Indirect Bayes¶

Overview¶

Provides Bayesian analysis routines primarily for use with QENS data.

Action Buttons¶

Settings

Opens the Settings GUI which allows you to customize the settings for the Indirect interfaces.

?

Opens this help page.

Manage Directories

Opens the Manage Directories dialog allowing you to change your search directories and default save directory and enable/disable data archive search.

ResNorm¶

This tab creates a group ‘normalisation’ file by taking a resolution file and fitting it to all the groups in the resolution (vanadium) data file which has the same grouping as the sample data of interest.

The routine fits the width of the resolution file to give a ‘stretch factor’ and the area provides an intensity normalisation factor.

The fitted parameters are in the group workspace with suffix _ResNorm with additional suffices of _Intensity & _Stretch.

The processing on this tab is provided by the ResNorm algorithm.

Quasi¶

The model that is being fitted is that of a \(\delta\)-function (elastic component) of amplitude \(A(0)\) and Lorentzians of amplitude \(A(j)\) and HWHM \(W(j)\) where \(j=1,2,3\). The whole function is then convolved with the resolution function. The -function and Lorentzians are intrinsically normalised to unity so that the amplitudes represent their integrated areas.

For a Lorentzian, the Fourier transform does the conversion: \(1/(x^{2}+\delta^{2}) \Leftrightarrow exp[-2\pi(\delta k)]\). If \(x\) is identified with energy \(E\) and \(2\pi k\) with \(t/\hbar\) where t is time then: \(1/[E^{2}+(\hbar / \tau)^{2}] \Leftrightarrow exp[-t /\tau]\) and \(\sigma\) is identified with \(\hbar / \tau\). The program estimates the quasielastic components of each of the groups of spectra and requires the resolution file and optionally the normalisation file created by ResNorm.

For a Stretched Exponential, the choice of several Lorentzians is replaced with a single function with the shape : \(\psi\beta(x) \Leftrightarrow exp[-2\pi(\sigma k)\beta]\). This, in the energy to time FT transformation, is \(\psi\beta(E) \Leftrightarrow exp[-(t/\tau)\beta]\). So \(\sigma\) is identified with \((2\pi)\beta\hbar/\tau\) . The model that is fitted is that of an elastic component and the stretched exponential and the program gives the best estimate for the \(\beta\) parameter and the width for each group of spectra.

Stretch¶

This is a variation of the stretched exponential option of Quasi. For each spectrum, a fit is performed for a grid of β and σ values. The distribution of goodness of fit values is plotted.