Likelihood: Journal of Statistics and Its Application

Bayesian Fitting of Univariate Skew Normal Distribution on Padua Temperature Dataset

2025-11-25T08:30:47+00:00

Data-driven distributional exploration is an important issue in selecting appropriate statistical methods. Due to the presence of skewness that deviates from the normal distribution, the annual average temperature data of Padua cannot be adequately fitted using a symmetric distribution such as the normal distribution. To address this issue, this study aims to fit a skew normal distribution on Padua temperature dataset. Under a Bayesian approach, we specified priors and constructed posterior distributions as the basis for inference. The sampling results and diagnostics indicate that the chains satisfy the convergence criteria. The posterior means for the three skew normal parameters are 12.05, 1.04, and 2.26, corresponding to the location, scale, and shape parameters, respectively. Lastly, this study not only relaxes the assumption of normality but also provides a modeling foundation for Padua temperature data that can support prediction, forecasting, mapping, and other advanced data analysis purposes.

Estimation of Geographically Weighted Regression With Fixed Kernel Gaussian

2026-03-30T08:21:35+00:00

In spatial analysis, the relationship between predictor and response variables is often not uniform across regions, a condition known as spatial heterogeneity. Global regression models such as Ordinary Least Squares (OLS) assume that regression parameters are constant across all locations, meaning that the effects of independent variables are considered identical for every observational unit. This assumption is often unrealistic because it does not account for differences in regional characteristics. If spatial heterogeneity is ignored, model estimates may become less accurate and fail to explain local variations adequately. Geographically Weighted Regression (GWR) is a model that allows regression parameters to vary according to geographic location. Under this approach, each region obtains its own local parameter estimates, enabling the model to capture spatially varying relationships more flexibly. The results indicate that the AIC value of the GWR model with Fixed Gaussian Kernel (347.8637) is smaller than that of the OLS model (382.1161), suggesting that GWR provides a better fit. Empirically, the Human Development Index (HDI) in 53 districts/cities is influenced by Life Expectancy, Expected Years of Schooling, and Per Capita Expenditure, while in 66 districts/cities it is influenced by Life Expectancy, Expected Years of Schooling, Poverty Rate, and Per Capita Expenditure.

Concrete Compressive Strength Prediction System Using K-Nearest Neighbor (KNN) Regression with k-Parameter Tuning Implementation

2026-06-17T14:22:12+00:00

Concrete compressive strength is a principal indicator of concrete quality, but standardized testing requires specimen preparation, controlled curing, equipment, and time. This study develops and internally evaluates a K-Nearest Neighbor (KNN) regression model for rapid strength estimation from mixture composition and curing age. The UCI Concrete Compressive Strength dataset contained 1,030 records; removing 25 repeated records yielded 1,005 unique observations with eight original predictors and compressive strength as the response. LogAge, Water-Cement Ratio, and Total Aggregate were added as engineered predictors. The cleaned data were divided into 80% training and 20% testing subsets, while data-dependent preprocessing and hyperparameter selection were performed using the training data only. Odd k values from 1 to 41 were assessed by 10-fold cross-validation repeated five times. The minimum cross-validated error occurred at k = 3. On the held-out test subset, the final model achieved an R² of 0.88, RMSE of 5.56 MPa, and MAE of 3.74 MPa. LogAge, Water-Cement Ratio, and cement content had the largest absolute correlations with strength, although these correlations are descriptive rather than KNN-specific importance measures. The results show that a tuned and standardized KNN model can provide useful preliminary strength estimates within the represented data domain. However, the model is intended to support mixture screening and quality-control decisions, not replace standardized laboratory testing. External validation and comparison with alternative algorithms are required before broader deployment.

