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The derivation of spatial cues representing source localization information is a typical component of multichannel spatial audio coders such as EAAC+ and MPEG Surround. Efficient compression of spatial cues based on the inter-frame difference distribution of spatial cues is investigated. Using a Bayesian Gradient model, the inter-frame correlations can be predicted more accurately. Results show that the proposed higher-order prediction method for spatial cue compression achieves about 20% bit-rate reduction with respect to the inter-freq differential coding method used in MPEG Surround.