Statistical Inference and Perfect Simulation for Point Processes Observed with Noise
نویسنده
چکیده
Physics under supervision of professor Mats Rudemo. The most recent version of the papers in this thesis can always be obtained from my homepage It is usual to thank a lengthy list of persons in the preface of your thesis. I could certainly make such a list as I know and I have met a lot of wonderful, nice, and helpful persons during my Ph.D. studies. However, I am afraid that I would forget some of you, so I prefer to simply say THANK YOU without mentioning anybody. Your support, advice, and encouragement has been invaluable to me. I owe you all a great debt of gratitude. iii iv Summary The main themes of this thesis are spatial statistics and simulation algorithms. The thesis is split into ve papers that may be read independently. All ve papers deal with spatial models. Lund & Rudemo (1999), Lund et al. (1999), and Lund & Thhnnes (1999b) deal with the same new model for point processes observed with noise, and Lund et al. and analyse a new model for point processes observed with noise. Usually the analysis of spatial point patterns assume that the observed points (the true points) are a realization from a speciic model. In contrast our approach is to assume the observed pattern generated by thinning and displacement of the true points, and allow for contamination by points not belonging to the true pattern. Lund & Rudemo (1999) develop the model for point processes observed with noise. The likelihood function for an observation of a noise corrupted point pattern given the true positions is derived. As data for our analysis is indeed a realization of the underlying true process and its associated noise corrupted point pattern we need not consider a model for the underlying process. The parameters in the model describe how many of the true points are lost, how large the displacements are, and the number of contaminating surplus points. For estimation of the parameters in the noise model a deterministic, iterative, and approximative maximum likelihood estimation algorithm is developed. The likelihood function is a sum of an excessive large number of terms, and the algorithm works by nding large dominating terms. Alternative estimation methods are discussed. Lund et al. (1999) analyse the model developed in Lund & Rudemo (1999) with respect to the now unobserved true points. We assume a noisy observation of a true point pattern …
منابع مشابه
Perfect simulation of point patterns from noisy observations
The paper is concerned with the Bayesian analysis of point processes which are observed with noise. It is shown how to produce exact samples from the posterior distribution of the unobserved true point pattern given a noisy observation. The algorithm is a perfect simulation method which applies dominated Coupling From The Past (CFTP) to a spatial birth-and-death process. Dominated CFTP is made ...
متن کاملProperties of Spatial Cox Process Models
Probabilistic properties of Cox processes of relevance for statistical modeling and inference are studied. Particularly, we study the most important classes of Cox processes, including log Gaussian Cox processes, shot noise Cox processes, and permanent Cox processes. We consider moment properties and point process operations such as thinning, displacements, and superpositioning. We also discuss...
متن کاملExact Statistical Inference for Some Parametric Nonhomogeneous Poisson Processes
Nonhomogeneous Poisson processes (NHPPs) are often used to model recurrent events, and there is thus a need to check model fit for such models. We study the problem of obtaining exact goodness-of-fit tests for certain parametric NHPPs, using a method based on Monte Carlo simulation conditional on sufficient statistics. A closely related way of obtaining exact confidence intervals in parametri...
متن کاملBayesian inference for multivariate point processes observed at sparsely distributed times
We consider statistical and computational aspects of simulation-based Bayesian inference for a multivariate point process which is only observed at sparsely distributed times. For specificity we consider a particular data set which has earlier been analyzed by a discrete time model involving unknown normalizing constants. We discuss the advantages and disadvantages of using continuous time proc...
متن کاملDeterminantal point process models and statistical inference
Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of repulsive spatial point processes, particularly in the ‘soft-core’ case. Such data are usually modelled by Gibbs point processes, where the likelihood and moment expressions are intractable and simulations are time consuming. We e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999