Marked Point Process Model Research Articles

A stochastic marked point process model for earthquakes

Abstract. A simplified stochastic model for earthquake occurrence focusing on the spatio-temporal interactions between earthquakes is presented. The model is a marked point process model in which each earthquake is represented by its magnitude and coordinates in space and time. The model incorporates the occurrence of aftershocks as well as the build-up and subsequent release of strain. The parameters of the model are estimated from a maximum likelihood calculation.

A Marked Point Process Model for the Source Proximity Effect in the Indoor Environment

In indoor air quality studies, discrepancies between personal and stationary indoor air quality monitors arise because of the source proximity effect, in which pollutant sources near the respondent cause elevated and highly variable exposures. In a set of experiments in a home, concentrations of a continuously emitting tracer gas were simultaneously monitored at different distances from the tracer gas source. Concentration time series are modeled at collinear monitoring sites as the sum of a slowly varying baseline time series and the superposition of transient elevated concentrations, or “microplumes.” Microplume arrivals appear as pulses in the time series, with pulse magnitudes and duration varying by location relative to the source. A nonparametric method is developed to estimate the time-varying parameters of the baseline time series. Parameters of superposed microplumes are estimated using the method of moments. Bias and sampling error of estimates are investigated using a simulation study. Estimates of superposition model parameters provide insight into the physical reasons behind the source proximity effect as well as a description of components of exposure at different distances from an emitting source.

A NONLINEAR FILTERING APPROACH TO VOLATILITY ESTIMATION WITH A VIEW TOWARDS HIGH FREQUENCY DATA

In this paper we consider a nonlinear filtering approach to the estimation of asset price volatility. We are particularly interested in models which are suitable for high frequency data. In order to describe some of the typical features of high frequency data we consider marked point process models for the asset price dynamics. Both jump-intensity and jump-size distribution of this marked point process depend on a hidden state variable which is closely related to asset price volatility. In our setup volatility estimation can therefore be viewed as a nonlinear filtering problem with marked point process observations. We develop efficient recursive methods to compute approximations to the conditional distribution of this state variable using the so-called reference probability approach to nonlinear filtering.

An integrated approach to human reliability analysis — decision analytic dynamic reliability model

Abstract The reliability of human operators in process control is sensitive to the context. In many contemporary human reliability analysis (HRA) methods, this is not sufficiently taken into account. The aim of this article is that integration between probabilistic and psychological approaches in human reliability should be attempted. This is achieved first, by adopting such methods that adequately reflect the essential features of the process control activity, and secondly, by carrying out an interactive HRA process. Description of the activity context, probabilistic modeling, and psychological analysis form an iterative interdisciplinary sequence of analysis in which the results of one sub-task maybe input to another. The analysis of the context is carried out first with the help of a common set of conceptual tools. The resulting descriptions of the context promote the probabilistic modeling, through which new results regarding the probabilistic dynamics can be achieved. These can be incorporated in the context descriptions used as reference in the psychological analysis of actual performance. The results also provide new knowledge of the constraints of activity, by providing information of the premises of the operator’s actions. Finally, the stochastic marked point process model gives a tool, by which psychological methodology may be interpreted and utilized for reliability analysis.

Temporal modelling of short-term rainfall using Cox processes

We study two marked point process models based on the Cox process. These models are used to describe the probabilistic structure of the rainfall intensity process. Mathematical formulation of the models is described and some second-moment characteristics of the rainfall depth, and aggregated processes are considered. The derived second-order properties of the accumulated rainfall amounts at different levels of aggregation are used in order to examine the model fit. A brief data analysis is presented. Copyright © 1998 John Wiley & Sons, Ltd.

Temporal modelling of short‐term rainfall using Cox processes

We study two marked point process models based on the Cox process. These models are used to describe the probabilistic structure of the rainfall intensity process. Mathematical formulation of the models is described and some second-moment characteristics of the rainfall depth, and aggregated processes are considered. The derived second-order properties of the accumulated rainfall amounts at different levels of aggregation are used in order to examine the model fit. A brief data analysis is presented. Copyright © 1998 John Wiley & Sons, Ltd.

Bayesian object recognition with baddeley's delta loss

A common problem in Bayesian object recognition using marked point process models is to produce a point estimate of the true underlying object configuration: the number of objects and the size, location and shape of each object. We use decision theory and the concept of loss functions to design a more reasonable estimator for this purpose, rather than using the common zero-one loss corresponding to the maximum a posteriori estimator. We propose to use the squared Δ-metric of Baddeley (1992) as our loss function and demonstrate that the corresponding optimal Bayesian estimator can be well approximated by combining Markov chain Monte Carlo methods with simulated annealing into a two-step algorithm. The proposed loss function is tested using a marked point process model developed for locating cells in confocal microscopy images.

