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Stochastic processes are a set of random variables indexed by some index set (e.g. time or integers). For instance, a sequence of stock prices \(\{ X_t \}_{0 \leq t \leq T }\) is a stochastic process where the index set is time \(t \in [0, T]\). The utility of defining distributions over stochastic processes is that it makes the model significantly more powerful; for instance, if the variables of the process are parameters for observations, then the model can have access to an unbounded number of parameters to use as appropriate. One interpretation is therefore that Bayesian Nonparametrics are distributions over function spaces, where the function maps the index set to the set of random variables.