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CAUCHY: Jurnal Matematika Murni dan Aplikasi
Published by Universitas Islam Negeri Maulana Malik Ibrahim Malang
ISSN : 20860382     EISSN : 24773344     DOI : 10.18860
Core Subject : Education,
Mathematics
Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh Mitra Bestari (reviewer) untuk dinilai substansi kelayakan naskah. Redaksi berhak mengedit naskah sejauh tidak mengubah substansi inti, hal ini dimaksudkan untuk keseragaman format dan gaya penulisan.
Arjuna Subject : -
Articles 579 Documents
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Bayesian Multiple Imputation Using Fully Conditional Specification for Handling Missing Values in Lung Cancer Data Usman Pagalay; Ria Dhea Layla Nur Karisma; Hawzah Saadati; Evawati Alisah; Ratnaning Palupi; Heni Widayani
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.45218

Abstract

Missing values in medical datasets can reduce statistical efficiency and introduce bias. This study applied Bayesian multiple imputation within the Fully Conditional Specification (FCS) framework and assessed its numerical stability. The data comprised 132 lung cancer patient records collected at Karsa Husada Hospital, Batu, between 2020 and 2025. The variables included age, sex, smoking status, comorbidity, family history, and lung cancer stage. Cancer stage was missing for 42.42% of patients (56/132). Associations between missingness indicators and observed variables were examined using 2 tests for categorical variables and independent t-tests for age. No statistically significant associations were detected (p 0.05). These findings provided no evidence against MCAR for the variables examined but did not establish MCAR or distinguish MAR from MNAR. Imputation was conducted under an assumed MAR mechanism. All incomplete variables were binary and were imputed using Bayesian logistic regression with posterior parameter draws generated through the MetropolisHastings algorithm. The primary analysis generated 20 completed datasets using 20 FCS iterations. Trace plots, acceptance rates, and effective sample sizes showed no clear evidence of systematic non-convergence. Mean bias-reduced logistic regression was fitted to each completed dataset, and estimates were pooled using Rubin's rules. No predictor was significantly associated with Stage IV disease. Precision was limited, particularly for sex (95% CI: 0.01222.40), smoking status (95% CI: 0.0095.95), and family history (95% CI: 0.2612.18). Sensitivity analyses using 50 and 100 completed datasets and a wider slope prior produced similar conclusions. The small sample size and high proportion of missing outcome data limited the precision of the estimates.
Explainable Machine Learning for Hypertension Status Classification Using NHANES: Performance and Cross-Model SHAP Analysis Diska Nur Isna Apriani; A'yunin Sofro
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.45787

Abstract

Hypertension is a major noncommunicable disease and an important public health concern. Its health burden is relevant to public-health risk management and broader disaster-risk contexts, supporting Sustainable Development Goal 3 (SDG 3), particularly Target 3.4 on reducing premature mortality from noncommunicable diseases. This study compares Logistic Regression (LR), Random Forest (RF), and Extreme Gradient Boosting (XGBoost) for classifying reported hypertension status, evaluates hyperparameter optimization, and examines predictor contributions using SHapley Additive exPlanations (SHAP). Using 5,008 NHANES 20212023 respondents and eight predictors, hypertension status was defined from BPQ020 as self-reported physician diagnosis. The data were divided using an 80:20 stratified split into training and independent test sets, with five-fold cross-validation applied to the training set for hyperparameter optimization. At a fixed threshold of 0.50, LR achieved the highest baseline ROC-AUC (0.7921), while XGBoost achieved the highest baseline Recall (0.5968) and F1-Score (0.6233). Tuning improved RF Recall from 0.5332 to 0.6048 and F1-Score from 0.5793 to 0.6316. SHAP identified Age, Waist circumference, and BMI as the top three predictors in both tuned models, with a Spearman rank correlation of 0.9286 and 100% top-three agreement. Bootstrap analysis yielded a median correlation of 0.9286 (95% CI: 0.90481.0000), with 100% top-three agreement across 2,000 replications. At the fixed threshold, tuned RF achieved the highest Recall and F1-Score, whereas LR yielded the highest ROC-AUC.
Panel Data Break the Diagnostics of Geographically Weighted Regression: Five Failures, Their Repair, and a Rice-Productivity Application in Indonesia Rahmawati Tri Iriani; Danang Ariyanto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.44351

