Statistical inference for point-process models of rainfall

1984 ◽  
Vol 16 (1) ◽  
pp. 22-22 ◽  
Author(s):  
James A. Smtih ◽  
Alan F. Karr
Keyword(s):  
Parameter Estimation ◽  
Statistical Inference ◽  
Point Processes ◽  
Process Models ◽  
Renewal Processes ◽  
Cox Processes ◽  
The Family ◽  
Point Process Models ◽  
Image Position ◽  
Rainfall Occurrences

In this paper we develop maximum likelihood procedures for parameter estimation and hypothesis testing for three classes of point processes that have been used to model rainfall occurrences; renewal processes, Neyman-Scott processes, and RCM processes (which are members of the family of Cox processes). The statistical inference procedures developed in this paper are based on the intensity process

scholarly journals MODELLING THE POSITION OF CELL PROFILES ALLOWING FOR BOTH INHOMOGENEITY AND INTERACTION

2011 ◽  
Vol 19 (3) ◽  
pp. 183 ◽  
Author(s):  
Linda Stougaard Nielsen
Keyword(s):  
Point Process ◽  
Mucous Membrane ◽  
Point Processes ◽  
Point Interaction ◽  
Process Models ◽  
Markov Point Processes ◽  
Point Process Models

It is of interest to consider models for point processes that allow for interaction between the points as well as for inhomogeneity in the intensity of the points. Markov point process models are very useful to describe point interaction and can also be used to describe inhomogeneity. A particular type of inhomogeneous Markov point processes obtained by transforming a homogeneous Markov point process will be considered. The position of cell proles in a 2D section of the mucous membrane in the stomach of a rat will be examined using this model.

scholarly journals INHOMOGENEITY IN SPATIAL COX POINT PROCESSES – LOCATION DEPENDENT THINNING IS NOT THE ONLY OPTION

2010 ◽  
Vol 29 (3) ◽  
pp. 133 ◽  
Author(s):  
Michaela Prokešová
Keyword(s):  
Point Process ◽  
Process Model ◽  
Point Processes ◽  
Homogeneous Model ◽  
Process Models ◽  
Point Patterns ◽  
Estimation Procedures ◽  
Markov Point Processes ◽  
Stationary Point Process ◽  
Point Process Models

In the literature on point processes the by far most popular option for introducing inhomogeneity into a point process model is the location dependent thinning (resulting in a second-order intensity-reweighted stationary point process). This produces a very tractable model and there are several fast estimation procedures available. Nevertheless, this model dilutes the interaction (or the geometrical structure) of the original homogeneous model in a special way. When concerning the Markov point processes several alternative inhomogeneous models were suggested and investigated in the literature. But it is not so for the Cox point processes, the canonical models for clustered point patterns. In the contribution we discuss several other options how to define inhomogeneous Cox point process models that result in point patterns with different types of geometric structure. We further investigate the possible parameter estimation procedures for such models.

Multivariate dependent renewal processes

1984 ◽  
Vol 16 (02) ◽  
pp. 347-362
Author(s):  
Eric Slud
Keyword(s):  
Asymptotic Behavior ◽  
Data Analysis ◽  
Survival Data ◽  
Process Models ◽  
Partial Likelihood ◽  
Renewal Processes ◽  
Likelihood Methods ◽  
New Class ◽  
New Models ◽  
Point Process Models

A new class of reliability point-process models for dependent components is introduced. The dependence is expressed through a regression, following a form suggested by Cox (1972) for survival data analysis involving the current life-length of the components. After formulating the current-life process as a Markov process with stationary transitions and stating some general results on asymptotic behavior, we describe the stationary distributions in some bivariate examples. Finally, we discuss statistical inference for the new models, exhibiting and justifying full- and partial-likelihood methods for their analysis.

