this paper. A modified regularization model is first built by applying the scene prior information to nearly acquire the number of nonzero elements based on Bayesian estimation, and then this model is solved by the Cauchy-Newton method. Additionally, an error correction method combined with our proposed pseudo-ℒ0-norm optimization algorithm is also present to eliminate defocusing in the motion-induced model. Finally, experiments with simulated signals and strip-map TerraSAR-X images are carried out to demonstrate the effectiveness and superiority of our proposed algorithm.

Impact of carbon fiscal policy on Zhejiang Economy-Evidence from E-DSGE.

This paper studies the impact of carbon fiscal policy on the Zhejiang economy through the lens of a DSGE model with an environmental sector. The model was estimated via Bayesian estimation using data from Zhejiang Province for the period from 2005Q1 to 2021Q4. We found that both carbon tax and carbon emission subsidy can improve environmental quality and reduce carbon emissions. However, the subsidy tends to stimulate output and employment more, while both policies have a negative impact on consumption and investment. We suggest that the government should exercise caution in implementing these policies, as their scale of impact is relatively small. The combination of the two policies could neutralize their impact on output but may enhance their impact on other sectors in Zhejiang. However, the structure and timing of these policies matter; implementing a low carbon tax first followed by a high carbon subsidy would be preferable. Furthermore, we examined and concluded that emission technology, particularly at the firm level, can play a significant role in mitigating the negative impact.

External financial and monetary policy shocks: Do they matter for Korean macroeconomy?

Given Korea's status as a small, open economy, it exhibits a pronounced sensitivity to external shocks. Consequently, this article seeks to elucidate the impact of external financial and monetary policy shocks on the fluctuation of critical macroeconomic variables within Korea. Employing Bayesian estimation alongside the impulse response function for empirical analysis, the findings reveal that external financial and monetary policy shocks precipitate declines in exports, output, employment, real wages, consumption, investment, and imports. Conversely, these shocks are associated with increases in both the price level and inflation, highlighting the multifaceted effects of external pressures on the domestic economic landscape. Further, through forecast error variance decomposition, this study demonstrates that, relative to shocks stemming from productivity, terms of trade, and real exchange rate variations, external financial and monetary policy shocks exert a considerably milder impact on the fluctuations of Korea's key macroeconomic variables. This insight suggests a potential area for enhancement in the existing Korean literature on this topic, advocating for the integration of these findings to enrich understanding and analysis. In summary, by delving into the nuanced effects of external shocks on Korea's economy, this article contributes valuable perspectives to the discourse, suggesting avenues for further research and policy formulation. The integration of these results into the broader body of Korean economic literature could significantly augment current understandings and interpretations of Korea's economic dynamics in the face of global financial and monetary turbulence.

Bayesian estimation of group event-related potential components (BEGEP): testing a model for synthetic and real datasets.

Objective.The spatial resolution of event-related potentials (ERPs) recorded on the head surface is quite low, since the sensors located on the scalp register mixtures of signals from several cortical sources. Bayesian models for multi-channel ERPs obtained from a group of subjects under multiple task conditions can aid in recovering signals from these sources.Approach.This study introduces a novel model that captures several important characteristics of ERP, including person-to-person variability in the magnitude and latency of source signals. Furthermore, the model takes into account that ERP noise, the main source of which is the background electroencephalogram, has the following properties: it is spatially correlated, spatially heterogeneous, and varies over time and from person to person. Bayesian inference algorithms have been developed to estimate the parameters of this model, and their performance has been evaluated through extensive experiments using synthetic data and real ERPs records in a large number of subjects (N= 351).Main results.The signal estimates obtained using these algorithms were compared with the results of the analysis of ERPs by conventional methods. This comparison showed that the use of this model is suitable for the analysis of ERPs and helps to reveal some features of source signals that are difficult to observe in their mixture signals recorded on the scalp.Significance.This study shown that the proposed method is a potentially useful tool for analyzing ERPs collected from groups of subjects in various cognitive neuroscience experiments.

Accurate gamma-ray dose measurement up to 10 MeV by glass dosimeter with a sensitivity control filter for BNCT.

Glass dosimeters are very useful and convenient detection elements in radiation dosimetry. In this study, this glass dosimeter was applied to a BNCT treatment field. Boron Neutron Capture Therapy (BNCT) is a next-generation radiation therapy that can selectively kill only cancer cells. In the BNCT treatment field, both neutrons and secondary gamma-rays are generated. In other words, it is a mixed radiation field of neutrons and gamma-rays. We thus proposed a novel method to measure only gamma-ray dose in the mixed field using two RPLGD (Radiophoto-luminescence Glass Dosimeter) and two sensitivity control filters in order to control the dose response of the filtered RPLGD to be proportional to the air kerma coefficients, even if the gamma-ray energy spectrum is unknown. As the filter material iron was selected, and it was finally confirmed that reproduction of the air kerma coefficients was excellent within an error of 5.3% in the entire energy range up to 10 MeV. In order to validate this method, irradiation experiments were carried out using standard gamma-ray sources. As the result, the measured doses were in acceptably good agreement with the theoretical calculation results by PHITS. In the irradiation experiment with a volume source in a nuclear fuel storage room, the measured dose rates showed larger compared with survey meter values. In conclusion, the results of the standard sources showed the feasibility of this method, however for the volume source the dependence of the gamma-ray incident angle on the dosimeter was found to be not neglected. In the next step, it will be necessary to design a thinner filter in order to suppress the effect of the incident angle.

