(A) Example AOI image (from Data set A in Table 1). The AOI image is a matrix of 14 × 14 pixel intensities which is shown here as both a 2-D grayscale image and as a 3-D intensity plot. The image contains two spots; one is centered at target location (image center) and the other is located off-target. (B) Examples of four idealized noise-free image representations (). Image representations consist of zero, one, or two idealized spots () superimposed on a constant background (). Each fluorescent spot is represented as a 2-D Gaussian parameterized by integrated intensity (), width (), and position (, ). The presence of spots is encoded in the binary spot existence indicator . (C) Simulated idealized images illustrating different values of the target-specific spot state parameter and index parameter . = 0 corresponds to a case when no specifically bound molecule is present ( = 0); = 1 or 2 corresponds to the cases in which specifically bound molecule is present ( = 1) and corresponds to spot 1 or 2, respectively. (D) Condensed graphical representation of the cosmos probabilistic model. Model parameters are depicted as circles and deterministic functions as diamonds. Observed image () is represented by a shaded circle. Related nodes are connected by edges, with an arrow pointing towards the dependent node (e.g., the shape of each 2-D Gaussian spot depends on spot parameters , , , , and ). Plates (rounded rectangles) contain entities that are repeated for the number of instances displayed at the bottom-right corner: number of total AOIs (), frame count (), and maximum number of spots in a single image ( = 2). Parameters outside of the plates are global quantities that apply to all frames of all AOIs. A more complete version of the graphical model specifying the relevant probability distributions is given in Figure 2—figure supplement 1.