A Computationally Efficient Method for Nonparametric Modeling of Neural Spiking Activity with Point Processes

2010 ◽  
Vol 22 (8) ◽  
pp. 2002-2030 ◽  
Author(s):  
Todd P. Coleman ◽  
Sridevi S. Sarma
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Intensity Function ◽  
Process Models ◽  
Conditional Intensity ◽  
Computationally Efficient ◽  
Neural Data ◽  
Neural Spiking ◽  
Point Process Models ◽  
Conditional Intensity Function

Point-process models have been shown to be useful in characterizing neural spiking activity as a function of extrinsic and intrinsic factors. Most point-process models of neural activity are parametric, as they are often efficiently computable. However, if the actual point process does not lie in the assumed parametric class of functions, misleading inferences can arise. Nonparametric methods are attractive due to fewer assumptions, but computation in general grows with the size of the data. We propose a computationally efficient method for nonparametric maximum likelihood estimation when the conditional intensity function, which characterizes the point process in its entirety, is assumed to be a Lipschitz continuous function but otherwise arbitrary. We show that by exploiting much structure, the problem becomes efficiently solvable. We next demonstrate a model selection procedure to estimate the Lipshitz parameter from data, akin to the minimum description length principle and demonstrate consistency of our estimator under appropriate assumptions. Finally, we illustrate the effectiveness of our method with simulated neural spiking data, goldfish retinal ganglion neural data, and activity recorded in CA1 hippocampal neurons from an awake behaving rat. For the simulated data set, our method uncovers a more compact representation of the conditional intensity function when it exists. For the goldfish and rat neural data sets, we show that our nonparametric method gives a superior absolute goodness-of-fit measure used for point processes than the most common parametric and splines-based approaches.

Multivariate dependent renewal processes

1984 ◽  
Vol 16 (2) ◽  
pp. 347-362 ◽  
Author(s):  
Eric Slud
Keyword(s):  
Asymptotic Behavior ◽  
Data Analysis ◽  
Survival Data ◽  
Process Models ◽  
Partial Likelihood ◽  
Renewal Processes ◽  
Likelihood Methods ◽  
New Class ◽  
New Models ◽  
Point Process Models

A new class of reliability point-process models for dependent components is introduced. The dependence is expressed through a regression, following a form suggested by Cox (1972) for survival data analysis involving the current life-length of the components. After formulating the current-life process as a Markov process with stationary transitions and stating some general results on asymptotic behavior, we describe the stationary distributions in some bivariate examples. Finally, we discuss statistical inference for the new models, exhibiting and justifying full- and partial-likelihood methods for their analysis.

SEGMENTED POINT PROCESS MODELS FOR MAINTAINED SYSTEMS

2007 ◽  
Vol 14 (05) ◽  
pp. 431-458 ◽  
Author(s):  
A. SYAMSUNDAR ◽  
V. N. A. NAIKAN
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Point Processes ◽  
Single Point ◽  
Process Models ◽  
Parameter Estimates ◽  
Minimal Repair ◽  
Homogeneous Poisson Process ◽  
Stable Conditions ◽  
Point Process Models

A maintained system is generally modeled using point processes. The most common processes used are the renewal process and the non homogeneous Poisson process corresponding to maximal and minimal repair situations with homogeneous Poisson process being a special case of both. A general repair formulation with a factor indicating the degree of repair is introduced into the minimal repair model to form an Arithmetic Reduction of Intensity model. These processes are generally able to model maintained systems with a fair degree of accuracy when the system is operating under stable conditions. However whenever there is a change in the environment these models which are monotonic in nature are not able to accommodate this change. Such systems operating under different environments need to be modelled by segmented models with the system domain divided into segments at the points of changes in the environment. The individual segments can then be modeled by any of the above point process models and these can be combined to form a composite model. This paper proposes a statistical model of such an operating/maintenance environment. Its purpose is to quantify the impacts of changes in the environment on the failure intensities. Field data from an industrial-setting demonstrate that appropriate parameter estimates for such phenomena can be obtained and such models are shown to more accurately describe the maintained system in a changing environment than the single point process models usually used.

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