Explore the vast range of titles available.

We consider full Bayesian inference in the multivariate normal mean model in the situation that the mean vector is sparse. The prior distribution on the vector of means is constructed hierarchically by first choosing a collection of nonzero means and next a prior on the nonzero values. We consider the posterior distribution in the frequentist set-up that the observations are generated according to a fixed mean vector, and are interested in the posterior distribution of the number of nonzero components and the contraction of the posterior distribution to the true mean vector. We find various combinations of priors on the number of nonzero coefficients and on these coefficients that give desirable performance. We also find priors that give suboptimal convergence, for instance, Gaussian priors on the nonzero coefficients. We illustrate the results by simulations.

Based on progressively Type-II censored samples, this paper deals with the estimation of multicomponent stress-strength reliability by assuming the Kumaraswamy distribution. Both stress and strength are assumed to have a Kumaraswamy distribution with different the first shape parameters, but having the same second shape parameter. Different methods are applied for estimating the reliability. The maximum likelihood estimate of reliability is derived. Also its asymptotic distribution is used to construct an asymptotic confidence interval. The Bayes estimates of reliability have been developed by using Lindley’s approximation and the Markov Chain Monte Carlo methods due to the lack of explicit forms. The uniformly minimum variance unbiased and Bayes estimates of reliability are obtained when the common second shape parameter is known. The highest posterior density credible intervals are constructed for reliability. Monte Carlo simulations are performed to compare the performances of the different methods, and one data set is analyzed for illustrative purposes.

A comprehensive representation of the road pavement state of health is of great interest. In recent years, automated data collection and processing technology has been used for pavement inspection. In this paper, a new signal on graph (SoG) model of road pavement distresses is presented with the aim of improving automatic pavement distress detection systems. A novel nonlinear Bayesian estimator in recovering distress metrics is also derived. The performance of the methodology was evaluated on a large dataset of pavement distress values collected in field tests conducted in Kazakhstan. The application of the proposed methodology is effective in recovering acquisition errors, improving road failure detection. Moreover, the output of the Bayesian estimator can be used to identify sections where the measurement acquired by the 3D laser technology is unreliable. Therefore, the presented model could be used to schedule road section maintenance in a better way.

IntroductionMycophenolate mofetil (MMF), a pro-drug of mycophenolic acid (MPA), has become a major therapeutic option in juvenile systemic lupus erythematosus (jSLE). Monitoring MPA exposure using area under curve (AUC) has proved its value to increase efficacy and safety in solid organ transplantation both in children and adults, but additional data are required in patients with autoimmune diseases. In order to facilitate MMF therapeutic drug monitoring (TDM) in children, Bayesian estimators (BE) of MPA AUC0–12 h using limited sampling strategies (LSS) have been developed. Our aim was to conduct an external validation of these LSS using rich pharmacokinetics and compare their predictive performance.MethodsPharmacokinetic blood samples were collected from jSLE treated by MMF and MPA plasma concentrations were determined using high-performance liquid chromatography system with ultraviolet detection (HPLC–UV). Individual AUC0–12 h at steady state was calculated using the trapezoid rule and compared with two LSS: (1) ISBA, a two-stage Bayesian approach developed for jSLE and (2) ADAPT, a non-linear mixed effects model with a parametric maximum likelihood approach developed with data from renal transplanted adults.ResultsWe received 41 rich pediatric PK at steady state from jSLE and calculated individual AUC0–12 h. The external validation MPA AUC0–12 h was conducted by selecting the concentration–time points adapted to ISBA and ADAPT: (1) ISBA showed good accuracy (bias: − 0.8 mg h/L), (2) ADAPT resulted in a bias of 6.7 mg L/h. The corresponding relative root mean square prediction error (RSME) was 23% and 43% respectively.ConclusionAccording to our external validation of two LSS of drug exposure, the ISBA model is recommended for Bayesian estimation of MPA AUC0–12 h in jSLE. In the literature focusing on MMF TDM, an efficacy cut-off for MPA AUC0–12 h between 30 and 45 mg h/L is proposed in jSLE but this requires additional validation.

