The maximum entropy method (MEM) is used as an inversion technique in a wide range of scientific fields including NMR, astronomy, mass spectrometry, the calculation of electron densities from x-ray and neutron scattering and muon spin rotation.

In this talk, I will introduce MEM in the context of transverse field muon spin rotation data in samples with static local fields b, for which the time spectra asymmetry is primarily the Fourier transform of the local magnetic field distribution P(b). MEM is used as an alternative to a Fourier transform, providing both noise suppression in regions of P(b) where the signal is absent or insignificant and deconvolution of the `resolution' function of the apparatus. I discuss how MEM differs from Fourier transform and from chi^2 fitting, and briefly describe how the deconvolution works. The maximum entropy method finds its solution in a way analogous to chi^2 fitting and calculation of a covariance matrix follows naturally. The covariance matrix demonstrates that the maximum entropy result P(b) has intrinsically correlated uncertainties. Errors can be estimated for properties of P(b) such as the mean, and second and third moments.

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