bayesian estimation

This paper aims to accurately estimate the parameters of the fractional Ornstein-Uhlenbeck model using the Bayesian method and the SIR simulation algorithm and to compare its performance with the Maximum Likelihood Estimation (MLE) method in the context of stochastic differential models with long-memory properties. The paper also seeks to evaluate the efficiency of the Bayesian approach in similar models, particularly in analyzing financial data with long-term dependencies.

In this study, the parameters of the fractional Ornstein-Uhlenbeck model are estimated for the first time using the Bayesian method, with appropriate prior distributions and the SIR algorithm employed for simulation. The efficiency of the Bayesian estimator is compared to the MLE estimator based on RMSE and variance indices.

The results demonstrate that the Bayesian estimator provides more accurate parameter estimates than the Maximum Likelihood method. Moreover, with an increase in the degree of long-term dependency on the data, the accuracy of estimates improves under both methods; however, the Bayesian approach consistently outperforms the MLE. Additionally, the parameter σ is estimated with higher precision compared to the parameters k and μ.

 The originality of this paper lies in the application of the SIR algorithm to estimate the parameters of the fractional Ornstein-Uhlenbeck model. This approach has not been previously explored. This innovation represents a significant contribution to the application of Bayesian methods for estimating parameters in stochastic differential models with long-memory properties, and it opens new avenues for applying similar techniques to models like the Heston model in future research.

In this paper, we examine the Bayesian inference of the parameters of the generalized power Lindley distribution in the presence of type two hybrid censored data.

In estimating the maximum likelihood of the parameters, given that the estimates cannot be obtained implicitly and do not have a closed form, we use the EM algorithm and use Fisher's information matrix to construct asymptotic confidence intervals. Also, in estimating the parameters of the generalized power Lindley distribution, which we display with EPL in the whole article, we use two Lindley approximation methods and Markov chain Monte Carlo under the error squared loss function. We obtain HPD confidence intervals according to Bayesian estimates. Then we compare two Bayesian methods using simulation studies.

It can be seen that the Monte Carlo method for the three-parameter distribution has less bias and is more consistent than the Bayesian parameter estimates from the Lindley approximation. In distributions with many parameters, the MCMC method provides better estimates than the Lindley approximation, and convergence occurs faster in this case. The MSE estimates in the Lindley approximation, according to Table 2, are much larger than the dispersion of data with a similar sample size from the MCMC method in Table 3. and at the end, we provide an example of real data.

 Given that no study has been conducted so far on the generalized Lindley power distribution in the presence of censored hybrid type II, the findings of this study can be used for future studies.