  Microflares are energetically smaller versions of solar flares, demonstrating
the same processes of plasma heating and particle acceleration. However, it
remains unclear down to what energy scales this impulsive energy release
continues, which has implications for how the solar atmosphere is heated. The
heating and particle acceleration in microflares can be studied through their
X-ray emission, finding predominantly thermal emission at lower energies;
however, at higher energies it can be difficult to distinguish whether the
emission is due to hotter plasma and/or accelerated elections. We present the
first application of nested sampling to solar flare X-ray spectra, an approach
which provides a quantitative degree of confidence for one model over another.
We analyse NuSTAR X-ray observations of a small active region microflare (A0.02
GOES/XRS class equivalent) that occurred on 2021 November 17, with a new Python
package for spectral fitting, sunkit-spex, to compute the parameter posterior
distributions and the evidence of different models representing the higher
energy emission as due to thermal or non-thermal sources. Calculating the Bayes
factor, we show there is significantly stronger evidence for the higher energy
microflare emission to be produced by non-thermal emission from flare
accelerated electrons than by an additional hot thermal source. Qualitative
confirmation of this non-thermal source is provided by the lack of hotter (10
MK) emission in SDO/AIA's EUV data. The nested sampling approach used in this
paper has provided clear support for non-thermal emission at the level of
3x10$^{24}$ erg s$^{-1}$ in this tiny microflare.
