Updating prior parameters based on likelihood Function-Bayesian method for parameter estimation at high measurement uncertainty

One approach in statistical analysis that distinguishes between frequentist and Bayesian is the inclusion of available prior information about the data even before measuring/surveying the data. Many researchers argued that the inclusion of prior information resulted in a better model prediction/parameter estimation. Bayesian inference is repeatedly used in inverse problems to retrieve parameters due to the development of high efficient sampling algorithms such as Markov Chain Monte-Carlo (MCMC). Inverse problems are generally ill-posed in nature. Nevertheless, the inclusion of prior information reduces the ill-posedness of the problem to an extent. Any inverse problem relies on measured data by physical sensors, therefore induced random errors greatly affects the quality of estimation. When the uncertainty of the measured data is high, the inferences made from the resulting sampling distributions are nearly the same as the supplied prior information. The reason is that, probability of samples nearer to prior information is more at higher uncertainties of measurement and has more chance to get repeatedly accepted than the samples that are close to actual value. Therefore, in this work an effort is made to update the prior hyper parameters in each iterations of the MCMC algorithm based on the history of the likelihood function. The applicability of method is demonstrated by retrieving parameters from 1-D fin experiment. Three thermal properties such as thermal conductivity, heat transfer coefficient and emissivity are retrieved simultaneously. The estimation is carried out for both error and errorless temperature measurements and the results show that, the estimated parameters with the proposed method are in excellent agreement with the true parameter value and a maximum of 7% deviation occurs in estimating heat transfer coefficient at a measurement error of ±0.3K.