It is vital to modern intelligence operations that the cycle of gathering, analysing and acting upon intelligence is as efficient as possible in the face of an ever increasing volume of available information. The collection, processing and subsequent analysis aspect of the intelligence cycle is modelled as a novel finite horizon Bayesian stochastic dynamic programming problem, namely the multi-armed bandit allocation (MABA) problem. The MABA framework models the efforts of a processor to search for intelligence items of the highest importance by making sequential samples from a collection of intelligence sources. Through Bayesian learning the processor learns about the importance distributions of the available sources over time, select a source from which to sample at each decision epoch, and decides whether or not to allocate sampled items for analysis. For source selection, a novel Lagrangian based index heuristic is developed and its performance is compared to existing index heuristics including knowledge gradient and Thompson sampling methods. The allocation policy is handled by thresholds which act as Lagrangian multipliers of the original MABA problem. Both a discrete Dirichlet-Multinomial and a continuous Exponential-Gamma-Gamma implementation of the MABA problem are developed, where the latter also models uncertainty in the processor's own ability to accurately assess the importance of sampled items.