Background: Yearly death rate is increasing due to heart disease. Major factors for the increasing death rate due to heart disease are (a) misdiagnosed by the medical doctors or (b) ignorance by the patients. Heart diseases can be described as any kind of disorder which affects the heart. Methods: The dataset of 'statlog' from the UCI Machine Learning with 270 patients related to heart disease isused in this article. The dataset comprises attributes of patients diagnosed with heart diseases. The diagnosis was used to confirm whether heart disease is present or absent in the patient. The present article aims to identify the risk factors/variables which influence this diagnosis. Classification is a very important part of the disease diagnosis but it is also relevant to identify the risk factors/variables. Two classification techniques namely Support Vector Machines (SVM), Multi-Layer Perceptrons ensembles (MLPE) and one advanced regression technique,Generalized additive model (GAM) with binomial distribution and'logit' link have been introduced for diagnosis and risk factors/variables identification. Results: GAM explains 65% deviance with adjusted R square value 0.70 approximately. Sensitivity analysis has been performed under SVM, which is the best model for this dataset with approximately 85% classification accuracy rate. MLPE gives 82% classification accuracy rate approximately.Maximum heart rate, vessel, old peak, chest pain, thallium scan are the most important factors/variables find through both sensitivity analysis under SVM and GAM. Conclusion: The present article attempt to remove some new information regarding heart disease through probabilistic modeling which may provide better assistance for treatment decision making using the individual patient risk factors and the benefits of a specific treatment. These findings may help the medical practitioners for better medical treatment.

In this article a generalization of the inverse Rayleigh distribution has been addressed by using DUS transformation, named as Exponential Transformed Inverse Rayleigh (ETIR) distribution. Some of the statistical properties of this newly proposed distribution like mode, quantiles, moment, moment generating function, survival and hazard rate function have been studied comprehensively. To estimate the parameter of this distribution, four different estimation procedures, such as maximum likelihood estimation (MLE), maximum product spacing method (MPS), least square method (LSE) and weighted least square method (WLSE) are briefly discussed. Performance of these estimates are compared using extensive simulations. As an application point of view the model superiority is verified through two real datasets.

In Bayesian analysis, empirical and hierarchical methods are two main approaches for the estimation of the parameter(s) involved in the prior distribution of one parameter. But in the multi-parameter model, e.g., Gamma(α, p), where both the parameters are unknown, idea of the ‘Partial Bayes (PB) Estimation’ is introduced. When we do no have proper belief regarding the joint parameters of the distribution of the variable and when we are estimating one parameter in presence of others, such method may be used. Partial Bayes estimation of the scale parameter p is done by putting the estimate of the another parameter α obtained by some other classical method in case of two parameter Gamma distribution. Using non-informative prior and computing the risk, it is found that the Partial Bayes estimator has less risk than the Bayes estimator. For this, simulation studies for some choices of shape parameter values have been done. In case of the shape parameter, posterior mean and posterior variance are evaluated through simulations to obtain the risk values for estimator of α with known scale parameter. Finally after fifitting this distribution, two real datasets are illustrated to see the performance of the Partial Bayes estimator.

Estimation of unknown parameters using different loss functions encompasses a major area in the decision theory. Specifically, distance loss functions are preferable as it measures the discrepancies between two probability density functions from the same family indexed by different parameters. In this article, Hellinger distance loss function is considered for scale parameter λ of two-parameter Rayleigh distribution. After simplifications, form of loss is obtained and that is meaningful if parameter is not large and Bayes estimate of λ is calculated under that loss function. So, the Bayes estimate may be termed as ‘Pseudo Bayes estimate’ with respect to the actual Hellinger distance loss function as it is obtained using approximations to actual loss. To compare the performance of the estimator under these loss functions, we also consider weighted squared error loss function (WSELF) which is usually used for the estimation of the scale parameter. An extensive simulation   is carried out to study the behaviour of the Bayes estimators under the three different loss functions, i.e. simplified, actual and WSE loss functions. From the numericalresults it is found that the estimators perform well under the Hellinger distance loss function in comparison with the traditionally used WSELF. Also, we demonstrate the methodology by analyzing two real-life datasets.

Background: Liver works as one of the most versatile organs in the human body. But any kind of disturbance occurs in the liver may cause the liver disease. One of the most common liver infections is hepatitis C which is caused by the Hepatitis C Virus (HCV). It is well known that liver is the largest solid organ in the human body and also it is called the exocrine gland as it secretes bile into the intestine. Aim: The aim of this study is to evaluate the causal relationship of Bilirubin with each liver biomarker using the advanced regression techniques. Methods: We use two advanced regression techniques, namely Joint Generalized Linear Model (JGLM) and Generalized Additive Model (GAM). For model selection, we check the AIC value, GCV score and adjusted R-square as well as the different diagnostic plots like Q-Q plot, Residual vs. Fitted plot etc. are displayed. Results: Bilirubin, a human liver disease biomarker, is a brownish yellow substance found in bile and it is produced in the liver when the old red blood cells break down. The present study reveals that Bilirubin is positively associated (p-value<0.05) with Aspartate Aminotransferase (AST), Creatinine (CREA), Gamma-Glutamyl Transpeptidase (GGT), Protein (PROT), Alkaline Phosphatase (ALP)*Albumin (ALB) and marginally associated with Choline Esterase (CHE)* Cholesterol (CHOL) (p-value=0.0591). While it is negatively associated (p-value < 0.05) with Age, Sex, Alkaline Phosphatase (ALP), Alanine Aminotransferase (ALT), Choline Esterase (CHE), Cholesterol (CHOL), Albumin (ALB), Creatinine (CREA)*Gamma-Glutamyl Transpeptidase (GGT) under JGLM. Besides of that, Bilirubin is positively associated with AST, CREA, GGT, (CREA*GGT), (CHE*CHOL) whereas it is negatively associated with Sex, ALT, CHE, CHOL. Also, ALB is highly positively significant as a non-parametric smoothing term (p-value < 0.001) under GAM. Conclusion: Both the advanced regression models JGLM and GAM explain the association between Bilirubin with other liver diseases biomarker in case of Hepatitis C.