Minimum Message Length Mixture Modelling of Rainfall Data
Yudi Agusta · 2023
Rainfall is an important part of people daily life, especially farmers. Agriculture, and also tourism, have been affected greatly by rainy season. As the climate changes, the chance of rainfall amount to change gets higher. Several studies have been performed regarding rainfall data including studies on rainfall model as well as clustering of regions based on rainfall data. However, assumption used in the studies is that the data comes from one class population. This paper reports a study conducted on rainfall data with assumptions that rainfall pattern changes and its data can come from several class populations. The rainfall data used in this study is taken from Badung Regency. The class population is also assumed to come from several distributions including Gamma, Gaussian, and Student t distributions. In developing the model, the Minimum Message Length (MML) principle is applied for both parameter estimation and model selection processes. The result shows that rainfall data comes from a one class Gamma distribution model. None of the classes has chosen Gaussian and Student t distributions as their class models. The model with a gamma value less than 1.0 is better fit with a less message length = 1076.329 bits compared to that with a gamma value greater than or equal to 1.0 with a message length = 1086.851 bits. The results also show that MML slightly performed better compared to Akaike Information Criterion (AIC) and Schwarz’s Bayesian Information Criterion (BIC), in terms of the probability bit-costings calculated from the modelling of sampled data. This shows that the uncertainty region involved in the MML modelling accommodates the unseen existing data better. The selected model implies that rainfall data is not normally distributed and tends to have higher probabilities for less rainfall amounts. This result can be further used in agricultural and tourism sectors in predicting the rainfall amount in the next period.