In today’s world, Public expenditures on health are one of the most important issues for governments. These increased expenditures are putting pressure on public budgets. Therefore, health policy makers have focused on the performance of their health systems and many countries have introduced reforms to improve the performance of their health systems. This study investigates the most important determinants of healthcare efficiency for OECD countries using second stage approach for Bayesian Stochastic Frontier Analysis (BSFA). There are two steps in this study. First we measure 29 OECD countries’ healthcare efficiency by BSFA using the data from the OECD Health Database. At second stage, we expose the multiple relationships between the healthcare efficiency and characteristics of healthcare systems across OECD countries using Bayesian beta regression.

Multivariate Adaptive Regression Splines (MARS) is a supervised learning model in machine learning, not obtained by an ensemble learning method. Ensemble learning methods are gathered from samples comprising hundreds or thousands of learners that serve the common purpose of improving the stability and accuracy of machine learning algorithms. This study presented REMARS (Random Ensemble MARS), a new MARS model selection approach obtained using the Random Forest (RF) algorithm. 200 training and test data set generated via the Bagging method were analysed in the MARS analysis engine. At the end of the analysis, two different MARS model sets were created, one yielding the smallest Mean Square Error for the test data (Test MSE) and the other yielding the smallest Generalised Cross-Validation (GCV) value. The best model was estimated for both Test MSE and GCV criteria by examining the error of measurement criteria, variable importance averages, and frequencies of the knot values for each model. Eventually, a new model was obtained via the ensemble learning method, i.e., REMARS, that yields result as good as the MARS model obtained from the original data set. The MARS model, which works better in the larger data set, provides more reliable results with smaller data sets utilising the proposed method.

Both frequentist and Bayesian statistics schools have improved statistical tools and model choices for the collected data or measurements. Model selection approaches have advanced due to the difficulty of comparing complicated hierarchical models in which linear predictors vary by grouping variables, and the number of model parameters is not distinct. Many regression model selection criteria are considered, including the maximum likelihood (ML) point estimation of the parameter and the logarithm of the likelihood of the dataset. This paper demonstrates the information complexity (ICOMP), Bayesian deviance information, or the widely applicable information criterion (WAIC) of the BRMS to hierarchical linear models fitted with repeated measures with a simulation and two real data examples. The Fisher information matrix for the Bayesian hierarchical model considering fixed and random parameters under maximizing a posterior estimation is derived. Using Gibbs sampling and Hybrid Hamiltonian Monte Carlo approaches, six different models were fitted for three distinct application datasets. The best-fitted candidate models were identified under each application dataset with the two MCMC approaches. In this case, the Bayesian hierarchical (mixed effect) linear model with random intercepts and random slopes estimated using the Hamiltonian Monte Carlo method best fits the two application datasets. Information complexity (ICOMP) is a better indicator of the best-fitted models than DIC and WAIC. In addition, the information complexity criterion showed that hierarchical models with gradient-based Hamiltonian Monte Carlo estimation are the best fit and have supper convergence relative to the gradient-free Gibbs sampling methods.

Diagnosis of a disease is one of the most important processes in the field of medicine. Thus, computer-aided detection systems are becoming increasingly important to assist physicians. The iron deficiency anemia (IDA) is a serious health problem that requires careful diagnosis. Diagnosis of IDA is a classification problem, and there are various studies conducted. Researchers also use feature selection approaches to detect significant variables. Studies so far investigate different classification problems such as outliers, class imbalance, presence of noise, and multicollinearity. However, datasets are usually affected by more than one of these problems. In this study, we aimed to create multiple systems that can separate diseased and healthy individuals and detect the variables that have a significant effect on these diseases considering influential classification problems. For this, we prepared different datasets based on the original dataset whose outliers were removed using different outlier detection methods. Then, a multistep classification algorithm was proposed for each dataset to see the results under irregular and regulated conditions. In each step, a different classification problem is handled. The results showed that it is important to consider each question together as it can and should change the outcome. Dataset and $R$ codes used in the study are available as supplementary files online.

There is an increasing interest in the use of hospital admission for Chronic obstructive pulmonary disease (COPD) in studies of short-term exposure effects attributed to air pollutants. However, little is known about the effect of air pollutan...