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A major key success factor regarding proficient Bayes threshold denoising refers to noise variance estimation. This paper focuses on assessing different noise variance estimations in three Bayes threshold models on two different characteristic brain lesions/tumor magnetic resonance imaging (MRIs).

Here, three Bayes threshold denoising models based on different noise variance estimations under the stationary wavelet transforms (SWT) domain are mainly assessed, compared to state-of-the-art non-local means (NLMs). Each of those three models, namely D1, GB and DR models, respectively, depends on the most detail wavelet subband at the first resolution level, on the entirely global detail subbands and on the detail subband in each direction/resolution. Explicit and implicit denoising performance are consecutively assessed by threshold denoising and segmentation identification results.

Implicit performance assessment points the first–second best accuracy, 0.9181 and 0.9048 Dice similarity coefficient (Dice), sequentially yielded by GB and DR; reliability is indicated by 45.66% Dice dropping of DR, compared against 53.38, 61.03 and 35.48% of D1 GB and NLMs, when increasing 0.2 to 0.9 noise level on brain lesions MRI. For brain tumor MRI under 0.2 noise level, it denotes the best accuracy of 0.9592 Dice, resulted by DR; however, 8.09% Dice dropping of DR, relative to 6.72%, 8.85 and 39.36% of D1, GB and NLMs is denoted. The lowest explicit and implicit denoising performances of NLMs are obviously pointed.

A future improvement of denoising performance possibly refers to creating a semi-supervised denoising conjunction model. Such model utilizes the denoised MRIs, resulted by DR and D1 thresholding model as uncorrupted image version along with the noisy MRIs, representing corrupted version ones during autoencoder training phase, to reconstruct the original clean image.

This paper should be of interest to readers in the areas of technologies of computing and information science, including data science and applications, computational health informatics, especially applied as a decision support tool for medical image processing.

In most cases, DR and D1 provide the first–second best implicit performances in terms of accuracy and reliability on both simulated, low-detail small-size region-of-interest (ROI) brain lesions and realistic, high-detail large-size ROI brain tumor MRIs.

This paper seeks to focus on the study and estimation of reliability characteristics of Maxwell distribution under Type‐II censoring scheme.

Maximum likelihood estimation and Bayes estimation methods have been used for the estimation of reliability characteristics. Monte‐Carlo simulation is used to compare the efficiency of the estimates developed by these estimation methods.

With prior information on the parameter of Maxwell distribution, Bayes estimation provides better estimates of reliability characteristics; otherwise Maximum likelihood estimation is good enough to use for reliability practitioners.

When items are costly, Type‐II censoring scheme can be used to save the cost of the experiment and the discussed methods provide the means to estimate the reliability characteristics of the proposed lifetime model under this scheme.

The study is useful for researchers and practitioners in reliability theory and also for scientists in physics and chemistry, where Maxwell distribution is widely used.

The purpose of this paper is to consider a General System Configuration (GSC), whose particular cases are all the popular system configurations. In reliability engineering one comes across various system configurations, for example, series, parallel and k‐out of‐m system models, which consist of a number of components.

The paper gives a general approach to express the reliability properties of the whole system in terms of component parameters. The reliability of a GSC is expressed as a polynomial of the component reliability. Lifetime data on components have been used to estimate the system reliability characteristics through classical and Bayes estimation procedures.

The paper finds that the underlying distribution is assumed to be Weibull and, in view of cost constraints, Type‐II censored information has been used.

The paper is useful for reliability practitioners as well as theoreticians. It provides an easy method to estimate the reliability of any system configuration.

Three types of estimation procedures for a general system configuration have been developed for the first time. The lifetimes of components are assumed to follow widely used Weibull distribution, whose particular case is the most popular exponential distribution.

The purpose of this paper is to estimate the multicomponent reliability by assuming the unit-Gompertz (UG) distribution. Both stress and strength are assumed to have an UG distribution with common scale parameter.

The reliability of a multicomponent stress–strength system is obtained by the maximum likelihood (MLE) and Bayesian method of estimation. Bayes estimates of system reliability are obtained by using Lindley’s approximation and Metropolis–Hastings (M–H) algorithm methods when all the parameters are unknown. The highest posterior density credible interval is obtained by using M–H algorithm method. Besides, uniformly minimum variance unbiased estimator and exact Bayes estimates of system reliability have been obtained when the common scale parameter is known and the results are compared for both small and large samples.

Based on the simulation results, the authors observe that Bayes method provides better estimation results as compared to MLE. Proposed asymptotic and HPD intervals show satisfactory coverage probabilities. However, average length of HPD intervals tends to remain shorter than the corresponding asymptotic interval. Overall the authors have observed that better estimates of the reliability may be achieved when the common scale parameter is known.

Most of the lifetime distributions used in reliability analysis, such as exponential, Lindley, gamma, lognormal, Weibull and Chen, only exhibit constant, monotonically increasing, decreasing and bathtub-shaped hazard rates. However, in many applications in reliability and survival analysis, the most realistic hazard rates are upside-down bathtub and bathtub-shaped, which are found in the unit-Gompertz distribution. Furthermore, when reliability is measured as percentage or ratio, it is important to have models defined on the unit interval in order to have plausible results. Therefore, the authors have studied the multicomponent stress–strength reliability under the unit-Gompertz distribution by comparing the MLEs, Bayes estimators and UMVUEs.

This paper aims to deal with the estimation of the empirical Bayesian exact confidence limits of reliability indexes of a cold standby series system with (n+k−1) units under the general progressive Type II censoring scheme.

