Soleiman Khazaei

Nowadays, Z‐numbers are known as the most powerful tool for describing the uncertainty process concerning the degree of confidence. In this matter, regression based on Z‐numbers is called an essential issue because it establishes a functional relationship among Z‐number variables. More importantly, quantile regression is an efficient statistical method for estimating and inferring conditional quantile functions. Thus, this paper aims to develop quantile regression under three models. The first model encompasses explanatory variables, response variable, and Z‐number parameters. The second one includes explanatory variables, a Z‐number response variable, and crisp parameters. Finally, the third one includes crisp explanatory variables, response variable, and Z‐number parameters. The idea of the method for the first model is to employ the mean squared error (MSE) method. On the other hand, the idea of the second model is to utilize a new ranking function. The concept of the third model is to propose a loss function between numbers based on Z‐numbers, which can render some quantiles based on Z‐numbers. Then, a quantile regression model is fitted based on the proposed loss function. Furthermore, two indices are defined to assess the goodness of fit of the optimal quantile regression models based on Z‐numbers. Meanwhile, several examples are solved to assess the efficiency of the proposed models. Eventually, the applicability of the proposed approach is surveyed in heart disease prediction modeling based on a realistically simulated dataset, and future validation on real patient data is recommended. The obtained results reveal that the proposed method outperforms in every condition where regression based on Z‐numbers fails and also provides in‐depth results.

Nonlinear regression models are widely utilized in many scientific disciplines. Precisely estimating an optimal nonlinear regression model is critical, especially when considering potential biases may arise in Bayesian optimal design. The current work introduces Bayesian and nonparametric Bayesian optimal designs based on the length of interconnected intervals for the unit exponential (UE) regression model. In cases where parameter information or historical data are limited, a nonparametric Bayesian method is employed through placing a Dirichlet process (DP) prior on the space of distribution functions. Lastly, the efficiency of various optimal designs is assessed and compared.

In this paper, we develop a Bayesian nonparametric approach for analyzing weighted survival data. Specifically, we employ the Dirichlet Process Burr XII Mixture Model (DPBMM) to estimate the underlying density and survival functions when the observed data are weighted. Parameters are inferred using Markov chain Monte Carlo (MCMC) methods, and the Metropolis- Hastings algorithm is applied to obtain de-biased samples from the weighted observations. Numerical illustrations are provided using both simulated and real lifetime data, including the presence of censored observations. The performance of the proposed method is compared with classical kernel density estimates to demonstrate its flexibility in modeling complex and heavy-tailed distributions.

Accelerated failure time models are used in survival analysis when the data is censored, especially when combined with auxiliary variables. When the models in question depend on an unknown parameter, one of the methods that can be applied is Bayesian methods, which consider the parameter space as infinitely dimensional. In ...

Nonlinear regression models are extensively applied across various scientific disciplines. It is vital to accurately fit the optimal nonlinear model while considering the biases of the Bayesian optimal design. We present a Bayesian optimal design by utilising the Dirichlet process as a prior. The Dirichlet process serves as a fundamental tool in the exploration of Nonparametric Bayesian inference, offering multiple representations that are well-suited for application. This research paper introduces a novel one-parameter model, referred to as the ’Unit-Exponential distribution’, specifically designed for the unit interval. Additionally, we employ a stick-breaking representation to approximate the D-optimality criterion considering the Dirichlet process as a functional tool. Through this approach, we aim to identify a Nonparametric Bayesian optimal design.

Background: In medical research and survival analysis, it is common for an individual or item's failure to be attributable to multiple causes, also known as competing risks. This article focuses on examining the competing risks model as the data increasingly becomes type II censored and randomly removed. The model assumes ...

In the sampling approaches framework, the combination of the information on the sizes of the nonsampled units can help to attain better estimators by using semiparametric models. Sometimes, the design variables that have an important role in the sampling mechanism are not available. Hence predictions require to be adapted for the consequence of selection. To infer the population mean in a sample survey, we study Bayesian nonparametric model with Dirichlet process prior by considering the inverse-probability weights as the only available information. Indeed, we present a Bayesian nonparametric mixture of regression models for the survey outcomes with the weights as predictors and impute the nonsampled units. Finally, the model-based estimators that are derived from the Bayesian (parametric and nonparametric) methods are compared with the design-based estimator based on the simulation approaches.

Kernel density estimation has been applied in many computational subjects. In this paper, we propose a density estimation procedure from a Bayesian nonparametric perspective using Dirichlet process prior for the length-biased data under an unknown kernel function. In this situation, the kernel within the Dirichlet process mixture model will be approximated by the kernel density estimator. We present a Bayesian nonparametric method for finding the bandwidth parameter in the kernel density estimation using a Markov chain Monte Carlo approach. Then, this approach is used to the simulated and real data set. Finally, we compare the proposed bandwidth estimation with the other estimations like cross-validation and Bayes based on the mean integrated squared error criterion.

Recently, the Bayesian nonparametric approaches in survival studies attract much more attentions. Because of multimodality in survival data, the mixture models are very common. We introduce a Bayesian nonparametric mixture model with Burr distribution (Burr type XII) as the kernel. Since the Burr distribution shares good properties of common distributions on survival analysis, it has more flexibility than other distributions. By applying this model to simulated and real failure time datasets, we show the preference of this model and compare it with Dirichlet process mixture models with different kernels. The Markov chain Monte Carlo (MCMC) simulation methods to calculate the posterior distribution are used.

Recently, the Bayesian nonparametric approach in survival studies attracts much more attentions. Because of multi modality in survival data, the mixture models are very common in this field. One of the famous priors on Bayesian nonparametric models is Dirichlet process prior. In this paper we introduce a Bayesian nonparametric mixture model with Burr distribution(Burr type XII) as the kernel of mixture model. Since the Burr distribution shares good properties of common distributions on survival analysis, it has more flexibility than other distributions. By applying this model to simulated and real failure time data sets, we show the preference of this model and compare it with other Dirichlet process mixture models with different kernels. And also we show that this model can be applied for the right censored data. For calculating the posterior of the parameters for inference and modeling, we used the MCMC simulation methods, especially Gibbs sampling.