Asian Journal of Probability and Statistics

Causal Inference in the Bayesian Framework: Principles and Applications

Mengli Wang — 2025-10-24

Causal inference is fundamental to scientific inquiry, yet its methodologies often lack a cohesive probabilistic framework. While the U.S. FDA advocates for Bayesian methods in drug development, their potential to unify and advance causal inference remains underexplored. This study addresses this gap by formalizing a Bayesian framework for causal inference, which provides a principled mechanism to integrate prior evidence and quantify full uncertainty in causal estimates. We delineate the theoretical underpinnings of this approach and demonstrate its practical utility through a numerical example. This framework not only calculates the posterior distribution of causal hypotheses, but also provides a method different from traditional hypothesis testing, advancing the methodology by better adapting to complex data structures and prior knowledge.

On Dual Hyperbolic Generalized Pierre Numbers

Sercan DOGAN — 2025-10-27

In this paper, we introduce and develop the concept of generalized dual hyperbolic Pierre numbers, a novel class of number sequences that extends the structural framework of classical Pierre-type sequences through duality and hyperbolic transformations. This generalization offers a unified approach that encompasses both established and newly constructed numerical models. As distinguished special cases, we examine the dual hyperbolic Pierre numbers and their Lucas-type counterparts, emphasizing their algebraic relationships and unique structural features. Our study presents a comprehensive set of mathematical results, including closed-form identities, matrix representations, and recurrence relations that define the behavior of these sequences. We further derive Binet-type formulas for explicit term computation and construct generating functions that capture their combinatorial and analytical properties. Additionally, we explore Simson’s formulas and establish various summation identities that reveal deeper interconnections among sequence elements. This investigation contributes to the broader theory of Pierre-type sequences and offers new tools for research in discrete mathematics, algebraic structures, and computational number theory.

Interpretable Deep Learning-Based Cox Proportional Hazards Model with Uncertainty Quantification

W.A.R.De Mel — 2025-10-29

Survival analysis is essential in clinical and actuarial domains, yet traditional models such as the Cox Proportional Hazards (CoxPH) model are constrained by linearity assumptions. This study introduces an Explainable DeepSurv with Uncertainty framework, which integrates deep neural networks into the CoxPH architecture to model non linear covariate effects while addressing interpretability and uncertainty estimation. The linear risk function is replaced by a non linear transformation learned by a neural network, enabling improved predictive performance. Uncertainty is quantified using Bayesian Neural Networks and Monte Carlo Dropout, while SHAP (SHapley Additive exPlanations) values and survival curves offer post hoc interpretability. The model was validated on a dataset predicting ten year coronary heart disease (CHD) risk, outperforming the baseline CoxPH (C Index = 0.5466) with a mean absolute error (MAE) of 0.2855 and a mean squared error (MSE) of 0.1555. Calibration metrics, including a Brier Score of 0.135 and Expected Calibration Error (ECE) of 0.074, ‘confirmed the model’s reliability, and a 5 fold cross validation yielded a mean C Index of 0.5464±0.0242 and MSE of 0.3164±0.0090. By addressing the core challenges of non linearity, censoring, and lack of transparency in survival models, this research presents a robust, interpretable, and uncertainty aware framework suitable for clinical decision making and personalized risk prediction.

A Comparative Deep Learning Methodology for Enhancing Activation Functions in Fraud Detection

