Interpretable Variational Graph Autoencoder with Noninformative Prior

Variational graph autoencoder, which can encode structural information and attribute information in the graph into low-dimensional representations, has become a powerful method for studying graph-structured data. However, most existing methods based on variational (graph) autoencoder assume that the prior of latent variables obeys the standard normal distribution which encourages all nodes to gather around 0. That leads to the inability to fully utilize the latent space. Therefore, it becomes a challenge on how to choose a suitable prior without incorporating additional expert knowledge. Given this, we propose a novel noninformative prior-based interpretable variational graph autoencoder (NPIVGAE). Specifically, we exploit the noninformative prior as the prior distribution of latent variables. This prior enables the posterior distribution parameters to be almost learned from the sample data. Furthermore, we regard each dimension of a latent variable as the probability that the node belongs to each block, thereby improving the interpretability of the model. The correlation within and between blocks is described by a block–block correlation matrix. We compare our model with state-of-the-art methods on three real datasets, verifying its effectiveness and superiority.

Bayesian Analysis of Three-Parameter Frechet Distribution with Medical Applications

The medical data are often filed for each patient in clinical studies in order to inform decision-making. Usually, medical data are generally skewed to the right, and skewed distributions can be the appropriate candidates in making inferences using Bayesian framework. Furthermore, the Bayesian estimators of skewed distribution can be used to tackle the problem of decision-making in medicine and health management under uncertainty. For medical diagnosis, physician can use the Bayesian estimators to quantify the effects of the evidence in increasing the probability that the patient has the particular disease considering the prior information. The present study focuses the development of Bayesian estimators for three-parameter Frechet distribution using noninformative prior and gamma prior under LINEX (linear exponential) and general entropy (GE) loss functions. Since the Bayesian estimators cannot be expressed in closed forms, approximate Bayesian estimates are discussed via Lindley’s approximation. These results are compared with their maximum likelihood counterpart using Monte Carlo simulations. Our results indicate that Bayesian estimators under general entropy loss function with noninformative prior (BGENP) provide the smallest mean square error for all sample sizes and different values of parameters. Furthermore, a data set about the survival times of a group of patients suffering from head and neck cancer is analyzed for illustration purposes.

An Assessment of the Effects of Prior Distributions on the Bayesian Predictive Inference

Predictive inference is one of the oldest methods of statistical analysis and it is based on observable data. Prior information plays an important role in the Bayesian methodology. Researchers in this field are often subjective to exercise noninformative prior. This study tests the effects of a range of prior distributions on the Bayesian predictive inference for different modelling situations such as linear regression models under normal and Student-t errors. Findings reveal that different choice of priors not only provide different prediction distributions of the future response(s) but also change the location and/or scale or shape parameters of the prediction distributions.

ANALISIS REGRESI BAYES LINEAR SEDERHANA DENGAN PRIOR NONINFORMATIF

The aim of this study is to apply Bayesian simple linear regression using noninformative prior. The data used in this study is 30 observational data with error generated from normal distribution. The noninformative prior was formed using Jeffreys’ rule. Computation was done using the Gibbs Sampler algorithm with 10.000 iteration. We obtain the following estimates for the parameters, with 95% Bayesian confidence interval (0,775775; 2,626025), with 95% Bayesian confidence interval (2,948; 3,052), and with 95% Bayesian confidence interval (0,375295; 1,114). These values are not very different compared to the actual value of the parameters.

Bayesian Estimate of Exponential Parameter with Missing Data

We discuss the empirical Bayesian estimation and the noninformative prior Bayesian estimation of Exponential parameter in the missing data occasion. By setting different prior distributions, we get different bayesian risks and compare the numerical simulation results through the MATLAB programming.