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When fitting transiting exoplanet lightcurves, it is usually desirable tohave ranges and/or priors for the parameters which are to be retrieved thatinclude our degree of knowledge (or ignorance) in the routines which are beingused. In Markov Chain Monte Carlo (MCMC) routines, for example, these enter asprior distributions. These can either represent our current knowledge of thedistribution of such parameters (e.g., based on their observed values) orphysically plausible parameters ranges to be sampled. Among the parameters thatare constrained by transiting exoplanet lightcurves, there are two which are ofmuch physical significance: the impact parameter of the orbit, $b = (a/R_*)\cosi $, and the planet-to-star radius ratio, $p = R_p/R_s$ (which defines thetransit depth, $\delta = p^2$). These two are natural parameters to extract andconstrain as they usually have well defined limits. A common set of"uninformative" priors used for those two parameters are uniform priors.However, this poses a sampling problem especially important for grazing orbits:given that we sample a value $p_i$ from the prior on $p$, the only physicallyplausible values for $b$ to be sampled given $p_i$ are those that satisfy $b <1 + p_i$. If we simply reject the sample if the sampled value of b is greaterthan $1 + p_i$, then we will reject points from a significant portion of theprior area depending on its size. It is desirable, thus, to have an algorithmthat efficiently samples values from the physically plausible zone in the$(b,p)$ plane. Here we present such an algorithm.

Efficient Joint Sampling of Impact Parameters and Transit Depths in Transiting Exoplanet Light Curves