Statistical inference for Nadarajah-Haghighi distribution under unified hybrid censored competing risks data.

Nadarajah and Haghighi distribution (NHD) inferences problem has been discussed under unified hybrid censoring scheme (UHCS) in the existence of competing risks model. Competing risks model is defined by time-to-failure under more than one cause of failure, which can be dependent or independent. This study focuses on discussing the case of failure partially observed causes of failure competing risks model. We obtain various inferences: we first obtain the MLE, in addition, we construct approximate confidence intervals (ACIs). Second, we obtain the Bayes estimator via SELF and related highest posterior density (HPD) using Markov Chain Monte Carlo (MCMC). Finally, an electrical appliances data set and simulation studies have been analyzed for further illustrations.

The 3-component mixture of power distributions under Bayesian paradigm with application of life span of fatigue fracture.

Mixture distributions are naturally extra attractive to model the heterogeneous environment of processes in reliability analysis than simple probability models. This focus of the study is to develop and Bayesian inference on the 3-component mixture of power distributions. Under symmetric and asymmetric loss functions, the Bayes estimators and posterior risk using priors are derived. The presentation of Bayes estimators for various sample sizes and test termination time (a fact of time after that test is terminated) is examined in this article. To assess the performance of Bayes estimators in terms of posterior risks, a Monte Carlo simulation along with real data study is presented.

Selection of random coefficients in ordered response models: a framework to detect heterogeneity in household surveys.

This paper develops a Bayesian method to detect heterogeneity in the relationship between covariates and the outcome in models with ordered responses. To this end, we construct an efficient Markov chain Monte Carlo algorithm for a hierarchical Bayesian model that selects random coefficients in ordered models. This method extends an approach for selecting random coefficients in linear mixed models into the ordered setting by adding two enhancements that are relevant to the latter category of models. First, we construct steps to efficiently estimate cut-points by addressing identification and ordering constraints. Second, we develop a framework to evaluate marginal effects that combine the fixed and random effects of each covariate. The marginal effects additionally allow for model uncertainty by averaging across models visited by the selection algorithm. Simulation studies demonstrate that this method detects random effects when they are present, estimates parameters accurately and efficiently samples from the posterior with low autocorrelations across successive draws. On applying this method on data from the survey of consumer expectations, we find clear support for the presence of household-level heterogeneity in relationships between demographic variables, and current as well as expected financial conditions.

Overlapping yet dissociable contributions of superiority illusion features to Ponzo illusion strength and metacognitive performance.

Humans are typically inept at evaluating their abilities and predispositions. People dismiss such a lack of metacognitive insight into their capacities while even enhancing (albeit illusorily) self-evaluation such that they should have more desirable traits than an average peer. This superiority illusion helps maintain a healthy mental state. However, the scope and range of its influence on broader human behavior, especially perceptual tasks, remain elusive. As belief shapes the way people perceive and recognize, the illusory self-superiority belief potentially regulates our perceptual and metacognitive performance. In this study, we used hierarchical Bayesian estimation and machine learning of signal detection theoretic measures to understand how the superiority illusion influences visual perception and metacognition for the Ponzo illusion. Our results demonstrated that the superiority illusion correlated with the Ponzo illusion magnitude and metacognitive performance. Next, we combined principal component analysis and cross-validated regularized regression (relaxed elastic net) to identify which superiority components contributed to the correlations. We revealed that the "extraversion" superiority dimension tapped into the Ponzo illusion magnitude and metacognitive ability. In contrast, the "honesty-humility" and "neuroticism" dimensions only predicted Ponzo illusion magnitude and metacognitive ability, respectively. These results suggest common and distinct influences of superiority features on perceptual sensitivity and metacognition. Our findings contribute to the accumulating body of evidence indicating that the leverage of superiority illusion is far-reaching, even to visual perception.

Point Cloud Denoising and Feature Preservation: An Adaptive Kernel Approach Based on Local Density and Global Statistics.

