FINEMAP uses a Shotgun Stochastic Search (SSS) algorithm (Hans et al., 2007). SSS has been inspired by Markov Chain Monte Carlo (MCMC) algorithms that are widely used for Bayesian inference. For a review on MCMC, see Andrieu et al. (2003). Standard MCMC methods, such as the Metropolis-Hastings algorithm (Hastings, 1970; Metropolis et al., 1953) and Gibbs sampler (Geman and Geman, 1984), perform a sequence of steps in the parameter space via a stochastic transition mechanism that ensures a valid approximation to the target distribution. MCMC can often quickly reach an interesting region of the parameter space, but, at each step, it only considers one of the possible neighboring states. This means that MCMC is often slow to explore a high-dimensional state space. To improve on this, SSS generates a whole set of neighboring configurations at each iteration and saves them all for further use in probability calculations. This way a large number of parameter configurations with relatively high probability is quickly explored.
