Confidence intervals through sequential Monte Carlo

Usually, confidence intervals are built through inversion of a hypothesis test. When the analytical shape of the test statistic distribution is unknown, Monte Carlo simulation can be used to construct the interval. In this direction, a sequential Monte Carlo method for interval estimation is introduced. The method produces intervals with guaranteed confidence coefficients. Because in practice one always needs to establish a truncation on the number of simulations, a simple rule of thumb is offered for choosing the number of simulations as a function of desired upper bounds for the coverage probability. As a novelty in the literature, the sequential Monte Carlo method presents equivalence with the conventional Monte Carlo test. In terms of performance, the superiority of the proposed method is illustrated for two different problems, estimation of gamma distribution means, and estimation of population sizes based on mark-recapture sampling. An example of application for real data is offered for relative risk estimation following the circular spatial scan test.