Asian Journal of Probability and Statistics

Diagnostic Approaches for State Space Models in Temperature Forecasting: A Critical Review

2026-06-30T13:07:48+00:00

State space models — the classical Kalman filter, dynamic linear models, structural time series formulations, and their nonlinear and ensemble-based descendants — have become a default methodological choice for representing, smoothing and forecasting temperature time series across climatology, meteorology and engineering. Yet the value of any such model depends less on the elegance of its formulation than on how carefully the fitted model is checked for adequacy once it has been estimated. This review traces the diagnostic machinery that has built up around state space modelling of temperature data, starting from the foundational recursive filtering theory and working through structural time series diagnostics, auxiliary residual analysis, outlier and structural-break detection, and on to the ensemble and particle-filter diagnostics demanded by nonlinear and non-Gaussian temperature dynamics. Particular attention is paid to how diagnostic checking interacts with substantive modelling decisions in temperature applications — trend and seasonal decomposition of station and gridded records, sea surface and land surface temperature reconstruction, missing-data imputation in high-resolution climate series, and probabilistic forecast verification. The review also considers how diagnostic thinking differs across linear Gaussian, nonlinear and data-assimilation settings, and how innovation-based, auxiliary-residual-based and ensemble-based diagnostics each expose a different kind of model failure. Several recurring problems are identified: a tendency to equate statistical adequacy with forecasting skill, inconsistent reporting of diagnostic evidence in applied temperature studies, and the genuine difficulty of diagnosing high-dimensional, non-Gaussian or strongly nonlinear thermal processes. The review concludes that the further maturation of state space temperature forecasting depends as much on the routine, transparent use of diagnostic checking as on continued methodological innovation.

Spline-Based Generalised Additive Models for Interpretable Nonlinear Regression: An Application to Air Quality Data

2026-06-12T06:45:12+00:00

Nonlinear relationships frequently arise in environmental data, challenging conventional linear regression models. This study investigates spline-based Generalised Additive Models (GAMs) as an interpretable semiparametric framework for capturing such nonlinearities. Using the UCI Air Quality dataset (9,358 hourly observations), we compare GAMs with linear regression and Random Forest models using blocked crossvalidation and multiple performance metrics. GAMs consistently outperformed linear regression, reducing root mean squared error (RMSE) by 11% for CO and by over 95% for benzene (from 0.796 to 0.034). GAMs achieved predictive accuracy comparable to Random Forest while retaining explicit, interpretable representations of predictor effects. Estimated smooth functions revealed meaningful nonlinear structures, including sensor saturation, nonlinear temperature dependencies, and a significant temperature–humidity interaction. Residual diagnostics confirmed improved model adequacy relative to linear specifications, and robustness analyses supported the stability of the proposed framework. These findings demonstrate that spline-based GAMs offer a statistically coherent and interpretable alternative to both classical linear models and black-box machine learning methods in environmental applications.

Statistical Analysis of Undergraduate Sleep Pattern and Lifte Style at Federal University of Lafia, Nasarawa State, Nigeria

2026-06-13T12:42:07+00:00

All is well that ends well is a common adage to emphasize the need to focus on the end of every activities in life. It is therefore imperative to focus on any factor that can lead to the success of student’s end. It is on this note that this research attempt to x-ray those factors that can lead to a successful end. Therefore, this study presents a comprehensive statistical analysis of sleep patterns and lifestyle factors among students at the Federal University of Lafia, with the goal of understanding how these variables influence academic performance. As sleep quality and lifestyle choices increasingly emerge as critical elements of student well-being and academic success, this research aim to uncover meaningful patterns and relationships among key behavioral indicators, including sleep duration, caffeine intake, screen time, and study habits. The sample size of 500 students was considered.

Inferential statistical tests were conducted to explore deeper relationships within the data. Independent samples t-test results showed no statistically significant difference in sleep quality between male and female students (p = 0.201). Similarly, ANOVA results indicated no significant variation in sleep quality across departments (p = 0.774), suggesting that academic field and gender do not play major roles in determining sleep quality. However, a strong negative Pearson correlation (r = -0.742, p < 0.01) was found between caffeine intake and sleep hours, indicating that increased caffeine consumption significantly reduces sleep duration. Based on the findings, the study concludes that while gender and academic department do not significantly affect sleep quality, lifestyle habits—particularly caffeine consumption—have a substantial impact on students’ sleep duration. The study recommends the implementation of sleep awareness programs, lifestyle management campaigns, and policy changes within the university to promote better sleep hygiene and healthier living among students. These efforts are crucial for fostering academic success, physical health, and mental well-being in the student population.

