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

Abstract. 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.