Abstract

Geographically weighted panel regression (GWPR) is assembled from cross-sectional tools. Five of them fail on a balanced panel whose units keep their coordinates over time. Each failure is stated as a proposition, derived in closed form, and repaired. An adaptive bandwidth in rows is not identified. A fold that holds out a whole unit cannot score a fixed-effects model without a plug-in level. A grid counted in units saturates at the inner training size, where its tie rule picks the bandwidth. A local and a global model share one information criterion only through a composite smoother. The BreuschPagan statistic reduces to a constant set by the sample size. The repairs are applied to 272 province-years, comprising 34 Indonesian provinces from 2018 to 2025, with log yield as the outcome. Under nested leave-one-province-out cross-validation, the global two-way fixed-effects model attains a cross-validated R2 of 0.100 and the GWPR 0.064. The GWPR loses in every variant tried. A province-block permutation test cannot distinguish Indonesia's real map from a random relabelling, and none of the 136 local slopes differs from its global counterpart. The R2 of 0.9997 in the earlier version of this study comes from the accounting identity between production and harvested area.
Comparing Cost-Sensitive LightGBM and TabPFN for Imbalanced Coronary Heart Disease Risk Prediction Arfian Jauhar Himawan; A'yunin Sofro
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.45897

Abstract

Coronary heart disease (CHD) constitutes a catastrophic non-communicable disease burden that operates as a non-natural disaster for health systems and directly threatening Sustainable Development Goal 3 (Target 3.4) on premature mortality; yet ten-year CHD risk prediction remains difficult because clinical cohorts are strongly class-imbalanced and most prior evaluations report point estimates without statistical or decision-analytic support. This study compares a fully tuned, cost-sensitive LightGBM pipeline with a zero-tuning tabular foundation model (TabPFN) on the imbalanced Framingham cohort of 4,240 records with a 15.19% event rate, under a common leakage-free protocol with validation-based threshold optimisation and an eight-scenario ablation, and evaluates the primary comparison with the DeLong test, bootstrap confidence intervals, a five-seed robustness check, calibration, and decision-curve analysis. TabPFN achieved higher discrimination, with an area under the receiver operating characteristic curve of 0.713 compared with 0.677 for the tuned ensemble (DeLong p = 0.0037), and better calibration, with a Brier score of 0.120 compared with 0.199. It also attained the best imbalance-aware detection, an F1-score of 0.380 and a Matthews correlation coefficient of 0.245, and remained superior under all five seeds, averaging 0.737 compared with 0.706. Threshold optimisation raised minority-class recall from 0.031 to at least 0.47 without resampling, and ten-predictor curation helped rather than harmed the foundation model. Shapley-based attribution yielded a transparent 0–100 score dominated by age, smoking, and blood pressure. A zero-tuning foundation model thus provides statistically significant, better-calibrated predictions than a tuned cost-sensitive ensemble, offering a scalable screening aid toward SDG 3 (Target 3.4) in resource-limited settings.
Identifying Regional Heterogeneity and Priority Factors for Infrastructure in Indonesia Using FIMIX-PLS and Importance-Performance Map Analysis Arum Nanda Putri Aprilia; Rahmawati Erma Standsyah
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.45621

