Being able to automatically predict digital picture quality, as perceived by human observers, has become important in many applications where humans are the ultimate consumers of displayed visual information. Standard dynamic range (SDR) images provide 8 b/color/pixel. High dynamic range (HDR) images, which are usually created from multiple exposures of the same scene, can provide 16 or 32 b/color/pixel, but must be tonemapped to SDR for display on standard monitors. Multi-exposure fusion techniques bypass HDR creation, by fusing the exposure stack directly to SDR format while aiming for aesthetically pleasing luminance and color distributions. Here, we describe a new no-reference image quality assessment (NR IQA) model for HDR pictures that is based on standard measurements of the bandpass and on newly conceived differential natural scene statistics (NSS) of HDR pictures. We derive an algorithm from the model which we call the HDR IMAGE GRADient-based Evaluator. NSS models have previously been used to devise NR IQA models that effectively predict the subjective quality of SDR images, but they perform significantly worse on tonemapped HDR content. Toward ameliorating this we make here the following contributions: 1) we design HDR picture NR IQA models and algorithms using both standard space-domain NSS features as well as novel HDR-specific gradient-based features that significantly elevate prediction performance; 2) we validate the proposed models on a large-scale crowdsourced HDR image database; and 3) we demonstrate that the proposed models also perform well on legacy natural SDR images. The software is available at: http://live.ece.utexas.edu/research/Quality/higradeRelease.zip.