Metode Bayesian untuk Estimasi Parameter Distribusi Eksponensial pada Data Tersensor

Abstract

Parameter is a value that describe the characteristics of a population. But the parameterof a real data, the value is unknown. To estimate the value of the parameter,there are several methods, which are maximum likelihood estimation method (MLE)and Bayesian parameter estimation method. In Bayesian method, the prior informationis applied to update the current data. The prior is determined based on the informationin the data. This mini thesis is using censored data with exponential distribution, andusing the conjugate prior. Followed by squared error loss function (SELF), the estimatedvalue function ot the λ parameter is ˆλ =α+Σ_{i=1}^{n}δ_{i}β+Σ_{i=1}^{n}t_{i}with α and β are hyperparameters,Σ_{i=1}^{n}δ_{i} is the number of objects that experienced the event and Σ_{i=1}^{n}t_{i} is the numberof the survival time. When the function was applied on Stanford heart transplant data,the value of ˆλ = 0.00089, which means the patient’s failure (death) probability is lowand the patient’s probability to survive is high.