Image-Based Empirical Importance Sampling: An Efficient Way of Estimating Intensities

Very recently, it has been suggested in the biomedical literature to combine computerized image analysis with non-uniform sampling to increase the efficiency of estimators of intensities of biological cell populations. We give this ingenious idea of empirical importance sampling a stochastic formulation, using point process theory and modern sampling theory. We develop statistical tools for assessing its efficiency and construct optimal model-based estimators of intensities. Examples of applications of empirical importance sampling in microscopy are provided.