A Probabilistic Framework for Dependent Migration: Modeling Multiple Dependence and Model Selection

2026-06-25T12:50:59+00:00

Research Problem: Migration data often exhibit complex dependence structures among migrants and their associated dependents, making conventional probability models inadequate for accurately capturing migration behavior. The presence of multiple dependence patterns can affect statistical inference and lead to inappropriate model selection in demographic studies.

Methodology: To address this issue, a novel probabilistic framework is proposed by combining the Himanshu and Poisson distributions for modeling dependent migration data. The model incorporates a conditional dependence structure that reflects demographic characteristics and allows a realistic representation of dependent migrant behavior. Model parameters are estimated using the Method of Moments (MoM) and Maximum Likelihood Estimation (MLE), ensuring reliable statistical inference.

Key Results: The proposed model demonstrates greater flexibility in representing complex dependence relationships among migrants and their dependents. Application to real demographic migration data indicates that the model provides improved goodness-of-fit and more accurate parameter estimation compared with traditional approaches. The analysis further highlights the importance of selecting an appropriate probability model for obtaining reliable and meaningful statistical results.

Main Contribution: This study introduces a flexible probabilistic framework that integrates multiple dependence structures within a unified modeling approach for migration data. The proposed methodology extends the existing literature on migration modeling and provides a useful statistical tool for demographic research, migration policy analysis, and population studies. The framework offers valuable insights into migration dynamics and supports evidence-based decision-making for researchers and policymakers.

Statistical Analysis of Heart Diseases Risk Factors Using Logistic Regression: Evidence from the Cleveland Dataset

2026-06-29T06:58:28+00:00

In low- and middle-income countries, including Nigeria, the burden of cardiovascular diseases (CVDs) is rising rapidly because of urbanisation, changing dietary patterns, physical inactivity and limited access to advanced diagnostic facilities. This study aimed to identify and quantify the major risk factors for heart disease using logistic regression and to evaluate the predictive performance of the model on the Cleveland Heart Disease Dataset. Secondary data were obtained from Cleveland Hospital through the UCI Machine Learning Repository. The Cleveland Heart Disease Dataset (n = 303 patients, 14 attributes) was used. Missing values were handled by median imputation, categorical variables were label-encoded, and continuous variables were standardised. Logistic regression was applied after a 70/30 train-test split. Model performance was assessed using accuracy, ROC-AUC, a confusion matrix and odds ratios. The analysis was performed in Python (scikit-learn). The logistic regression model achieved an accuracy of 84.62% and a ROC-AUC of 0.9046, indicating excellent discriminative ability. The number of major vessels coloured by fluoroscopy (ca), thalassemia type (thal), exercise-induced angina (exang), chest pain type (cp), and serum cholesterol were the strongest predictors. Odds ratios showed that each additional vessel with blockage increased the odds of heart disease by more than 2.5 times. Logistic regression provides an interpretable and clinically useful approach for heart disease risk prediction. The identified risk factors align with established medical knowledge, supporting the validity of the model. Its transparency makes logistic regression valuable in resource-constrained settings where explainable models are preferred over black-box algorithms.

Competing Risks Survival Analysis of Cervical Cancer Progression and Regression among Women in Kenya

2026-07-01T10:45:59+00:00

Background: Cervical cancer is a leading cause of cancer-related death among Kenyan women. The bidirectional natural history of cervical intraepithelial neoplasia (CIN) – both progression and regression – remains poorly understood in low-resource settings. We quantified competing risks of CIN progression and regression and identified their predictors using longitudinal data from a Kenyan referral hospital.

Methods: We conducted a retrospective cohort study of 550 women with histologically confirmed CIN or normal cervix and documented HPV testing at Meru Level 5 Hospital. Progression (to a higher grade lesion or invasive cancer) and regression (to a lower grade lesion or normal epithelium) were competing first events. Cause-specific Cox and Fine-Gray subdistribution hazard models estimated associations with age, HPV status, HIV status, smoking, parity, and screening frequency. Cumulative incidence functions and bootstrap resampling assessed model stability.