Damilare Matthew Oladimeji — 2025-10-30

Detecting fraud in financial systems is challenging due to highly imbalanced datasets, where fraudulent transactions make up less than 1%. Misclassifying these rare cases can be costly. This study examines how activation function choice affects the performance of artificial neural networks (ANNs) in fraud detection using the Financial Fraud Alert Review (FiFAR) dataset of one million transactions. A consistent ANN with two hidden layers was tested across seven activation functions: Sigmoid, Tanh, ReLU, Leaky ReLU, ELU, GELU, and Swish. Model performance was evaluated using accuracy, recall, F1 score, ROC-AUC, PR-AUC, and false positive rate (FPR). The Sigmoid function achieved the highest recall (0.6976), ROC-AUC (0.8182), and PR-AUC (0.0871), indicating superior fraud detection, though it had a higher FPR (0.2110) and low precision (0.0356). Compared to Logistic Regression, which had higher accuracy (0.1188) but low recall (0.1799), and Support Vector Machines (recall = 0.5238; FPR = 0.16395), the Sigmoid-based ANN performed better at identifying fraudulent cases. The results show that ANNs with suitable activation functions can capture complex patterns in imbalanced datasets more effectively than traditional models. In conclusion, selecting an appropriate activation function is crucial in fraud detection. Sigmoid offers optimal recall, while Tanh, Swish, and GELU provide better trade-offs between recall and false positives. The study offers practical guidance for optimizing neural network designs in fraud detection systems.

Assessing Nigeria’s Resilience to Oil-price Volatility: Evidence from a Vector Autoregression of GDP Dynamics and Policy Buffers

Korter Grace Oluwatoyin — 2025-10-31

Aim: This study constructs a first-difference Vector Autoregression (VAR) model to analyze the dynamic interplay between global oil-price shocks and Nigeria’s real GDP over the period 1990–2023.

Methodology: This study began by subjecting annual series of Brent crude prices and the World Bank’s GDP index to Augmented Dickey-Fuller and Phillips-Perron tests, confirming their integration of order one and justifying modeling in first differences. Optimal lag length is determined via Akaike, Schwarz, Hannan-Quinn, and FPE criteria, leading to a VAR(3) specification. Orthogonalized impulse-response functions reveal that a one-standard-deviation oil-price innovation yields a modest, transitory GDP response-peaking at approximately +0.9% in the second year and dissipating by year five-with all 95% confidence bands encompassing zero. Forecast-error variance decomposition further shows that oil-price shocks explain no more than 13% of GDP forecast variance at horizon ten, while endogenous dynamics dominate. Conversely, GDP innovations account for roughly 30% of oil-price variance after four years, underscoring limited feedback.

Result: These findings corroborate rapid mean reversion documented in commodity-dependent economies and mirror evidence that oil revenues contribute marginally to output volatility.

Conclusion: The paper concludes with policy prescriptions for rule-based stabilization funds, automatic fiscal triggers, and accelerated diversification into agriculture, manufacturing, and services to bolster macroeconomic resilience and sustain non-oil growth.

Optimization of Bioethanol Yield from Pineapple Peels Using Response Surface Methodology

Kabue Timothy Gichuki — 2025-11-01

The Laboratory experiments were conducted using a second order rotatable design in four dimensions constructed using balanced incomplete block designs. Obtained data was applied in developing a semi-empirical model based on a second degree polynomial for predicting bioethanol yield. The model testing using ANOVA in R resulted in a correlation coefficient of 0.95 and an adjusted R-squared value of 0.911 for the E-optimal design, which indicates a good model fit. The model was used to generate contour plots and response surface for bioethanol yield. A maximum yield of 12.35 g/L of ethanol was realized at factor settings of 54.35 h, 4.96 level of pH, 34.67 ⁰C temperature and 28.03 g/L of substrate concentration using the E-optimal design which was found to be the most efficient design relative to the general design which had an optimal yield of 12.39 g/L at factor settings of 56.45 h, 4.95 pH level, 34.59 ⁰C level of temperature and 28.30 g/l of substrate concentrations. A yield of 12.35 g/L of ethanol for a substrate concentration of 28.03 g/L. translates to 0.441 g of ethanol per gram of substrate comparing well with many other findings in literature from similar studies which is roughly 86% of the theoretical yield (0.511 g/g of substrate). A second order rotatable design in four dimensions constructed using balanced incomplete block designs when the number of replications (r) are less than three the number of times (\(\lambda\)) pairs of treatments occur together ( r<\(\lambda\)) in the design was applied and found reliable in modeling, optimizing and studying the effects of the four factors and their interaction to the processes of fermentation of pineapples peels as substrate for ethanol production using Saccharomyces cerevisiae.