Analysis of magnetic field fluctuation thermometry using Bayesian inference

A Bayesian approach is proposed for the analysis of magnetic field fluctuation thermometry. The approach addresses the estimation of temperature from the measurement of a noise power spectrum as well as the analysis of previous calibration measurements. A key aspect is the reliable determination of uncertainties associated with the obtained temperature estimates, and the proposed approach naturally accounts for both the uncertainties in the calibration stage and the noise in the temperature measurement. Erlang distributions are employed to model the fluctuations of thermal noise power spectra and we show that such a procedure is justified in the light of the data. We describe in detail the Bayesian approach and briefly refer to Markov Chain Monte Carlo techniques used in the numerical calculation of the results. The MATLAB (R) software package we used for calculating our results is provided. The proposed approach is validated using magnetic field fluctuation power spectra recorded in the sub-kelvin region for which an independently determined reference temperature is available. As a result, the obtained temperature estimates were found to be fully consistent with the reference temperature.