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.

In this paper, statistical modeling of online advertising systems is addressed. The proposed model relies on the highest bidding price estimation in an auction network and the click-through rate estimation of the ad campaign. The estimation problem is faced with serious challenges due to the extremely time-varying and nonlinear behavior of users, the competitive behavior of the ad campaigns, and the variety of strategies incorporated by the demand-side platforms. Accordingly, estimation algorithms based on Kalman filtering may fail to provide reliable solutions in a real-time setting. In this paper, particle filtering is utilized to estimate the probability distribution of the highest bidding price. Advertisers observe the highest bidding price only if they win the auction. Otherwise, they do not have access to the highest bidding price. Thus, a biconditional update rule is proposed for the particles. The weighting scheme modifies the posterior distribution in case of winning or losing the auction. Next, the click-through rate of the ad campaign is introduced based on the Bayesian estimation. Since the user response is extremely variable over time, an adaptation rule is proposed to update the forgetting factor and the level of emphasis on the recent observations. Finally, by estimation of the highest bidding price and the click-through rate distributions, the input-output model of the ad campaign is developed. The input is the bidding signal or the control signal and the output is the total number of winning impressions for the campaign. The results are reported for a campaign with four individual segments and confirm that the proposed statistical approach can provide a reliable model for ad campaigns.

Magnetic Resonance Imaging (MRI) is a notable medical imaging technique that is based on Nuclear Magnetic Resonance (NMR). MRI is a safe imaging method with high contrast between soft tissues, which made it the most popular imaging technique in clinical applications. MR Imagechr('39')s visual quality plays a vital role in medical diagnostics that can be severely corrupted by existing noise during the acquisition process. Therefore, the denoising of these images has great importance in medical applications. During the last decades, lots of MR denoising approaches from various groups of techniques have been proposed that can be classified into two general groups of acquisition-based noise reduction and post-acquisition denoising methods. The first groupchr('39')s approaches will add imaging time and led to a much time-consuming process. The second groupchr('39')s issues are its complicated mathematical equations required for image denoising, in which stochastic algorithms are usually required to solve these complex equations.This study aims to find an appropriate statical post-acquisition denoising MR imaging method based on the Bayesian technique. Finding the appropriate prior density function also has great importance since the Bayesian techniquechr('39')s performance is related to its prior density function. In this study, the uniform distribution has been applied as the prior density function. The prior uniform distribution function will reduce the Bayesian algorithm to its simplest possible state and lower computational complexity and time consumption. The proposed method can solve the numerical problems with an adequate timing process without complex algorithms and remove noise in less than 120 seconds on average in all cases. To quantitatively assess image improvement, we used the Structural Similarity Function (SSIM) in MATLAB. The similarity with this function shows an average improvement of more than 0.1 in all images. Considering the results, it can be concluded that combining the uniform distribution function as a prior density function and the Bayesian algorithm can significantly reduce the imagechr('39')s noise without the time and computational cost.