Problems at the intersection of compression and statistical inference recur frequently due to the concurrent use of signal and image compression and classification algorithms in many applications. This dissertation addresses two such problems: statistical inference on compressed data, and rate-allocation for joint compression and classification.Features of the JPEG2000 standard make possible the development of computationally efficient algorithms to achieve such a goal for imagery compressed using this standard. We propose the use of the information content (IC) of wavelet subbands, defined as the number of bytes that the JPEG2000 encoder spends to compress the subbands, for content analysis. Applying statistical learning frameworks for detection and classification, we present experimental results for compressed-domain texture image classification and cut detection in video. Our results indicate that reasonable performance can be achieved, while saving computational and bandwidth resources. IC features can also be used for preliminary analysis in the compressed domain to identify candidates for further analysis in the decompressed domain.In many applications of image compression, the compressed image is to be presented to human observers and statistical decision-making systems. In such applications, the fidelity criterion with respect to which the image is compressed must be selected to strike an appropriate compromise between the (possibly conflicting) image quality criteria for the human and machine observers. We present tractable distortion measures based on the Bhattacharyya distance (BD) and a new upper bound on the quantized probability of error that make possible closed form expressions for rate allocation to image subbands and show their efficacy in maintaining the aforementioned balance between compression and classification. The new bound offers two advantages over the BD in that it yields closed-form solutions for rate-allocation in problems involving correlated sources and more than two classes.