Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring

In this paper, Bayesian and non-Bayesian estimation of the inverted Topp-Leone distribution shape parameter are studied when the sample is complete and random censored. The maximum likelihood estimator (MLE) and Bayes estimator of the unknown parameter are proposed. The Bayes estimates (BEs) have been computed based on the squared error loss (SEL) function and using Markov Chain Monte Carlo (MCMC) techniques. The asymptotic, bootstrap (p,t), and highest posterior density intervals are computed. The Metropolis Hasting algorithm is proposed for Bayes estimates. Monte Carlo simulation is performed to compare the performances of the proposed methods and one real data set has been analyzed for illustrative purposes.

BAYESIAN ESTIMATION AND AN APPLICATION OF GIBBS SAMPLING TECHNIQUE AND RANDOM WALK METROPOLIS - HASTING ALGORITHM IN TWO PHASE LINEAR REGRESSION MODEL

Here, in this research paper, we have applied the Gibbs Sampling Technique and RWM-H (Random Walk Metropolis - Hasting) Algorithm for the Bayesian Estimation of m, β1, β2 and 1/2. Also we have assumed that at some point of time say 'm', the co-efficient of regression changes from β1 to β2. Further, we have discussed about the effects of prior information on the Bayes estimates on the basis of the TPLR (Two Phase Linear Regression) Model with a Bayesian approach.

Estimation and Prediction for Nadarajah-Haghighi Distribution under Progressive Type-II Censoring

The paper discusses the estimation and prediction problems for the Nadarajah-Haghighi distribution using progressive type-II censored samples. For the unknown parameters, we first calculate the maximum likelihood estimates through the Expectation–Maximization algorithm. In order to choose the best Bayesian estimator, a loss function must be specified. When the loss is essentially symmetric, it is reasonable to use the square error loss function. However, for some estimation problems, the actual loss is often asymmetric. Therefore, we also need to choose an asymmetric loss function. Under the balanced squared error and symmetric squared error loss functions, the Tierney and Kadane method is used for calculating different kinds of approximate Bayesian estimates. The Metropolis-Hasting algorithm is also provided here. In addition, we construct a variety of interval estimations of the unknown parameters including asymptotic intervals, bootstrap intervals, and highest posterior density intervals using the sample derived from the Metropolis-Hasting algorithm. Furthermore, we compute the point predictions and predictive intervals for a future sample when facing the one-sample and two-sample situations. At last, we compare and appraise the performance of the provided techniques by carrying out a simulation study and analyzing a real rainfall data set.

Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions

A composite dynamic system (CDS) is composed of multiple components. Each component failure can equally induce higher loading on the surviving components and, hence, enhances the hazard rate of each surviving component. The applications of CDS and the reliability evaluation of CDS has earned more attention in the recent two decades. Because the lifetime quality of components could be inconsistent, the lifetimes of components in the CDS is considered to follow heterogeneous baseline Gompertz distributions in this study. A power-trend hazard rate function is used in order to characterize the hazard rate of the CDS. In order to overcome the difficulty of obtaining reliable estimates of the parameters in the CDS model, the Bayesian estimation method utilizing a hybrid Gibbs sampling and Metropolis-Hasting algorithm to implement the Markov chain Monte Carlo approach is proposed for obtaining the Bayes estimators of the CDS parameters. An intensive simulation study is carried out to evaluate the performance of the proposed estimation method. The simulation results show that the proposed estimation method is reliable in providing reliability evaluation information for the CDS. An example regarding the service system of small electric carts is used for illustration.

Affine-transformation invariant clustering models

We develop a cluster process which is invariant with respect to unknown affine transformations of the feature space without knowing the number of clusters in advance. Specifically, our proposed method can identify clusters invariant under (I) orthogonal transformations, (II) scaling-coordinate orthogonal transformations, and (III) arbitrary nonsingular linear transformations corresponding to models I, II, and III, respectively and represent clusters with the proposed heatmap of the similarity matrix. The proposed Metropolis-Hasting algorithm leads to an irreducible and aperiodic Markov chain, which is also efficient at identifying clusters reasonably well for various applications. Both the synthetic and real data examples show that the proposed method could be widely applied in many fields, especially for finding the number of clusters and identifying clusters of samples of interest in aerial photography and genomic data.

