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Stan has two mechanisms for parallelizing calculations used in a model: reduce with summation and rectangular map.
The advantages of reduce with summation are:
- More flexible argument interface, avoiding the packing and unpacking that is necessary with rectanguar map.
- Partitions data for parallelization automatically (this is done manually in rectanguar map).
- Is easier to use.
The advantages of rectangular map are:
- Returns a list of vectors, while the reduce summation returns only a scalar.
- Can be parallelized across multiple cores and multiple computers, while reduce summation can only parallelized across multiple cores on a single machine.
The actual speedup gained from using these functions will depend on many details. It is strongly recommended to only parallelize the computationally most expensive operations in a Stan program. Oftentimes this is the evaluation of the log likelihood for the observed data. Since only portions of a Stan program will run in parallel, the maximal speedup one can achieve is capped, a phenomen described by Amdahl’s law.