Comparative Spatial Regression Modeling of HIV Cases in Indonesia in 2023

2026-07-19T14:42:22+00:00

Reported HIV cases vary substantially across Indonesian provinces and may exhibit spatial dependence that is not adequately represented by conventional regression. This study compared spatial autoregressive (SAR), spatial error (SEM), and General Spatial Model (GSM) specifications for reported HIV cases in 34 Indonesian provincial units in 2023. The response was the annual number of reported HIV cases, and the explanatory variables were population density, the Gini Index, the open unemployment rate, and mean years of schooling. Global Moran's I, Lagrange Multiplier tests, maximum-likelihood estimation, and Akaike information criterion (AIC) were used to assess spatial dependence and compare models. Reported HIV cases exhibited significant positive spatial autocorrelation (I = 0.61893, p < .001). Robust LM-lag was significant (p = .026019), whereas robust LM-error was not significant (p = .950388), providing stronger support for a spatial lag specification. SAR had the lowest AIC (594.07), compared with GSM (595.67) and SEM (596.00), and was therefore selected as the preferred model. In the SAR model, population density, the Gini Index, and the open unemployment rate were positively associated with reported HIV cases, while mean years of schooling was negatively associated; all four explanatory variables were statistically significant. The spatial lag parameter was positive but not significant (rho = 0.21451, p = .10170). These ecological findings support geographically coordinated HIV surveillance and prevention while requiring cautious interpretation because reported case counts reflect population size, testing, and reporting coverage.

Confidence Intervals for Semiparametric Regression Curves Based on the Truncated Spline Estimator for Longitudinal Data

2026-06-17T15:49:53+00:00

Confidence intervals are required to quantify uncertainty in an estimated regression curve, but their construction becomes more complex when the model combines parametric and nonparametric components for repeated measurements. This study develops a pointwise confidence interval for a semiparametric regression curve based on a truncated spline estimator for continuous longitudinal data. The parametric component was specified as linear, whereas the unknown age effect was represented by a truncated-power spline. Model parameters were estimated using weighted least squares, spline order and knots were selected through generalized cross-validation, and a Student's t pivotal quantity was used when the common variance scale was unknown. The procedure was applied to 252 height measurements from 16 infants aged 0-24 months in Surabaya, comprising eight male and eight female infants. The selected model was a second-order truncated spline with four knots at 4, 8, 12, and 16 months. It produced a GCV value of 8.8505, an MSE of 8.2975, and a coefficient of determination of 91.0469%. The fitted curve indicated the largest average monthly increase during 0-4 months and the smallest during 16-24 months. The sex coefficient indicated an estimated constant mean-height difference of 0.4926 cm, rather than a difference in growth velocity. The proposed interval is conditional on the selected spline specification, normal-error assumption, and diagonal working covariance. Consequently, the empirical results are illustrative and should not be interpreted as simultaneous-band coverage or as a population growth standard.

Baseline Projection of Outpatient Visits Using Simple Linear Regression: A Case Study at RSU Ananda Purwokerto

2026-07-07T14:14:36+00:00

Anticipating outpatient demand can support hospital planning, although forecasts based on short and fluctuating annual series require cautious interpretation. This study aimed to develop a transparent baseline projection of outpatient visits at RSU Ananda Purwokerto using simple linear regression. The analysis used eight annual aggregate observations from 2018–2025; the 2025 value represented visits from January through October, whereas the preceding observations covered complete calendar years. Calendar year was used as the predictor and outpatient visits as the outcome. Manual calculations were compared with the Linear Regression output in RapidMiner, and in-sample fit was evaluated using the Mean Absolute Percentage Error (MAPE). The fitted model produced a slope of -2,103.57 visits per year and projected 62,590 visits in 2026, declining to 54,176 in 2030. However, the slope was not statistically significant (p = .369), and the model explained only 13.6% of the observed variation (R² = .136). The in-sample MAPE was 15.66%, which met the study's descriptive “good” category but did not constitute independent validation of future forecast accuracy. Therefore, the projections should be interpreted as preliminary baseline scenarios rather than certain future totals. The model may support initial operational discussion, but decisions should also consider current hospital information and should be updated using complete, preferably monthly, observations.