This paper describes the SimSQL system, which allows for SQL-based specification, simulation, and querying of database-valued Markov chains, i.e., chains whose value at any time step comprises the contents of an entire database. SimSQL extends the earlier Monte Carlo database system (MCDB), which permitted Monte Carlo simulation of static database-valued random variables. Like MCDB, SimSQL uses user-specified to generate the simulated data values that are the building blocks of a simulated database. The enhanced functionality of SimSQL is enabled by the ability to parametrize VG functions using stochastic tables, so that one stochastic database can be used to parametrize the generation of another stochastic database, which can parametrize another, and so on. Other key extensions include the ability to explicitly define recursive versions of a stochastic table and the ability to execute the simulation in a MapReduce environment. We focus on using SimSQL to specify Bayesian machine learning modelsin a concise and natural manner, and then to analyze such models at scale using Markov Chain Monte Carlo methods.