Forecasting Surabaya Rainfall in 2017 Using First Order Autoregressive Model through INLA Bayesian Approach

Abstract

Water is one of the natural factors which affects the life of organisms on earth. If in one area, there is a sufficient amount of rain, then it will support the life of organisms in that area. However, if an area has an excessive amounts of rain, flooding will occur and it will damage the infrastructure, the agricultural land and some existing ecosystems. One way to reduce unwanted floods is by predicting accurate flood discharge. It can be used not only to design water buildings but also to manage water flow. Flood discharge can be predicted using the time series method, namely the First Order Autoregressive model, also known as the AR model (1). Estimating parameters in the AR model (1) can be done using the Moment, least Square and Maximum Likelihood methods. However, because the sample size used in this study is small then the Bayesian method can be used to estimate the AR model parameters (1). It has some advantages such as: 1. It can produce logical interpretations to conclude statistically in time series analysis 2. The output can always be updated based on the latest information. The Markov Chain Monte Carlo method is one method that can be used for Bayesian inference calculations, specifically the Gibbs sampler and Metropolis-Hastings algorithms. Both of these algorithms are more flexible and easily adapted to estimate complex models with many parameters or characterized by posterior nonstandard distributions. The MCMC theory states that the convergence distribution of the simulation value to the posterior distribution has a number of iterations to infinity, the posterior distribution will not be feasible. So that the processing of data consume a lot of time to reach convergence, then if it is not stopped then it will give suggestions about how some MCMC iterations become convergent. If the model is more complex then the MCMC algorithm is slower and the calculation becomes not feasible. Therefore, Rue et al. (2009) proposed a fast and accurate algorithm called the Integrated Nested Laplace Approximation Algorithm (INLA).