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

2008 ◽  
Vol 2 (0) ◽  
pp. 234-264 ◽  
Author(s):  
Jean-Michel Billiot ◽  
Jean-François Coeurjolly ◽  
Rémy Drouilhet
Keyword(s):  
Exponential Family ◽  
Point Processes ◽  
Gibbs Point Processes ◽  
Maximum Pseudolikelihood ◽  
Family Models

scholarly journals Existence of Gibbs point processes with stable infinite range interaction

2020 ◽  
Vol 57 (3) ◽  
pp. 775-791
Author(s):  
David Dereudre ◽  
Thibaut Vasseur
Keyword(s):  
Point Processes ◽  
Existence Results ◽  
Pairwise Interaction ◽  
Range Interaction ◽  
Pairwise Interactions ◽  
Gibbs Point Processes ◽  
Infinite Range Interactions ◽  
Finite Configuration ◽  
Multi Body ◽  
Infinite Range

AbstractWe provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability assumption, which means that the energy of any finite configuration is superlinear with respect to the number of points. The second assumption is the so-called intensity regularity, which controls the long range of the interaction via the intensity of the process. This assumption is new and introduced here since it is well adapted to the entropy approach. As a corollary of our main result we improve the existence results by Ruelle (1970) for pairwise interactions by relaxing the superstabilty assumption. Note that our setting is not reduced to pairwise interaction and can contain infinite-range multi-body counterparts.

scholarly journals Fast approximation of the intensity of Gibbs point processes

2012 ◽  
Vol 6 (0) ◽  
pp. 1155-1169 ◽  
Author(s):  
Adrian Baddeley ◽  
Gopalan Nair
Keyword(s):  
Point Processes ◽  
Gibbs Point Processes

scholarly journals Nonstandard conditionally specified models for nonignorable missing data

2020 ◽  
Vol 117 (32) ◽  
pp. 19045-19053
Author(s):  
Alexander M. Franks ◽  
Edoardo M. Airoldi ◽  
Donald B. Rubin
Keyword(s):  
Systems Biology ◽  
Missing Data ◽  
Joint Distribution ◽  
Exponential Family ◽  
Nonignorable Missing Data ◽  
Data Analyses ◽  
Missingness Mechanism ◽  
Conditionally Specified Models ◽  
Nonignorable Missing ◽  
Family Models

Data analyses typically rely upon assumptions about the missingness mechanisms that lead to observed versus missing data, assumptions that are typically unassessable. We explore an approach where the joint distribution of observed data and missing data are specified in a nonstandard way. In this formulation, which traces back to a representation of the joint distribution of the data and missingness mechanism, apparently first proposed by J. W. Tukey, the modeling assumptions about the distributions are either assessable or are designed to allow relatively easy incorporation of substantive knowledge about the problem at hand, thereby offering a possibly realistic portrayal of the data, both observed and missing. We develop Tukey’s representation for exponential-family models, propose a computationally tractable approach to inference in this class of models, and offer some general theoretical comments. We then illustrate the utility of this approach with an example in systems biology.

scholarly journals Variational Inference over Nonstationary Data Streams for Exponential Family Models

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1942
Author(s):  
Andrés R. Masegosa ◽  
Darío Ramos-López ◽  
Antonio Salmerón ◽  
Helge Langseth ◽  
Thomas D. Nielsen
Keyword(s):  
Bayesian Inference ◽  
Variational Methods ◽  
Latent Variables ◽  
Exponential Family ◽  
Concept Drift ◽  
Variational Inference ◽  
Model Parameters ◽  
Time Step ◽  
Data Set ◽  
Family Models

In many modern data analysis problems, the available data is not static but, instead, comes in a streaming fashion. Performing Bayesian inference on a data stream is challenging for several reasons. First, it requires continuous model updating and the ability to handle a posterior distribution conditioned on an unbounded data set. Secondly, the underlying data distribution may drift from one time step to another, and the classic i.i.d. (independent and identically distributed), or data exchangeability assumption does not hold anymore. In this paper, we present an approximate Bayesian inference approach using variational methods that addresses these issues for conjugate exponential family models with latent variables. Our proposal makes use of a novel scheme based on hierarchical priors to explicitly model temporal changes of the model parameters. We show how this approach induces an exponential forgetting mechanism with adaptive forgetting rates. The method is able to capture the smoothness of the concept drift, ranging from no drift to abrupt drift. The proposed variational inference scheme maintains the computational efficiency of variational methods over conjugate models, which is critical in streaming settings. The approach is validated on four different domains (energy, finance, geolocation, and text) using four real-world data sets.

Bartlett corrections for one-parameter exponential family models

1995 ◽  
Vol 53 (3-4) ◽  
pp. 211-231 ◽  
Author(s):  
Gauss M. Cordeiro ◽  
Franciso. Cribari-Neto ◽  
Elisete C. Q. Aubin ◽  
Silvia L. P. Ferrari
Keyword(s):  
Exponential Family ◽  
Family Models
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