The basal ganglia are a subcortical group of interconnected nuclei involved in mediating action selection within cortex. A recent proposal is that this selection leads to optimal decision making over multiple alternatives because the basal ganglia anatomy maps onto a network implementation of an optimal statistical method for hypothesis testing, assuming that cortical activity encodes evidence for constrained gaussian-distributed alternatives. This letter demonstrates that this model of the basal ganglia extends naturally to encompass general Bayesian sequential analysis over arbitrary probability distributions, which raises the proposal to a practically realizable theory over generic perceptual hypotheses. We also show that the evidence in this model can represent either log likelihoods, log-likelihood ratios, or log odds, all leading proposals for the cortical processing of sensory data. For these reasons, we claim that the basal ganglia optimize decision making over general perceptual hypotheses represented in cortex. The relation of this theory to cortical encoding, cortico-basal ganglia anatomy, and reinforcement learning is discussed.