Bayesian Inversion Method and its Information Determination for the Estimation of Particle Size Distribution in Ferrofluids

Using Gaussian numerical integration formula, the problem of estimating the particle size distribution (PSD) in ferrofluids can be converted into an electromagnetic inverse problem. Then we present two Bayesian analytical estimators, minimum mean-square error estimator and maximum a posteriori estimator, to reconstruct the PSD of magnetic particles. In the implementation, weighted minimum norm approach, maximum likelihood estimator, and weighted least square estimator are employed to determine prior information for the unknown parameter. We also present two methods to provide the noise information for the error term. Finally, using Monte Carlo method, we give a ferrofluid example to illustrate the efficiency of the proposed methods.