Segmentation and Analysis of Anterior Lamina Cribrosa Surface using Non Local MRF and Metropolis Hasting Algorithm

The segmentation of anterior Lamina Cribrosa surface from the OCT image is an essential task for analysis of glaucomatous damage. A Bayesian method is used to segment LC surface whereas prior knowledge about shape and position of LC layer is obtained by the non local Markov Random field and K-means segmentation. The Metropolis-Hastings (MH) algorithm provides autocorrelation graph and distribution of samples from a probability distribution. By using this technique acceptance probability is calculated. Finally, the LC layer is analysed whether it is normal or abnormal. This technique provides an accuracy of 96.7%

Effects of the Temporal Aggregation and Meteorological Conditions on the Parameter Robustness of OCO-2 SIF-Based and LUE-Based GPP Models for Croplands

Global retrieval of solar-induced chlorophyll fluorescence (SIF) using remote sensing by means of satellites has been developed rapidly in recent years. Exploring how SIF could improve the characterization of photosynthesis and its role in the land surface carbon cycle has gradually become a very important and active area. However, compared with other gross primary production (GPP) models, the robustness of the parameterization of the SIF model under different circumstances has rarely been investigated. In this study, we examined and compared the effects of temporal aggregation and meteorological conditions on the stability of model parameters for the SIF model ( ε / S I F yield ), the one-leaf light-use efficiency (SL-LUE) model ( ε max ), and the two-leaf LUE (TL-LUE) model ( ε msu and ε msh ). The three models were parameterized based on a maize–wheat rotation eddy-covariance flux tower data in Yucheng, Shandong Province, China by using the Metropolis–Hasting algorithm. The results showed that the values of the ε / S I F yield and ε max were similarly robust and considerably more stable than ε msu and ε msh for all temporal aggregation levels. Under different meteorological conditions, all the parameters showed a certain degree of fluctuation and were most affected at the mid-day scale, followed by the monthly scale and finally at the daily scale. Nonetheless, the averaged coefficient of variation ( C V ) of ε / S I F yield was relatively small (15.0%) and was obviously lower than ε max ( C V = 27.0%), ε msu ( C V = 43.2%), and ε msh ( C V = 53.1%). Furthermore, the SIF model’s performance for estimating GPP was better than that of the SL-LUE model and was comparable to that of the TL-LUE model. This study indicates that, compared with the LUE-based models, the SIF-based model without climate-dependence is a good predictor of GPP and its parameter is more likely to converge for different temporal aggregation levels and under varying environmental restrictions in croplands. We suggest that more flux tower data should be used for further validation of parameter convergence in other vegetation types.

Combined size and shape optimization of truss structures using subset simulation optimization

This paper presents an approach to solve the combined size and shape design optimization problems using recently developed subset simulation optimization for both continuous and discrete design variables. Except for the componentwise Metropolis–Hasting algorithm, a recently developed adaptive conditional sampling algorithm is also employed as an alternative approach for generating new conditional samples (candidate designs) for each simulation level, which enhances the accuracy and stability of the optimization process. Besides, a double-criterion sorting algorithm is used to handle the design constraints and integrate them in the generation of conditional samples during the Markov Chain Monte Carlo simulation, and the inverse transform method is employed to deal with the discrete design variables. Totally, four numerical examples are considered, including a 15-bar 2D truss, an 18-bar 2D truss, a 39-bar 3D truss and a truss-type landing gear of an unmanned aerial vehicle. The optimal designs obtained from subset simulation optimization using either the componentwise Metropolis–Hasting algorithm or the adaptive conditional sampling algorithm succeed in substantially reducing the weights of the truss-type structures under design constraints in terms of the member stress, the Euler buckling and the nodal displacement. The computational results indicate the proposed method can be taken as an alternative tool for structural optimization design on truss structures when involving the combined size and shape design.