  A logconcave likelihood is as important to proper statistical inference as a
convex cost function is important to variational optimization. Quantization is
often disregarded when writing likelihood models, ignoring the limitations of
the physical detectors used to collect the data. These two facts call for the
question: would including quantization in likelihood models preclude
logconcavity? are the true data likelihoods logconcave? We provide a general
proof that the same simple assumption that leads to logconcave continuous-data
likelihoods also leads to logconcave quantized-data likelihoods, provided that
convex quantization regions are used.
