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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 ignition model with X-ray observations of the accretion-powered millisecond pulsar SAX J1808.4–3658 in outburst. We used a Bayesian analysis approach to marginalize over the parameters of interest and determine parameters such as fuel composition, distance/anisotropy factors, neutron star mass, and neutron star radius. 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 a flat disc model. This method can be applied to any accreting source that exhibits 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 the accreted 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 a neutron 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 $1.9^{+0.7}_{-0.4}\times 10^{14}\, \mathrm{cm}\, \mathrm{s}^{-2}$ for SAX J1808.4–3658.