Results: HPV positivity was the strongest predictor of progression (cause-specific HR = 7.90, 95% CI 4.71–13.26; subdistribution HR = 7.22, 95% CI 4.27–12.21). Higher parity reduced progression risk (HR = 0.88 per additional birth, 95% CI 0.78–0.98). Five-year progression probabilities increased with baseline CIN stage: 0.09 (CIN1), 0.25 (CIN2), 0.45 (CIN3). The model showed good short-term discrimination (1-year AUC = 0.882). Bootstrap confirmed robustness.

Conclusion: HPV infection and parity are key determinants of CIN progression in this Kenyan cohort. Competing risks modelling provides clinically meaningful estimates of progression and regression that can support risk-based cervical cancer screening and management in resource-limited settings.

Competing-risk Prognostic Modelling of Breast Cancer-specific Mortality in Ghana: Stability Selection, Internal Validation, and Risk Stratification

2026-07-03T10:58:38+00:00

Background: Breast cancer outcomes are heterogeneous, and disease-specific mortality may be inaccurately estimated when deaths from other causes are treated as simple censoring.

Aim: This study developed and internally validated a competing-risk prognostic model for breast-cancer-specific mortality in a Ghanaian cohort.

Methods: A retrospective cohort of 558 patients diagnosed with breast cancer and followed for up to 60 months between 2010 and 2015 was analysed. Breast-cancer-specific mortality was defined as the event of interest; deaths from other causes were treated as competing events, and patients alive at the end of follow-up were censored. Predictor reproducibility was assessed using Cox-LASSO stability selection. Stable predictors were incorporated into a Fine-Gray subdistribution hazard model, and estimates were compared with those from a cause-specific Cox model. Model performance was assessed using concordance indices, inverse probability of censoring-weighted Brier scores, calibration at 36 months, bootstrap optimism correction, decision-curve analysis, and risk-stratified cumulative incidence functions.

Results: Stability selection identified metastatic status (selection frequency = 1.00) and the ER+/PR+/HER2- subtype (selection frequency = 0.82) as the most reproducible predictors. In the Fine-Gray model, metastatic disease was associated with higher breast-cancer-specific mortality risk (sHR = 46.70, 95% CI: 19.66-110.94, p < 0.001), whereas the ER+/PR+/HER2- subtype was associated with lower risk (sHR = 0.56, 95% CI: 0.48-0.66, p < 0.001). The model showed good discrimination (Harrell's C-index = 0.83, 95% CI: 0.81-0.85), minimal bootstrap optimism, reasonable 36-month calibration, and positive net benefit across threshold probabilities of 0.05-0.25.

Conclusion: Metastatic status and molecular subtype were the principal prognostic factors in this cohort. External validation is required before broader clinical application.

Does Nutritional Support Improve Treatment Outcomes among Undernourished Tuberculosis Patients?

2026-07-09T06:43:36+00:00

Undernutrition is common among patients with tuberculosis (TB) and is associated with poor treatment outcomes. Although the World Health Organization recommends nutritional support, evidence from routine programme settings in sub-Saharan Africa remains limited. We conducted a retrospective cohort study of undernourished adults (body mass index [BMI] < 18.5 kg/m²) with drug-susceptible TB in Embu County, Kenya, from 2017 to 2024. The exposure of interest was food-based nutritional support, including ready-to-use therapeutic foods (RUTF), fortified blended foods (FBF), or nutritional counselling (NC). The primary outcome was a favourable treatment outcome (defined as cure or treatment completion). We estimated associations using multivariable logistic regression, propensity score matching (1:1 matching with a caliper of 0.2 standard deviations), and inverse probability of treatment weighting (IPTW). Among 2,138 patients (mean age 38.9 years; 82.7% male), 1,761 (82.4%) received nutritional support. In multivariable analysis, nutritional support was not associated with a favourable outcome (adjusted odds ratio [AOR] = 1.08, 95% confidence interval [CI]: 0.69–1.66; p = 0.724). Propensity score matching yielded 371 matched pairs with a matched odds ratio of 1.14 (95% CI: 0.73–1.77; p = 0.574). IPTW analysis produced a weighted odds ratio of 1.17 (95% CI: 0.77–1.74; p = 0.519). There was no evidence of effect modification by severity of undernutrition (p for interaction = 0.974). Subgroup analyses by HIV status, patient type, and sputum smear positivity similarly showed no significant associations. In routine TB care in Kenya, food-based nutritional support was not associated with improved treatment outcomes among undernourished patients. These findings suggest that current supplementation strategies may be insufficient in this setting. Future research should evaluate higher-calorie, longer-duration, and better-monitored nutritional interventions. Strengthening nutritional assessment and counselling remains important, but routine food supplementation as currently implemented may not improve TB treatment outcomes.