Recently, an improved adaptive Type-II progressive censoring scheme is proposed to ensure that the experimental time will not pass a pre-fixed time and ends the test after recording a pre-fixed number of failures. This paper studies the inference of the competing risks model from Weibull distribution under the improved adaptive progressive Type-II censoring. For this goal, we used the latent failure time model with Weibull lifetime distributions with common shape parameters. The point and interval estimation problems of parameters, reliability and hazard rate functions using the maximum likelihood and Bayesian estimation methods are considered. Moreover, making use of the asymptotic normality of classical estimators and delta method, approximate intervals are constructed via the observed Fisher information matrix. Following the assumption of independent gamma priors, the Bayes estimates of the scale parameters have closed expressions, but when the common shape parameter is unknown, the Bayes estimates cannot be formed explicitly. To solve this difficulty, we recommend using Markov chain Monte Carlo routine to compute the Bayes estimates and to construct credible intervals. A comprehensive Monte Carlo simulation is conducted to judge the behavior of the offered methods. Ultimately, analysis of electrodes data from the life-test of high-stress voltage endurance is provided to illustrate all proposed inferential procedures.

In the classical Poisson model, the distribution represents the number of events occurring within a given time or spatial interval. This study introduces new Bayesian methods for point estimation of the Poisson parameter, utilizing precautionary, entropy, and general entropy loss functions, particularly focusing on cases where the constants are c = 2 and 3. These methods are compared to traditional Bayesian estimators based on squared error and quadratic loss functions. A Monte Carlo simulation study was conducted to evaluate the performance of the proposed estimators, using mean squared error (MSE) as the primary criterion. The results demonstrate that the Bayesian approach, employing quadratic, entropy, and general entropy loss functions with c = 2, provided the most accurate estimates for smaller true parameter values ( 2 = 0.5, 1, or 2), yielding the lowest MSE. For moderately larger true parameter values (2=3, 5), the squared error and quadratic loss functions produced the minimum MSE across a range of sample sizes. For larger true parameter values (2 = 10, 20, 30, and 50), the precautionary loss function exhibited superior performance. These findings underscore the versatility and accuracy of different Bayesian loss functions for Poisson parameter estimation under varying conditions.

- This study estimates the parameters of the ToppLeone exponential distribution through the Bayesian method by applying Lindley's and Tierney-Kadane's (T-К) approximation techniques. The shape and scale parameters are derived using symmetric loss functions such as Squared Error Loss Function (SELF) and Quadratic Loss Function (QLF). The posterior distribution for Exponential, Gamma, Log-normal, and Weibull priors are analyzed by comparing the estimators based on Bayes risk for simulated and real data. It is seen that Bayes estimators using the T-К approximation method produce lower Bayes risk than Lindley's approximation for both the shape and scale parameters under QLF for simulated data whereas, Lindley's approximation outperforms the T-К method for both parameters in the case of real data.

This paper introduces a novel approach that combines symbolic data analysis with matrix theory through the concept of interval-valued random matrices. This framework is designed to address the complexities of real-world data, offering enhanced statistical modeling techniques particularly suited for large and complex datasets where traditional methods may be inadequate. We develop both frequentist and Bayesian methods for the statistical inference of interval-valued random matrices, providing a comprehensive analytical framework. We conduct extensive simulations to compare the performance of these methods, demonstrating that Bayesian estimators outperform maximum likelihood estimators under the Frobenius norm loss function. The practical utility of our approach is further illustrated through an application to climatology and temperature data, highlighting the advantages of interval-valued random matrices in real-world scenarios.

We accurately reconstruct the Local Field Potential time series obtained from anesthetized and awake rats, both before and during CO 2 euthanasia. We apply the Eigensystem Realization Algorithm to identify an underlying linear dynamical system capable of generating the observed data. Time series exhibiting more intricate dynamics typically lead to systems of higher dimensions, offering a means to assess the complexity of the brain throughout various phases of the experiment. Our results indicate that anesthetized brains possess complexity levels similar to awake brains before CO 2 administration. This resemblance undergoes significant changes following euthanization, as signals from the awake brain display a more resilient complexity profile, implying a state of heightened neuronal activity or a last fight response during the euthanasia process. In contrast, anesthetized brains seem to enter a more subdued state early on. Our data-driven techniques can likely be applied to a broader range of electrophysiological recording modalities.

Consider a mobile robot exploring an office building with the aim of observing as much human activity as possible over several days. It must learn where and when people are to be found, count the observed activities, and revisit popular places at the right time. In this paper we present a series of Bayesian estimators for the levels of human activity that improve on simple counting. We then show how these estimators can be used to drive efficient exploration for human activities. The estimators arise from modelling the human activity counts as a partially observable Poisson process (POPP). This paper presents novel extensions to POPP for the following cases: (i) the robot’s sensors are correlated, (ii) the robot’s sensor model, itself built from data, is also unreliable, (iii) both are combined. It also combines the resulting Bayesian estimators with a simple, but effective solution to the exploration-exploitation trade-off faced by the robot in a real deployment. A series of 15 day robot deployments show how our approach boosts the number of human activities observed by 70% relative to a baseline and produces more accurate estimates of the level of human activity in each place and time.