Noise removal is a critical stage in the preprocessing of point clouds, exerting a significant impact on subsequent processes such as point cloud classification, segmentation, feature extraction, and 3D reconstruction. The exploration of methods capable of adapting to and effectively handling the noise in point clouds from real-world outdoor scenes remains an open and practically significant issue. Addressing this issue, this study proposes an adaptive kernel approach based on local density and global statistics (AKA-LDGS). This method constructs the overall framework for point cloud denoising using Bayesian estimation theory. It dynamically sets the prior probabilities of real and noise points according to the spatial function relationship, which varies with the distance from the points to the center of the LiDAR. The probability density function (PDF) for real points is constructed using a multivariate Gaussian distribution, while the PDF for noise points is established using a data-driven, non-parametric adaptive kernel density estimation (KDE) approach. Experimental results demonstrate that this method can effectively remove noise from point clouds in real-world outdoor scenes while maintaining the overall structural features of the point cloud.

Birnbaum Saunders distribution for imprecise data: statistical properties, estimation methods, and real life applications.

A neutrosophic statistic is a random variable and it has a neutrosophic probability distribution. So, in this paper, we introduce the new neutrosophic Birnbaum-Saunders distribution. Some statistical properties are derived, using Mathematica 13.1.1 and R-Studio Software. Two different estimation methods for parameters estimation are introduced for new distribution: maximum likelihood estimation method and Bayesian estimation method. A Monte-Carlo simulation study is used to investigate the behavior of parameters estimates of new distribution, compare the performance of different estimates, and compare between our distribution and the classical version of Birnbaum-Saunders. Finally, study the validity of our new distribution in real life.

A Bayesian benchmark concentration analysis for urinary fluoride and intelligence in adults in Guizhou, China.

Environmental fluoride exposure has been linked to numerous cases of fluorosis worldwide. Previous studies have indicated that long-term exposure to fluoride can result in intellectual damage among children. However, a comprehensive health risk assessment of fluorosis-induced intellectual damage is still pending. In this research, we utilized the Bayesian Benchmark Dose Analysis System (BBMD) to investigate the dose-response relationship between urinary fluoride (U-F) concentration and Raven scores in adults from Nayong, Guizhou, China. Our research findings indecate a dose-response relationship between the concentration of U-F and intelligence scores in adults. As the benchmark response (BMR) increased, both the benchmark concentration (BMCs) and the lower bound of the credible interval (BMCLs) increased. Specifically, BMCs for the association between U-F and IQ score were determined to be 0.18 mg/L (BMCL1 = 0.08 mg/L), 0.91 mg/L (BMCL5 = 0.40 mg/L), 1.83 mg/L (BMCL10 = 0.83 mg/L) when using BMRs of 1 %, 5 %, and 10 %. These results indicate that U-F can serve as an effective biomarker for monitoring the loss of IQ in population. We propose three interim targets for public policy in preventing interllectual harm from fluoride exposure.

Estimation for the P(X > Y) of Lomax distribution under accelerated life tests.

The system or unit survives when strength is more significant than the stress enjoined. This procedure is usually used in many companies to test their product. The reliability or the quality of the scheme or component is described by the parameters of stress-strength reliability (R=P(X>Y)) where X denotes strength and Y indicates stress. In this article, we adopted the statistical inference of R while the two arbitrary factors X and Y are independent and approach the Lomax lifetime distribution with common scale parameters. Also, the strength and stress variables are subjected to a partial step-stress-quickened life experiment. The classical estimation and Bayes method create the point estimate of R. Confidence intervals of R are computed with asymptotic distribution, bootstrap technique, and Bayesian credible intervals. All results are evaluated and compared under an extensive simulation study. Finally, the lifetime data sets generated from the Lomax distribution are used to analyze the system's reliability by estimating R.

Kinetic Modeling of Brain [18-F]FDG Positron Emission Tomography Time Activity Curves with Input Function Recovery (IR) Method.

Accurate positron emission tomography (PET) data quantification relies on high-quality input plasma curves, but venous blood sampling may yield poor-quality data, jeopardizing modeling outcomes. In this study, we aimed to recover sub-optimal input functions by using information from the tail (5th-100th min) of curves obtained through the frequent sampling protocol and an input recovery (IR) model trained with reference curves of optimal shape. Initially, we included 170 plasma input curves from eight published studies with clamp [18F]-fluorodeoxyglucose PET exams. Model validation involved 78 brain PET studies for which compartmental model (CM) analysis was feasible (reference (ref) + training sets). Recovered curves were compared with original curves using area under curve (AUC), max peak standardized uptake value (maxSUV). CM parameters (ref + training sets) and fractional uptake rate (FUR) (all sets) were computed. Original and recovered curves from the ref set had comparable AUC (d = 0.02, not significant (NS)), maxSUV (d = 0.05, NS) and comparable brain CM results (NS). Recovered curves from the training set were different from the original according to maxSUV (d = 3) and biologically plausible according to the max theoretical K1 (53//56). Brain CM results were different in the training set (p < 0.05 for all CM parameters and brain regions) but not in the ref set. FUR showed reductions similarly in the recovered curves of the training and test sets compared to the original curves (p < 0.05 for all regions for both sets). The IR method successfully recovered the plasma inputs of poor quality, rescuing cases otherwise excluded from the kinetic modeling results. The validation approach proved useful and can be applied to different tracers and metabolic conditions.