An Uncertainty-decomposed Generalized Linear Mixed Modelling Framework for Global Diabetes Prevalence: A Comparative and Interpretable Approach

2026-07-09T11:01:21+00:00

Global diabetes incidence shows substantial heterogeneity across regions and over time, which complicates reliable modelling, comparisons, and policy planning. This study presents an uncertainty-decomposed generalized linear mixed model (UD-GLMM) framework that extends classical mixed-effects modelling by partitioning the response into three interpretable components: signal (Truth), uncertainty (Indeterminacy), and contradiction or noise (Falsity). The analysis used data from the NCD-RisC Global Diabetes Repository for 1990--2022, comprising 528 region‒year observations across eight global regions and stratified by sex. The proposed framework was compared with conventional generalized linear model (GLM), generalized mixed model (GMM), and generalized linear mixed model (GLMM) approaches. Model performance was assessed via the Akaike information criterion, Bayesian information criterion, mean absolute error, root mean squared error, cross-validation, and alternative data-partitioning schemes. The UD-GLMM produced stable and improved predictive performance, with the 80--10--10 partition yielding MAE = 0.00557, RMSE = 0.00736, R-squared = approximately 0.85, Theil's U = 0.00178, and concordance above 0.92. Lagged prevalence was the principal predictor of current prevalence, indicating strong temporal persistence, whereas lagged treatment coverage showed a weak overall association but moderated the relationship between past and current prevalence. Mediation analysis indicated that approximately 10% of the temporal effect was transmitted through treatment coverage, whereas most of the effect remained direct. Overall, the findings suggest that uncertainty decomposition can strengthen the interpretability of mixed-effects epidemiological modelling by distinguishing reliable signals from indeterminate and contradictory variations. The framework provides a transparent comparative approach for global diabetes surveillance and for identifying where prediction certainty, regional heterogeneity, and treatment-related dynamics require careful interpretation.

Joint Spatio-Temporal Modelling of Malaria Incidence and Mortality in Kenya

2026-07-09T13:31:02+00:00

Understanding how malaria incidence and mortality vary across space and time is important for strengthening malaria surveillance and supporting evidence-based planning of control interventions. This study examined the joint spatial and temporal patterns of malaria incidence and mortality in Kenya, identified high-risk counties and assessed whether the two outcomes shared common distributions. County-level malaria incidence and mortality data for 2013 to 2024 were analysed using a joint Bayesian hierarchical model based on a spatio-temporal conditional autoregressive framework, which accounted for spatial dependence among neighbouring counties and temporal correlation across successive years. Model performance was compared with a multivariate spatio-temporal modelling framework to evaluate shared and outcome-specific variation. Integrated Nested Laplace Approximation was used for Bayesian inference. Weighted adjacency matrices were constructed, and structured and unstructured spatial effects were incorporated to account for spatial heterogeneity, temporal dependence and unexplained variability. The results showed persistent spatial clustering of both outcomes throughout the study period. Counties in the lake-endemic region, particularly Kisumu, Siaya and Busia, consistently had higher spatial risks for malaria incidence and mortality than most other counties. The spatial distributions of incidence and mortality were positively associated, indicating that counties with higher incidence tended to have higher mortality. Temporal patterns differed between the outcomes, with incidence showing broader fluctuation and mortality showing less pronounced change. The findings indicate that joint spatio-temporal modelling can support malaria surveillance and guide spatially targeted control interventions in Kenya.