Abstract

Infrastructure development is important for reducing regional disparities, but Indonesian provinces differ in economic conditions, human resources, and regional characteristics. This study examines the relationships between the Economy, Human Resources, and Regional Characteristics and Infrastructure in the 38 provinces of Indonesia, based on secondary data from Statistics Indonesia (BPS) for 2024 and 2025. To examine the structural relationships, Partial Least Squares Structural Equation Modeling (PLS-SEM) was employed, and to investigate unobserved heterogeneity, Finite Mixture PLS (FIMIX-PLS) was used together with ImportancePerformance Map Analysis (IPMA) to determine the priorities within the segments. The model accounted for 82.3% of the variance in Infrastructure (R2 = 0.823). Yet none of the structural paths were found to be statistically significant at the 5% level: for Economy (t = 1.195, p = 0.232), for Human Resources (t = 0.895, p = 0.371), and for Regional Characteristics (t = 1.928, p = 0.054). FIMIX-PLS identified a two-segment solution, with the final partition assigning 27 provinces to Segment 1 and 11 provinces to Segment 2. IPMA showed different patterns across segments: Regional Characteristics had the highest importance in Segment 1, while Economy ranked highest in Segment 2. Regional Characteristics also had the lowest performance in both segments. As this construct represents disaster exposure rather than development quality, the results highlight the need to consider disaster risks and economic differences when setting infrastructure priorities. However, the findings remain exploratory because none of the overall structural paths were statistically significant, and the segmentation is exploratory.
The Comparative Analysis of Hybrid Sampling, EasyEnsemble, and SVM-SMOTE Performance for Imbalanced Data Based on Bayesian Optimization Megawati Zein Waliulu; Kusman Sadik; Asep Saefuddin
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42968

Abstract

Imbalanced data represents a common challenge in classification modeling, as it can lead to prediction bias and reduce the models ability to correctly identify minority classes, which are often more critical. This study aims to compare the performance of three imbalance-handling techniquesHybrid Sampling, EasyEnsemble, and SVM-SMOTEapplied to the XGBoost classifier with hyperparameter tuning using Bayesian Optimization. A simulation study was conducted under a factorial completely randomized design involving three factors: class proportion (70:30, 80:20, 90:10), predictor variable types (10 categorical variables and a combination of 5 categorical and 5 numeric variables), and imbalance handling methods. Model performance was evaluated using balanced accuracy, sensitivity, and specificity. During the optimization process, 20 hyperparameter combinations were initially selected as prior evaluation points, followed by 20 additional optimization iterations to refine the search for the optimal hyperparameter configuration. The Bayesian Optimization process produced different optimal hyperparameter combinations for each simulation scenario, reflecting the distinct characteristics of the data under different experimental conditions. The analysis of variance revealed that both the main effects and the interactions among all factors significantly influenced classification performance. Among the evaluated methods, EasyEnsemble consistently achieved the best performance across all class imbalance scenarios. For all class proportions (70:30, 80:20, and 90:10), both in datasets consisting of 10 categorical predictor variables and in datasets comprising a combination of 5 categorical and 5 numerical predictor variables, EasyEnsemble achieved balanced accuracy, sensitivity, and specificity values consistently exceeding 0.90. Furthermore, Bayesian Optimization effectively enhanced the classification performance of XGBoost by efficiently identifying optimal hyperparameter configurations. Overall, the findings demonstrate that the combination of EasyEnsemble and Bayesian Optimization provides an effective approach for addressing class imbalance and improving classification performance.
Vine Copula-Based Multivariate Value-at-Risk for Extreme Rainfall Risk Assessment Lailatul Maziyah Wildan Mufaridho; Dewi Susanawati; Wahyu Joko Saputro
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.45628

