The Point and Interval Estimations of Parameter on Bernoulli Distributions by Bayesian Approach

This research compares the efficiency of the probability of success in each experiment or the parameter under the Bernoulli distribution by maximum likelihood estimation and the Bayesian approach. The maximum likelihood estimation is the standard method to approximate parameter statistics. The Bayesian approach consists of Bayes' and Markov Chain Monte Carlo (MCMC) methods. The Bayes' method evaluates the parameter using posterior distribution depending on the probability distribution and prior distribution using the beta distribution. The MCMC method draws the random sample from the posterior distribution via the Gibbs sampling algorithm. The objective of this study is to estimate the point estimation and interval estimation based on the Bernoulli parameter. The performance of point estimation mentions the minimum mean squared error and the minimum average width for the interval estimation. By simulating data with Bernoulli distribution, the actual parameters are 0.3, 0.5, and 0.7 and determine the sample sizes: small sample sizes (10 and 20), moderate sample sizes (30 and 40), and large sample sizes (80 and 100). The confidence interval level is 90%, 95%, and 99%. The research results showed that the point estimation of Bayes' method provided good performance for all parameters and sample sizes. Bayes' and MCMC methods outperformed the maximum likelihood estimation in interval estimation.