Title: A new framework to follow up candidates from continuous gravitational-wave searches

Abstract: Searches for continuous gravitational waves from unknown neutron stars are limited in sensitivity due to their high computational cost. For this reason, developing new methods or improving existing ones can increase the probability of making a detection. In this paper we present a new framework that uses MCMC or nested sampling methods to follow-up candidates of continuous gravitational-wave searches. This framework aims to go beyond the capabilities of PYFSTAT (which is limited to the PTEMCEE sampler), by allowing a flexible choice of sampling algorithm (using BILBY as a wrapper) and multi-dimensional correlated prior distributions. We show that MCMC and nested sampling methods can recover the maximum posterior point for much bigger parameter-space regions than previously thought (including for sources in binary systems), and we present tests that examine the capabilities of the new framework: a comparison between the DYNESTY, NESSAI, and PTEMCEE samplers, the usage of correlated priors, and its improved computational cost.