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We present a new method of matching observations of Type I (thermonuclear)X-ray bursts with models, comparing the predictions of a semi-analytic ignitionmodel with X-ray observations of the accretion-powered millisecond pulsar SAXJ1808.4--3658 in outburst. We used a Bayesian analysis approach to marginaliseover the parameters of interest and determine parameters such as fuelcomposition, distance/anisotropy factors, neutron star mass and neutron starradius. Our study includes a treatment of the system inclination effects,inferring that the rotation axis of the system is inclined$\left(69^{+4}_{-2}\right)^\circ$ from the observers line of sight, assuming aflat disc model. This method can be applied to any accreting source thatexhibits Type I X-ray bursts. We find a hydrogen mass fraction of$0.57^{+0.13}_{-0.14}$ and CNO metallicity of $0.013^{+0.006}_{-0.004}$ for theaccreted fuel is required by the model to match the observed burst energies,for a distance to the source of $3.3^{+0.3}_{-0.2}\,\mathrm{kpc}$. We infer aneutron star mass of $1.5^{+0.6}_{-0.3}\,\mathrm{M}_{\odot}$ and radius of$11.8^{+1.3}_{-0.9}\,\mathrm{km}$ for a surface gravity of$1.9^{+0.7}_{-0.4}\times10^{14}\,\mathrm{cm}\,\mathrm{s}^{-2}$ for SAXJ1808.4--3658.

A Bayesian Approach to Matching Thermonuclear X-ray Burst Observations with Models