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.
翻译:日对数可能性对于适当的统计推断和对等成本功能一样重要,对于变式优化非常重要。当写入概率模型时,往往忽略量化,忽略了用于收集数据的物理探测器的局限性。这两个事实引出一个问题:是否将概率模型的量化排除了日对数?真实的数据概率是否为日对数?我们提供了一般性证据,证明导致对coccocave连续数据概率的简单假设也会导致对数量化数据概率,只要使用对数量化区域。