Maximum pseudolikelihood estimator for exponential family models of marked Gibbs point processes

Billiot, Jean-Michel; Coeurjolly, Jean‐François; Drouilhet, Rémy

doi:10.1214/07-ejs160

Cited by 33 publications

(68 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Billiot et al () extended the results in Jensen and Møller () and Jensen and K^^fcnsch () and obtained consistency and asymptotic normality of the MPLE for a large class of models including the examples presented in Section 2.2. We now state the central limit theorem for the MPLE.…”

Section: Gibbs Point Processes and Pseudo‐likelihoodmentioning

confidence: 83%

“…We point out that does not require the ergodicity of

P_{θ^{★}}

, and it therefore applies even if a phase transition occurs (see Jensen and K^^fcnsch ( for a proof of this). Furthermore, we refer to Billiot et al () for a proof of the positive definiteness of the matrix Σ for a large class of models (including the ones presented in this paper).…”

Section: Covariance Of Innovationsmentioning

confidence: 99%

See 1 more Smart Citation

Fast Covariance Estimation for Innovations Computed from a Spatial Gibbs Point Process

Coeurjolly

Rubak

2013

Scandinavian J Statistics

Self Cite

View full text Add to dashboard Cite

In this paper, we derive an exact formula for the covariance of two innovations computed from a spatial Gibbs point process and suggest a fast method for estimating this covariance. We show how this methodology can be used to estimate the asymptotic covariance matrix of the maximum pseudo‐likelihood estimator of the parameters of a spatial Gibbs point process model. This allows us to construct asymptotic confidence intervals for the parameters. We illustrate the efficiency of our procedure in a simulation study for several classical parametric models. The procedure is implemented in the statistical software R, and it is included in spatstat, which is an R package for analyzing spatial point patterns.

show abstract

Section: Gibbs Point Processes and Pseudo‐likelihoodmentioning

confidence: 83%

“…We point out that does not require the ergodicity of

P_{θ^{★}}

Section: Covariance Of Innovationsmentioning

confidence: 99%

Fast Covariance Estimation for Innovations Computed from a Spatial Gibbs Point Process

Coeurjolly

Rubak

2013

Scandinavian J Statistics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Its suitability to a wide range of Gibbs point processes has been recently proved by [Billiot et al 2008]. It admits a unique extremum in the (Γ, ∆) parameter space which we find using a Newton-Raphson approach.…”

Section: Interaction Strengths γ MM ′ and Category Occurrence Probabmentioning

confidence: 83%

Appearance-guided synthesis of element arrangements by example

Hurtut

Landes

Thollot

et al. 2009

Proceedings of the 7th International Symposium on Non-Photorealistic Animation and Rendering

View full text Add to dashboard Cite

Figure 1: Given a reference arrangement composed of vector elements (top left), our analysis scheme divides the raw element set into appearance categories (bottom left). Spatial interactions based on appearance can be learned by statistical modeling and exploited to yield visually similar arrangements (right). AbstractWe present a technique for the analysis and re-synthesis of 2D arrangements of stroke-based vector elements. The capture of an artist's style by the sole posterior analysis of his/her achieved drawing poses a formidable challenge. Such by-example techniques could become one of the most intuitive tools for users to alleviate creation process efforts. Here, we propose to tackle this issue from a statistical point of view and take specific care of accounting for information usually overlooked in previous research, namely the elements' very appearance. Composed of curve-like strokes, we describe elements by a concise set of perceptually relevant features. After detecting appearance dominant traits, we can generate new arrangements that respect the captured appearance-related spatial statistics using multitype point processes. Our method faithfully reproduces visually similar arrangements and relies on neither heuristics nor post-processes to ensure statistical correctness.

show abstract

“…For instance, if X is the Strauss point process or the area interaction process, then the score function of the pseudo-likelihood which is one of the most well-known methods to estimate a parametric model (see e.g. Møller and Waagepetersen, 2007;Billiot et al, 2008) …”

Section: Resultsmentioning

confidence: 99%