Assuming that the lifetime of each unit in the system is identical and independent random variable with exponential distribution, the exact confidence limits of the reliability indexes are derived by using an empirical Bayes approach when an exponential prior distribution of the failure rate parameter is considered. The accuracy of these confidence limits is examined in terms of their coverage probabilities by means of Monte-Carlo simulations.

The simulation results show that accuracy of exact confidence limits of reliability indexes of a cold standby series system is efficient. Therefore, this approach is good enough to use for reliability practitioners in order to improve the system reliability.

When items are costly, the general progressive Type II censoring scheme is used to reduce the total test time and the associated cost of an experiment. The proposed method provides the means to estimate the exact confidence limits of reliability indexes of the proposed cold standby series system under this scheme.

The application of the proposed technique will help the reliability engineers/managers/system engineers in various industrial and other setups where a cold standby series system is widely used.

The study based on the estimation of the stress–strength reliability parameter plays a vital role in showing system efficiency. In this paper, considering independent strength and stress random variables distributed as inverted exponentiated Rayleigh model, the author have developed estimation procedures for the stress–strength reliability parameter R = P(X>Y) under Type II hybrid censored samples.

The maximum likelihood and Bayesian estimates of R based on Type II hybrid censored samples are evaluated. Because there is no closed form for the Bayes estimate, the author use the Metropolis–Hastings algorithm to obtain approximate Bayes estimate of the reliability parameter. Furthermore, the author construct the asymptotic confidence interval, bootstrap confidence interval and highest posterior density (HPD) credible interval for R. The Monte Carlo simulation study has been conducted to compare the performance of various proposed point and interval estimators. Finally, the validity of the stress–strength reliability model is demonstrated via a practical case.

The performance of various point and interval estimators is compared via the simulation study. Among all proposed estimators, Bayes estimators using MHG algorithm show minimum MSE for all considered censoring schemes. Furthermore, the real data analysis indicates that the splashing diameter decreases with the increase of MPa under different hybrid censored samples.

The frequentist and Bayesian methods are developed to estimate the associated parameters of the reliability model under the hybrid censored inverted exponentiated Rayleigh distribution. The application of the proposed stress–strength reliability model will help the reliability engineers and also other scientists to estimate the system reliability.

The step-stress accelerated test is the most appropriate statistical method to obtain information about the reliability of new products faster than would be possible if the product was left to fail in normal use. This paper presents the multiple step-stress accelerated life test using type-II censored data and assuming a cumulative exposure model. The authors propose a Bayesian inference with the lifetimes of test item under gamma distribution. The choice of the loss function is an essential part in the Bayesian estimation problems. Therefore, the Bayesian estimators for the parameters are obtained based on different loss functions and a comparison with the usual maximum likelihood (MLE) approach is carried out. Finally, an example is presented to illustrate the proposed procedure in this paper.

A Bayesian inference is performed and the parameter estimators are obtained under symmetric and asymmetric loss functions. A sensitivity analysis of these Bayes and MLE estimators are presented by Monte Carlo simulation to verify if the Bayesian analysis is performed better.

The authors demonstrated that Bayesian estimators give better results than MLE with respect to MSE and bias. The authors also consider three types of loss functions and they show that the most dominant estimator that had the smallest MSE and bias is the Bayesian under general entropy loss function followed closely by the Linex loss function. In this case, the use of a symmetric loss function as the SELF is inappropriate for the SSALT mainly with small data.

Most of papers proposed in the literature present the estimation of SSALT through the MLE. In this paper, the authors developed a Bayesian analysis for the SSALT and discuss the procedures to obtain the Bayes estimators under symmetric and asymmetric loss functions. The choice of the loss function is an essential part in the Bayesian estimation problems.

The purpose of this paper is to discuss and demonstrate “best practices” for creating quantitative behavioural investigative advice (i.e. statements to assist police with psychological and behavioural aspects of investigations) where complex statistical modelling is not available.

Using a sample of 361 serial stranger sexual offenses and a cross-validation approach, the paper demonstrates prediction of offender characteristics using base rates and using Bayes’ Theorem. The paper predicts four dichotomous offender characteristic variables, first using simple base rates, then using Bayes’ Theorem with 16 categorical crime scene variable predictors.

Both methods consistently predict better than chance. By incorporating more information, analyses based on Bayes’ Theorem (74.6 per cent accurate) predict with 11.1 per cent more accuracy overall than analyses based on base rates (63.5 per cent accurate), and provide improved advising estimates in line with best practices.

The study demonstrates how useful predictions of offender characteristics can be acquired from crime information without large (i.e. >500 cases) data sets or “trained” statistical models. Advising statements are constructed for discussion, and results are discussed in terms of the pragmatic usefulness of the methods for police investigations.

This chapter proposes semiparametric estimation of the relationship between growth rate of GDP per capita, growth rates of physical and human capital, labor as well as other covariates and common trends for a panel of 23 OECD countries observed over the period 1971–2015. The observed differentiated behaviors by country reveal strong heterogeneity. This is the motivation behind using a mixed fixed- and random coefficients model to estimate this relationship. In particular, this chapter uses a semiparametric specification with random intercepts and slopes coefficients. Motivated by Lee and Wand (2016), the authors estimate a mean field variational Bayes semiparametric model with random coefficients for this panel of countries. Results reveal nonparametric specifications for the common trends. The use of this flexible methodology may enrich the empirical growth literature underlining a large diversity of responses across variables and countries.

We put forward the idea that for model selection the intrinsic priors are becoming a center of a cluster of a dominant group of methodologies for objective Bayesian Model Selection.

The intrinsic method and its applications have been developed in the last two decades, and has stimulated closely related methods. The intrinsic methodology can be thought of as the long searched approach for objective Bayesian model selection and hypothesis testing.

In this paper we review the foundations of the intrinsic priors, their general properties, and some of their applications.