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The purpose of this study is to propose an appropriate model to predict chemical composition during water purification at the Regional Water Company (PDAM) Surabaya, in order to achieve proper drinking water standards. Drinking water treatment is very expensive, so the model serves as a basis for determining the composition of chemicals used in the water purification process at PDAM Surabaya. This study examines a model of the relationship between the level of clarity of drinking water and the composition of the chemicals used. The government can obtain important benefits from the forecasting model to formulate policies for the company. One of the objectives of developing the estimation method involved in this research is to efficiently determine the exact chemical composition resulting from the water purification process, which will inform the financing and control of water quality. We used a multivariable linear approach for some parametric components, a multivariable Fourier Series approach for some nonparametric components, and a multivariable Kernel approach for semiparametric regression. Using the penalized least square (PLS) approach, a mixed estimator of the Fourier and Kernel Series was obtained with semiparametric regression. The smoothing parameters were selected using a common cross-validation technique (GCV). The performance of this technique was evaluated using the Gaussian Kernel and Fourier Series with data trends in the drinking water clarity level obtained from PDAM Surabaya. The findings showed that this technique performed well, so we recommend that the government conduct an in-depth analysis to determine correct chemical composition so that the cost of water treatment can be minimized. [ABSTRACT FROM AUTHOR]

The model developed considers the uniqueness of a data-driven binary response (indicated by 0 and 1) identified as having a Bernoulli distribution with finite mixture components. In social science applications, Bernoulli's constructs a hierarchical structure data. This study introduces the Hierarchical Bernoulli mixture model (Hibermimo), a new analytical model that combines the Bernoulli mixture with hierarchical structure data. The proposed approach uses a Hamiltonian Monte Carlo algorithm with a No-U-Turn Sampler (HMC/NUTS). The study has performed a compatible syntax program computation utilizing the HMC/NUTS to analyze the Bayesian Bernoulli mixture aggregate regression model (BBMARM) and Hibermimo. In the model estimation, Hibermimo yielded a result of ~90% compliance with the modeling of each district and a small Widely Applicable Information Criteria (WAIC) value. [ABSTRACT FROM AUTHOR]