High dynamic range (HDR) imaging has gained increasing popularity for its ability to faithfully reproduce the luminance levels in natural scenes. Accordingly, HDR image quality assessment (IQA) is crucial but has been superficially treated. The majority of existing IQA models are developed for and calibrated against low dynamic range (LDR) images, which have been shown to be poorly correlated with human perception of HDR image quality. In this work, we propose a family of HDR IQA models by transferring the recent advances in LDR IQA. The key step in our approach is to specify a simple inverse display model that decomposes an HDR image to a set of LDR images with different exposures, which will be assessed by existing LDR quality models. The local quality scores of each exposure are then aggregated with the help of a simple well-exposedness measure into a global quality score for each exposure, which will be further weighted across exposures to obtain the overall quality score. When assessing LDR images, the proposed HDR quality models reduce gracefully to the original LDR ones with the same performance. Experiments on four human-rated HDR image datasets demonstrate that our HDR quality models are consistently better than existing IQA methods, including the HDR-VDP family. Moreover, we demonstrate their strengths in perceptual optimization of HDR novel view synthesis.