Enterprise applications need sophisticated in-database analytics in addition to traditional online analytical processing from a database. To meet customers' pressing demands, database vendors have been pushing advanced analytical techniques into databases. Most major DBMSes offer User-Defined Aggregate (UDA), a data-driven operator, to implement many of the analytical techniques in parallel. However, UDAs can not be used to implement statistical algorithms such as Markov chain Monte Carlo (MCMC), where most of the work is performed by iterative transitions over a large state that can not be naively partitioned due to data dependency. Typically, this type of statistical algorithm requires pre-processing to setup the large state in the first place and demands post-processing after the statistical inference. This paper presents General Iterative State Transition (GIST), a new database operator for parallel iterative state transitions over large states. GIST receives a state constructed by a UDA, and then performs rounds of transitions on the state until it converges. A final UDA performs post-processing and result extraction. We argue that the combination of UDA and GIST (UDA-GIST) unifies data-parallel and state-parallel processing in a single system, thus significantly extending the analytical capabilities of DBMSes. We exemplify the framework through two high-profile applications: cross-document coreference and image denoising. We show that the in-database framework allows us to tackle a 27 times larger problem than solved by the state-of-the-art for the first application and achieves 43 times speedup over the state-of-the-art for the second application.