PEMODELAN RANTAI MARKOV MENGGUNAKAN ALGORITMA METROPOLIS-HASTINGS

Harizahayu Harizahayu

Abstract


Pada tulisan ini akan dijelaskan bentuk distribusi posterior P(probabilitas klaim) = Beta (β│α) dengan proses simulasi implementasi algoritma yang disederhanakan dan penerapan algoritma Markov Chain Monte Carlo dengan mengunkan analisis sistem Bayes dengan pendekatan model Markov Monte Carlo. Algoritma Markov Chain Monte Carlo adalah suatu kelas algoritma untuk melakukan sampling dari distribusi probabilitas dengan membangun rantai Markov pada suatu distribusi tertentu yang stasioner. Algoritma Metropolis merupakan algoritma untuk membangkitkan barisan sampel menggunakan mekanisme penerimaan dan penolakan (accept-reject) dari suatu distribusi probabilitas yang sulit untuk dilakukan penarikan sampel. Penggunaan perangkat lunak R sebagai media untuk mengeksplorasi algoritma dan diagnostik yang umum untuk implementasi MCMC. Hampir semua program dapat dijalankan dengan fungsionalitas dasar R yang berarti tidak diperlukan overhead penyetelan untuk menjalankan blok kode selain versi kerja R dan tersedia gratis secara online untuk semua sistem operasi.

Abstract

In this paper, we will describe the form of the posterior distribution of  (claim probability) =  with A simplified algorithm implementation simulation process and the application of the Markov Chain Monte Carlo algorithm are given by the Bayes system analysis with the Markov Monte Carlo model approach. The Monte Carlo algorithm of the Markov Chain is a class of algorithms for sampling the distribution of probability through the construction of a Markov chain in a particular stationary distribution. The Metropolis-Hastings algorithm is an algorithm used to produce sample sequences from a probability distribution that is difficult for sampling using an accept-reject mechanism. Usage of R program as a platform for MCMC implementations to explore popular algorithms and diagnostics. It is possible to run almost any program with simple R features, which means that no overhead configuration is needed to run code blocks other than the working version of R, and all operating systems are available online free of charge.

Keywords


Distribusi Posterior, Rantai Markov Monte Carlo, Metropolish, Peluang Klaim

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