This paper examines the distribution of eigenvalues for a $2\times 2$ random confusion matrix used in machine learning evaluation. We also analyze the distributions of the matrix’s trace and the difference between the traces of random confusion matrices. Furthermore, we demonstrate how these distributions can be applied to calculate the superiority probability of machine learning models. By way of example, we use the superiority probability to compare the accuracy of four disease outcomes machine learning prediction tasks.

This paper proposes a novel two-stage ensemble framework combining Long Short-Term Memory (LSTM) and Bidirectional LSTM (BiLSTM) with randomized feature selection to enhance diabetes prediction accuracy and calibration. The method first trains multiple LSTM/BiLSTM base models on dynamically sampled feature subsets to promote diversity, followed by a meta-learner that integrates predictions into a final robust output. A systematic simulation study conducted reveals that feature selection proportion critically impacts generalization: mid-range values (0.5–0.8 for LSTM; 0.6–0.8 for BiLSTM) optimize performance, while values close to 1 induce overfitting. Furthermore, real-life data evaluation on three benchmark datasets—Pima Indian Diabetes, Diabetic Retinopathy Debrecen, and Early Stage Diabetes Risk Prediction—revealed that the framework achieves state-of-the-art results, surpassing conventional (random forest, support vector machine) and recent hybrid frameworks with an accuracy of up to 100%, AUC of 99.1–100%, and superior calibration (Brier score: 0.006–0.023). Notably, the BiLSTM variant consistently outperforms unidirectional LSTM in the proposed framework, particularly in sensitivity (98.4% vs. 97.0% on retinopathy data), highlighting its strength in capturing temporal dependencies.

The most important ingredient in Bayesian analysis is prior or prior distribution. A new prior determination method was developed under the framework of parametric empirical Bayes using bootstrap technique. By way of example, Bayesian estimations of the parameters of a normal distribution with unknown mean and unknown variance conditions were considered, as well as its application in comparing the means of two independent normal samples with several scenarios. A Monte Carlo study was conducted to illustrate the proposed procedure in estimation and hypothesis testing. Results from Monte Carlo studies showed that the bootstrap prior proposed is more efficient than the existing method for determining priors and also better than the frequentist methods reviewed.

Random forest (RF) is a widely used data prediction and variable selection technique. However, the variable selection aspect of RF can become unreliable when there are more irrelevant variables than relevant ones. In response, we introduced the Bayesian random forest (BRF) method, specifically designed for high-dimensional datasets with a sparse covariate structure. Our research demonstrates that BRF possesses the oracle property, which means it achieves strong selection consistency without compromising the efficiency or bias.

High-dimensional longitudinal data present significant analytical challenges due to intricate within-subject correlations and an overwhelming ratio of predictors to observations. To address these challenges, we introduce Mixed-Effect Gradient Boosting (MEGB), a novel R package that synergises gradient boosting with mixed-effects modelling to simultaneously account for population-level fixed effects and subject-specific random variability. MEGB provides a unified framework for analysing repeated measures data that accommodates complex covariance structures while harnessing gradient boosting’s inherent regularisation for robust feature selection and prediction. In comprehensive simulations spanning linear and nonlinear data-generating processes, MEGB achieved 35-76% lower mean squared error (MSE) compared to state-of-the-art alternatives like Mixed-Effect Random Forests (MERF) and REEMForest, while maintaining 55-70% true positive rates for variable selection in ultra-high-dimensional regimes \((p=2000)\). Demonstrating practical utility, we applied MEGB to maternal cell-free plasma RNA data \((n=12\) subjects, \(p=33,297\) transcripts), where it identified 9 key placental transcripts driving fetal RNA dynamics across pregnancy trimesters.