Bayesian object recognition with baddeley's delta loss

A common problem in Bayesian object recognition using marked point process models is to produce a point estimate of the true underlying object configuration: the number of objects and the size, location and shape of each object. We use decision theory and the concept of loss functions to design a more reasonable estimator for this purpose, rather than using the common zero-one loss corresponding to the maximum a posteriori estimator. We propose to use the squared Δ-metric of Baddeley (1992) as our loss function and demonstrate that the corresponding optimal Bayesian estimator can be well approximated by combining Markov chain Monte Carlo methods with simulated annealing into a two-step algorithm. The proposed loss function is tested using a marked point process model developed for locating cells in confocal microscopy images.

Marked Point Process Models of Raindrop-Size Distributions

The principal process considered in this paper is the flux of raindrops through a volume of the atmosphere. This process is of fundamental importance for a wide variety of engineering and environmental problems, notably remote sensing of precipitation, infiltration of rainfall, soil erosion, atmospheric deposition of pollutants, and design of microwave communication systems. A marked point process model is developed in which the point process represents the arrival times of drops at the upper surface of a sample volume and the mark associated with a drop is its diameter. In the model, both the rate of occurrence of raindrops and the distribution of drop diameters vary randomly over time. Results that relate the drop-size distribution within the sample volume to the probability law of the drop-arrival process are presented. These results allow straightforward comparisons between temporal characterizations of drop-size distributions and spatial characterizations. Representations for derived processes such as rainfall rate and reflectivity are shown to be quite accurate using raindrop data from North Carolina.

Sedimentology and Shale Modeling of a Sandstone-Rich Fluvial Reservoir: Upper Statfjord Formation, Statfjord Field, Northern North Sea

Sandstone-rich fluvial reservoirs of the upper part of the Statfjord Formation in Statfjord field, northern North Sea, include significant proportions of interstratified shale beds which complicate the production of oil under a high-pressure miscible gas flood. Flood-plain mudstones, characterized by pedogenic alteration, and finely laminated abandoned channel facies form the most important flow barriers. Mudstones deposited in flood plains are expected to have a greater lateral continuity than those deposited in abandoned channels. Fluctuations in allogenic factors such as base level and sediment-supply rates have led to a variable preservation of the mudstones. This combination of different facies types and fluctuating allogenic control has led to a complex barrier dist ibution within the reservoir which is difficult to describe using conventional mapping techniques. A procedure, based on two stochastic simulation techniques, has been adopted in order to model the complex barrier distribution. A two-dimensional Markov field model is used as an alternative to conventional shale mapping to describe the distribution of shale beds that are correlated between two or more wells. The model is based on probabilistic estimations of shale continuity between well pairs and allows the simulation of local channel incision through otherwise extensive shale beds. A marked-point process model is adopted to describe the distribution of smaller scale discontinuous barriers within the reservoir sand bodies. It is based on probabilistic estimations of shale dimensions defined using cumulative frequency distributions. The stochastic modeling procedure allows greater flexibility to include a variety of geological interpretations and assumptions in the heterogeneity model, and the increased geological input results in more realistic models of communication between and vertical permeability within the reservoir sand bodies.

A novel method for assessing position-sensitive detector performance

A marked-point process model of a position-sensitive detector is developed which includes the effects of detector efficiency, spatial response, energy response, and source statistics. The average mutual information between the incident distribution of gamma -rays and the detector response is derived and used as a performance index of detector optimization. A brief example is presented which uses this figure-of-merit for optimization of light-guide dimensions for the SPRINT IT modular scintillation camera. >

Stochastic Analysis of Precipitation Series by Means of Marked Point Process Model

Stochastic Analysis of Precipitation Series by Means of Marked Point Process Model

Multivariate point process models for response times in multiprogrammed systems

We consider the formulation of marked multivariate point process models for job response times in multiprogrammed computer systems. Complementing queueing network representation of the structure of the system to be modeled, the particularR-process (Response time process) model we propose permits representation of resource contention, facilitates the incorporation of realistic workload characteristics into system performance predictions, and can reproduce inhomogeneities observed in running systems. Specification of the structure of theR-process model is conditional on workload marks; this effectively separates the difficult problem of formal representation of workload characteristics from the overall problem of response time prediction. To illustrate these ideas, an application to database management systems is considered. Evidence of the predictive capability of theR-process model, based on statistical analysis of response time data from an IMS system, is also given.