Abstract

Extreme rainfall occurring simultaneously across multiple locations can generate spatially dependent risks that are not adequately captured by independent univariate models. This study develops an R-vine copula-based framework to model spatial dependence and quantify joint extreme rainfall risk across seven rainfall stations in DKI Jakarta and West Java, Indonesia. Station-specific marginal distributions were fitted using a mixed discrete-continuous framework to account for zero and positive rainfall observations. The probability integral transform was then applied to construct the dependence structure using an R-vine copula, followed by Monte Carlo simulation to generate multivariate rainfall scenarios and estimate Value-at-Risk (VaR) at the 95% and 99% confidence levels. The fitted R-vine consists of six tree levels and 21 pair-copulas, representing heterogeneous unconditional and conditional dependence among the stations. Model adequacy was evaluated by comparing Kendall’s tau, empirical cumulative distribution functions (ECDF), and quantile-quantile (QQ) plots between observed and simulated data. Bootstrap resampling was used to assess the uncertainty of the multivariate VaR estimates. The results yield a Kendall’s tau RMSE of 0.0935, indicating a relatively small discrepancy between observed and simulated dependence structures. Based on 100,000 simulations, the multivariate VaR estimates are 46.0744 mm at the 95% confidence level and 92.3355 mm at the 99% confidence level, with bootstrap confidence intervals of 45.4340–46.7030 mm and 90.4392–94.6717 mm, respectively. The ECDF and QQ plots indicate satisfactory agreement between observed and simulated rainfall distributions. Kupiec backtesting further confirms the adequacy of the univariate VaR estimates at both confidence levels. Overall, the proposed R-vine copula framework provides a flexible approach for quantifying spatially dependent joint extreme rainfall risk.
Evaluating Predictive Mathematical Models of Shipboard Operational Decision-Making Performance Using Scenario-Based Assessment Novitasari Novitasari; Achmad Dhany Fachrudin; Eka Nurmala Sari Agustina; I’ie Suwondo; Antonius Edy Kristiyono; Arif Fadhlur Rohman Fattah
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.46178

Abstract

Shipboard operational decision making requires seafarers to interpret numerical information, identify operational risks, apply procedures, use onboard technology, and coordinate actions under changing conditions. This study evaluated predictive mathematical models of shipboard operational decision-making performance using scenario-based assessment. Data were obtained from 78 experienced seafarers enrolled in Recognition of Prior Learning programs in Nautical Studies and Marine Engineering. Five self-reported constructs were examined: operational data understanding, seafaring experience, SOP and checklist use, shipboard technology utilization, and communication and coordination. The outcome was the mean of four discipline-specific scenario scores. During manuscript revision, all scenario responses were re-evaluated with the predefined 1–5 rubric by discipline-specific subject-matter lecturers, and all analyses were repeated using these expert-assessed scores. OLS with HC3 robust standard errors was used as the inferential baseline, while Ridge regression was assessed using repeated nested stratified five-fold cross-validation. The OLS model yielded R² = 0.198 and adjusted R² = 0.130; X1–X5 were not jointly significant after program adjustment (p = 0.231). The best predictive model, Ridge with X1–X5 and program, achieved mean cross-validated R² = 0.075 (SD = 0.030), RMSE = 1.099, and MAE = 0.950. These findings indicate modest out-of-sample prediction and support cautious use of self-reported operational constructs as predictors of scenario-demonstrated performance.
Application of a Heterogeneous Graph for Analyzing Workforce Competency Networks Nasya Lailatur Romadona; Muhammad Husnul Khuluq
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.46006

Abstract

Recruitment in outsourcing companies requires effective matching between candidate competencies and job requirements. This study constructs and analyzes a heterogeneous candidatecompetencyposition graph using real recruitment data from an outsourcing company to examine the structural roles of competencies and their community organization. The recruitment database comprised 28,289 records collected from October 2025 to August 2026, with 875 unique candidates across five selected positions: Fitter, Maintenance, Mechanical Technician, Electrical Technician, and Welder. Using stratified, criterion-based purposive sampling with equal allocation, 20 candidates were selected from each position, resulting in 100 candidates. The resulting graph contained 115 vertices and 665 edges, consisting of 634 candidatecompetency relationships and 31 competencyposition relationships. Normalized betweenness centrality ranked Technical Drawing Reading highest (CB = 0.197077), followed by Welding (0.185315) and Teamwork (0.141790). Louvain community detection with resolution 1.0, weight=None, and random seed 38 identified five communities with modularity Q = 0.079237. A 30-run stability analysis produced three to six communities, with a mean pairwise ARI of 0.137730, indicating variation across random initializations. The findings are interpreted as exploratory structural patterns rather than statistically representative community structures.

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