Second-order quasi-likelihood for spatial point processes.

Applications of spatial point processes for large and complex data sets with inhomogeneities as encountered, example, in tropical rain forest ecology call for estimation methods that are both statistically and computationally efficient. We propose a novel second-order quasi-likelihood procedure to estimate the parameters for a second-order intensity reweighted stationary spatial point process. Our approach is to derive first- and second-order estimating functions and then combine them linearly using appropriate weight functions. In the stationary case, we argue that the asymptotically optimal weight functions are respectively a constant and a function of lags between distinct locations in the observation window. This leads to a considerable gain in computational efficiency. We further exploit this simplification in the nonstationary case. Simulations show that, when compared with several existing approaches, our method can achieve significant gains in statistical efficiency. An application to a tropical rain forest data set further illustrates the advantages of our procedure.

Analysis of shape and spatial interaction of synaptic vesicles using data from focused ion beam scanning electron microscopy (FIB-SEM).

The spatial interactions of synaptic vesicles in synapses were assessed after a detailed characterization of size, shape, and orientation of the synaptic vesicles. We hypothesized that shape and orientation of the synaptic vesicles are influenced by their movement toward the active zone causing deviations from spherical shape and systematic trends in their orientation. We studied three-dimensional representations of synapses obtained by manual annotation of focused ion beam scanning electron microscopy (FIB-SEM) images of male mouse brain. The configurations of synaptic vesicles were regarded as marked point patterns, where the points are the centers of the vesicles, and the mark of a vesicle is given by its size, shape, and orientation characteristics. Statistics for marked point processes were employed to study spatial interactions between vesicles. We found that the synaptic vesicles in excitatory synapses appeared to be of oblate ellipsoid shape and in inhibitory synapses appeared to be of cigar ellipsoid shape, and followed a systematic pattern regarding their orientation toward the active zone. Moreover, there was strong evidence of spatial alignment in the orientations of pairs of synaptic vesicles, and of repulsion between them only in excitatory synapses, beyond that caused by their physical extent.