<p>Yes it's certainly possible but requires a bit more work. Stan (and popular MCMC tools that I know of) are not designed to be run in a distributed setting, via Spark or otherwise. In general, distributed MCMC is an area of active research. For a recent review, I'd recommend section 4 of <a href="http://arxiv.org/abs/1602.05221" rel="noreferrer">Patterns of Scalable Bayesian Inference</a> (PoFSBI). There are multiple possible ways you might want to split up a big MCMC computation but I think one of the more straightforward ways would be splitting up the data and running an off-the-shelf tool like Stan, with the same model, on each partition. Each model will produce a <em>subposterior</em> which can be reduce'd together to form a posterior. PoFSBI discusses several ways of combining such subposteriors.</p>

<p>I've <a href="https://gist.github.com/strongh/0ba143d21e2382e3ec61f6a0bdc2f55d" rel="noreferrer">put together</a> a very rough proof of concept using pyspark and pystan (python is the common language with the most Stan and Spark support). It's a rough and limited implementation of the weighted-average consensus algorithm in PoFSBI, running on the tiny 8-schools dataset. I don't think this example would be practically very useful but it should provide some idea of what might be necessary to run Stan as a Spark program: partition data, run stan on each partition, combine the subposteriors.</p>
MC-Stan on Spark?
<p>I hope to use <a href="http://mc-stan.org/" rel="nofollow">MC-Stan</a> on <a href="http://spark.apache.org/" rel="nofollow">Spark</a>, but it seems there is no related page searched by Google.</p>

<p>I wonder if this approach is even possible on Spark, therefore I would appreciate if someone let me know.</p>

<p>Moreover, I also wonder what is the widely-used approach to use MCMC on Spark. I heard Scala is widely used, but I need some language that has a decent MCMC library such as MC-Stan.</p>