Jesper Møller

Statistical inference and simulation for spatial point processes

EXAMPLES OF SPATIAL POINT PATTERNS INTRODUCTION TO POINT PROCESSES Point Processes on R^d Marked Point Processes and Multivariate Point Processes Unified Framework Space-Time Processes POISSON POINT PROCESSES Basic Properties Further Results Marked Poisson Processes SUMMARY STATISTICS First and Second Order Properties Summary Statistics Nonparametric Estimation Summary Statistics for Multivariate Point Processes Summary Statistics for Marked Point Processes COX PROCESSES Definition and Simple Examples Basic Properties Neyman-Scott Processes as Cox Processes Shot Noise Cox Processes Approximate Simulation of SNCPs Log Gaussian Cox Processes Simulation of Gaussian Fields and LGCPs Multivariate Cox Processes MARKOV POINT PROCESSES Finite Point Processes with a Density Pairwise Interaction Point Processes Markov Point Processes Extensions of Markov Point Processes to R^d Inhomogeneous Markov Point Processes Marked and Multivariate Markov Point Processes METROPOLIS-HASTINGS ALGORITHMS Description of Algorithms Background Material for Markov Chains Convergence Properties of Algorithms SIMULATION-BASED INFERENCE Monte Carlo Methods and Output Analysis Estimation of Ratios of Normalising Constants Approximate Likelihood Inference Using MCMC Monte Carlo Error Distribution of Estimates and Hypothesis Tests Approximate MissingData Likelihoods INFERENCE FOR MARKOV POINT PROCESSES Maximum Likelihood Inference Pseudo Likelihood Bayesian Inference INFERENCE FOR COX PROCESSES Minimum Contrast Estimation Conditional Simulation and Prediction Maximum Likelihood Inference Bayesian Inference BIRTH-DEATH PROCESSES AND PERFECT SIMULATION Spatial Birth-Death Processes Perfect Simulation APPENDICES History, Bibliography, and Software Measure Theoretical Details Moment Measures and Palm Distributions Perfect Simulation of SNCPs Simulation of Gaussian Fields Nearest-Neighbour Markov Point Processes Results for Spatial Birth-Death Processes References Subject Index Notation Index

Log Gaussian Cox processes

Planar Cox processes directed by a log Gaussian intensity process are investigated in the univariate and multivariate cases. The appealing properties of such models are demonstrated theoretically as well as through data examples and simulations. In particular, the first, second and third-order properties are studied and utilized in the statistical analysis of clustered point patterns. Also empirical Bayesian inference for the underlying intensity surface is considered.

Non-and semi-parametric estimation of interaction in inhomogeneous point patterns

We develop methods for analysing the ‘interaction’ or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely non‐parametric study of interactions is possible using an analogue of the K‐function. Alternatively one may assume a semi‐parametric model in which a (parametrically specified) homogeneous Markov point process is subjected to (non‐parametric) inhomogeneous independent thinning. The effectiveness of these approaches is tested on datasets representing the positions of trees in forests.

The structural basis of calcium transport by the calcium pump.

The sarcoplasmic reticulum Ca2+-ATPase, a P-type ATPase, has a critical role in muscle function and metabolism. Here we present functional studies and three new crystal structures of the rabbit skeletal muscle Ca2+-ATPase, representing the phosphoenzyme intermediates associated with Ca2+ binding, Ca2+ translocation and dephosphorylation, that are based on complexes with a functional ATP analogue, beryllium fluoride and aluminium fluoride, respectively. The structures complete the cycle of nucleotide binding and cation transport of Ca2+-ATPase. Phosphorylation of the enzyme triggers the onset of a conformational change that leads to the opening of a luminal exit pathway defined by the transmembrane segments M1 through M6, which represent the canonical membrane domain of P-type pumps. Ca2+ release is promoted by translocation of the M4 helix, exposing Glu 309, Glu 771 and Asn 796 to the lumen. The mechanism explains how P-type ATPases are able to form the steep electrochemical gradients required for key functions in eukaryotic cells.

Nearest-Neighbour Markov Point Processes and Random Sets

Summary The Markov point processes introduced by Ripley & Kelly are generalised by replacing fixed-range spatial interactions by interactions between neighbouring particles, where the neighbourhood relation may depend on the point configuration. The corresponding HammersleyClifford characterisation theorem is proved. The results are used to construct new models for point processes, multitype point processes and random processes of geometrical objects. Monte Carlo simulations of these models can be generated by running spatial birth-and-death processes.

Modulatory and catalytic modes of ATP binding by the calcium pump

We present crystal structures of the calcium‐free E2 state of the sarcoplasmic reticulum Ca2+‐ATPase, stabilized by the inhibitor thapsigargin and the ATP analog AMPPCP. The structures allow us to describe the ATP binding site in a modulatory mode uncoupled from the Asp351 phosphorylation site. The Glu439 side chain interacts with AMPPCP via an Mg2+ ion in accordance with previous Fe2+‐cleavage studies implicating this residue in the ATPase cycle and in magnesium binding. Functional data on Ca2+ mediated activation indicate that the crystallized state represents an initial stage of ATP modulated deprotonation of E2, preceding the binding of Ca2+ ions in the membrane from the cytoplasmic side. We propose a mechanism of Ca2+ activation of phosphorylation leading directly from the compact E2‐ATP form to the Ca2E1‐ATP state. In addition, a role of Glu439 in ATP modulation of other steps of the functional cycle is suggested.

Perfect simulation using dominating processes on ordered spaces, with application to locally stable point processes

In this paper we investigate the application of perfect simulation, in particular Coupling from the Past (CFTP), to the simulation of random point processes. We give a general formulation of the method of dominated CFTP and apply it to the problem of perfect simulation of general locally stable point processes as equilibrium distributions of spatial birth-and-death processes. We then investigate discrete-time Metropolis-Hastings samplers for point processes, and show how a variant which samples systematically from cells can be converted into a perfect version. An application is given to the Strauss point process.

Random Tessellations in Rd

This paper presents a general theory of random tessellations (i.e. stochastic aggregates of disjoint and space-filling cells) in d-dimensional Euclidean space. Some particular models of random tessellations are discussed in detail.

Random Johnson-Mehl tessellations

A unified exposition of random Johnson-Mehl tessellations in d-dimensional Euclidean space is presented. In particular, Johnson-Mehl tessellations generated by time-inhomogeneous Poisson processes and nucleation-exclusion models are studied. The «practical» cases d = 2 and d = 3 are discussed in detail. Several new results are established, including first- and second-order moments of various characteristics for both Johnson-Mehl tesselations and sectional Johnson-Mehl tessellations

Shot noise Cox processes

Shot noise Cox processes constitute a large class of Cox and Poisson cluster processes in ℝ d , including Neyman-Scott, Poisson-gamma and shot noise G Cox processes. It is demonstrated that, due to the structure of such models, a number of useful and general results can easily be established. The focus is on the probabilistic aspects with a view to statistical applications, particularly results for summary statistics, reduced Palm distributions, simulation with or without edge effects, conditional simulation of the intensity function and local and spatial Markov properties.