scholarly journals Gibbs Point Process Model for Young Star Clusters in M33

2020 ◽  
Author(s):  
Dayi Li ◽  
Pauline Barmby
Keyword(s):  
Point Process ◽  
Process Model ◽  
Function Analysis ◽  
Cluster Formation ◽  
Process Models ◽  
Spatial Distributions ◽  
Galactocentric Distance ◽  
Stellar Cluster ◽  
Positive Effects ◽  
Gibbs Point Process

Abstract We demonstrate the power of Gibbs point process models from the spatial statistics literature when applied to studies of resolved galaxies. We conduct a rigorous analysis of the spatial distributions of objects in the star formation complexes of M33, including giant molecular clouds (GMCs) and young stellar cluster candidates (YSCCs). We choose a hierarchical model structure from GMCs to YSCCs based on the natural formation hierarchy between them. This approach circumvents the limitations of the empirical two-point correlation function analysis by naturally accounting for the inhomogeneity present in the distribution of YSCCs. We also investigate the effects of GMCs’ properties on their spatial distributions. We confirm that the distribution of GMCs and YSCCs are highly correlated. We found that the spatial distributions of YSCCs reaches a peak of clustering pattern at ∼250 pc scale compared to a Poisson process. This clustering mainly occurs in regions where the galactocentric distance ≳ 4.5 kpc. Furthermore, the galactocentric distance of GMCs and their mass have strong positive effects on the correlation strength between GMCs and YSCCs. We outline some possible implications of these findings for our understanding of the cluster formation process.

Gibbs point process models with mixed effects

2009 ◽  
Vol 21 (3-4) ◽  
pp. 341-353 ◽  
Author(s):  
Janine B. Illian ◽  
Ditte K. Hendrichsen
Keyword(s):  
Point Process ◽  
Mixed Effects ◽  
Process Models ◽  
Gibbs Point Process ◽  
Point Process Models

Bayesian object recognition with baddeley's delta loss

1998 ◽  
Vol 30 (1) ◽  
pp. 64-84 ◽  
Author(s):  
Håvard Rue ◽  
Anne Randi Syversveen
Keyword(s):  
Object Recognition ◽  
Point Process ◽  
Loss Function ◽  
Process Model ◽  
Marked Point ◽  
Process Models ◽  
Bayesian Estimator ◽  
Marked Point Process ◽  
Point Estimate ◽  
Step Algorithm

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.

Self-exciting point process models for political conflict forecasting

2017 ◽  
Vol 29 (4) ◽  
pp. 685-707 ◽  
Author(s):  
N. JOHNSON ◽  
A. HITCHMAN ◽  
D. PHAN ◽  
L. SMITH
Keyword(s):  
Point Process ◽  
Early Warning ◽  
Early Warning System ◽  
Process Model ◽  
Warning System ◽  
Political Conflict ◽  
Process Models ◽  
Hawkes Process ◽  
Point Process Models ◽  
Using Data

In 2008, the Defense Advanced Research Project Agency commissioned a database known as the Integrated Crisis Early Warning System to serve as the foundation for models capable of detecting and predicting increases in political conflict worldwide. Such models, by signalling expected increases in political conflict, would help inform and prepare policymakers to react accordingly to conflict proliferation both domestically and internationally. Using data from the Integrated Crisis Early Warning System, we construct and test a self-exciting point process, or Hawkes process, model to describe and predict amounts of domestic, political conflict; we focus on Colombia and Venezuela as examples for this model. By comparing the accuracy of fitted models to the observed data, we find that we are able to closely describe occurrences of conflict in each country. Thus, using this model can allow policymakers to anticipate relative increases in the amount of domestic political conflict following major events.

scholarly journals Point Process Models for the Spread of Coccidioidomycosis in California

2021 ◽  
Vol 13 (2) ◽  
pp. 558-570
Author(s):  
Jiajia Wang ◽  
Ryan J. Harrigan ◽  
Frederic P. Schoenberg
Keyword(s):  
Public Health ◽  
Infectious Disease ◽  
United States ◽  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Process Models ◽  
Squared Error ◽  
Point Process Models

Coccidioidomycosis is an infectious disease of humans and other mammals that has seen a recent increase in occurrence in the southwestern United States, particularly in California. A rise in cases and risk to public health can serve as the impetus to apply newly developed methods that can quickly and accurately predict future caseloads. The recursive and Hawkes point process models with various triggering functions were fit to the data and their goodness of fit evaluated and compared. Although the point process models were largely similar in their fit to the data, the recursive point process model offered a slightly superior fit. We explored forecasting the spread of coccidioidomycosis in California from December 2002 to December 2017 using this recursive model, and we separated the training and testing portions of the data and achieved a root mean squared error of just 3.62 cases/week.

scholarly journals Hybrids of Gibbs Point Process Models and Their Implementation

2013 ◽  
Vol 55 (11) ◽  
Author(s):  
Adrian Baddeley ◽  
Rolf Turner ◽  
Jorge Mateu ◽  
Andrew Bevan
Keyword(s):  
Point Process ◽  
Process Models ◽  
Gibbs Point Process ◽  
Point Process Models

Penalized composite likelihoods for inhomogeneous Gibbs point process models

2018 ◽  
Vol 124 ◽  
pp. 104-116
Author(s):  
Jeffrey Daniel ◽  
Julie Horrocks ◽  
Gary J. Umphrey
Keyword(s):  
Point Process ◽  
Process Models ◽  
Gibbs Point Process ◽  
Point Process Models

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.

scholarly journals Variational estimators for the parameters of Gibbs point process models

Bernoulli ◽  
2013 ◽  
Vol 19 (3) ◽  
pp. 905-930 ◽  
Author(s):  
Adrian Baddeley ◽  
David Dereudre
Keyword(s):  
Point Process ◽  
Process Models ◽  
Gibbs Point Process ◽  
Point Process Models

scholarly journals Computing Confidence Intervals for Point Process Models

2011 ◽  
Vol 23 (11) ◽  
pp. 2731-2745 ◽  
Author(s):  
Sridevi V. Sarma ◽  
David P. Nguyen ◽  
Gabriela Czanner ◽  
Sylvia Wirth ◽  
Matthew A. Wilson ◽  
...  
Keyword(s):  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Parametric Bootstrap ◽  
Process Models ◽  
Model Parameters ◽  
Bootstrap Sampling ◽  
Confidence Bounds ◽  
Extrinsic Factors ◽  
Point Process Models

Characterizing neural spiking activity as a function of intrinsic and extrinsic factors is important in neuroscience. Point process models are valuable for capturing such information; however, the process of fully applying these models is not always obvious. A complete model application has four broad steps: specification of the model, estimation of model parameters given observed data, verification of the model using goodness of fit, and characterization of the model using confidence bounds. Of these steps, only the first three have been applied widely in the literature, suggesting the need to dedicate a discussion to how the time-rescaling theorem, in combination with parametric bootstrap sampling, can be generally used to compute confidence bounds of point process models. In our first example, we use a generalized linear model of spiking propensity to demonstrate that confidence bounds derived from bootstrap simulations are consistent with those computed from closed-form analytic solutions. In our second example, we consider an adaptive point process model of hippocampal place field plasticity for which no analytical confidence bounds can be derived. We demonstrate how to simulate bootstrap samples from adaptive point process models, how to use these samples to generate confidence bounds, and how to statistically test the hypothesis that neural representations at two time points are significantly different. These examples have been designed as useful guides for performing scientific inference based on point process models.

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