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Motivated primarily by the large uncertainties in the thermonuclear rate ofthe $^{30}$P$(p,\gamma)^{31}$S reaction that limit our understanding ofclassical novae, we carried out lifetime measurements of $^{31}$S excitedstates using the Doppler Shift Lifetimes (DSL) facility at the TRIUMF IsotopeSeparator and Accelerator (ISAC-II) facility. The $^{31}$S excited states werepopulated by the $^{3}$He$(^{32}$S$,\alpha)^{31}$S reaction. The deexcitation$\gamma$ rays were detected by a clover-type high-purity germanium detector incoincidence with the $\alpha$ particles detected by a silicon detectortelescope. We have applied modern Markov chain Monte Carlo-based Bayesianmethods to perform lineshape analyses of Doppler-shift attenuation method$\gamma$-ray data for the first time. We have determined the lifetimes of thetwo lowest-lying $^{31}$S excited states. First experimental upper limits onthe lifetimes of four higher-lying states have been obtained. The experimentalresults were compared to shell-model calculations using five universal$sd$-shell Hamiltonians. Evidence for $\gamma$ rays originating from theastrophysically important $J^\pi=3/2^+$, 260-keV $^{30}$P$(p,\gamma)^{31}$Sresonance has also been observed, although strong constraints on the lifetimewill require better statistics.

First application of Markov Chain Monte Carlo-based Bayesian data analysis to the Doppler-Shift Attenuation Method