Using neural networks to estimate parameters in spatial point process models

In this paper, I show how neural networks can be used to simultaneously estimate all unknown parameters in a spatial point process model from an observed point pattern. The method can be applied to any point process model which it is possible to simulate from. Through a simulation study, I conclude that the method recovers parameters well and in some situations provide better estimates than the most commonly used methods. I also illustrate how the method can be used on a real data example.Comment: 18 pages, 17 figures, R code is attached as ancillary file

Determinantal shot noise Cox processes

We present a new class of cluster point process models, which we call determinantal shot noise Cox processes (DSNCP), with repulsion between cluster centres. They are the special case of generalized shot noise Cox processes where the cluster centres are determinantal point processes. We establish various moment results and describe how these can be used to easily estimate unknown parameters in two particularly tractable cases, namely when the offspring density is isotropic Gaussian and the kernel of the determinantal point process of cluster centres is Gaussian or like in a scaled Ginibre point process. Through a simulation study and the analysis of a real point pattern data set we see that when modelling clustered point patterns, a much lower intensity of cluster centres may be needed in DSNCP models as compared to shot noise Cox processes.Comment: 14 pages, 6 figures, 3 table

Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation

In this paper, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not expressible in closed form but it is easy to simulate realisations under the model. We therefore explain how to use approximate Bayesian computation (ABC) to carry out statistical inference for this model. We suggest a method for model validation based on posterior predictions and global envelopes. We illustrate the ABC procedure and model validation approach using both simulated point patterns and a real data example.Comment: 37 pages, 10 figures; one line was adde

Layer III pyramidal cells in the prefrontal cortex reveal morphological changes in subjects with depression, schizophrenia, and suicide

Brodmann Area 46 (BA46) has long been regarded as a hotspot of disease pathology in individuals with schizophrenia (SCH) and major depressive disorder (MDD). Pyramidal neurons in layer III of the Brodmann Area 46 (BA46) project to other cortical regions and play a fundamental role in corticocortical and thalamocortical circuits. The AutoCUTS-LM pipeline was used to study the 3-dimensional structural morphology and spatial organization of pyramidal cells. Using quantitative light microscopy, we used stereology to calculate the entire volume of layer III in BA46 and the total number and density of pyramidal cells. Volume tensors estimated by the planar rotator quantified the volume, shape, and nucleus displacement of pyramidal cells. All of these assessments were carried out in four groups of subjects: controls (C, n = 10), SCH (n = 10), MDD (n = 8), and suicide subjects with a history of depression (SU, n = 11). SCH subjects had a significantly lower somal volume, total number, and density of pyramidal neurons when compared to C and tended to show a volume reduction in layer III of BA46. When comparing MDD subjects with C, the measured parameters were inclined to follow SCH, although there was only a significant reduction in pyramidal total cell number. While no morphometric differences were observed between SU and MDD, SU had a significantly higher total number of pyramidal cells and nucleus displacement than SCH. Finally, no differences in the spatial organization of pyramidal cells were found among groups. These results suggest that despite significant morphological alterations in layer III of BA46, which may impair prefrontal connections in people with SCH and MDD, the spatial organization of pyramidal cells remains the same across the four groups and suggests no defects in neuronal migration. The increased understanding of pyramidal cell biology may provide the cellular basis for symptoms and neuroimaging observations in SCH and MDD patients

Cellular 3D-reconstruction and analysis in the human cerebral cortex using automatic serial sections

Techniques involving three-dimensional (3D) tissue structure reconstruction and analysis provide a better understanding of changes in molecules and function. We have developed AutoCUTS-LM, an automated system that allows the latest advances in 3D tissue reconstruction and cellular analysis developments using light microscopy on various tissues, including archived tissue. The workflow in this paper involved advanced tissue sampling methods of the human cerebral cortex, an automated serial section collection system, digital tissue library, cell detection using convolution neural network, 3D cell reconstruction, and advanced analysis. Our results demonstrated the detailed structure of pyramidal cells (number, volume, diameter, sphericity and orientation) and their 3D spatial organization are arranged in a columnar structure. The pipeline of these combined techniques provides a detailed analysis of tissues and cells in biology and pathology

Should We Condition on the Number of Points When Modelling Spatial Point Patterns?

We discuss the practice of directly or indirectly assuming a model for the number of points when modelling spatial point patterns even though it is rarely possible to validate such a model in practice since most point pattern data consist of only one pattern. We therefore explore the possibility to condition on the number of points instead when fitting and validating spatial point process models. In a simulation study with different popular spatial point process models, we consider model validation using global envelope tests based on functional summary statistics. We find that conditioning on the number of points will for some functional summary statistics lead to more narrow envelopes and that it can also be useful for correcting for some conservativeness in the tests when testing composite hypothesis. However, for other functional summary statistics, it makes little or no difference to condition on the number of points. When estimating parameters in popular spatial point process models, we conclude that for mathematical and computational reasons it is convenient to assume a distribution for the number of points.Comment: 22 pages; 2 figures; R-code is attached as ancillary file