Investigating mesh‐based approximation methods for the normalization constant in the log Gaussian Cox process likelihood

Stat ◽  
2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Martin Jullum
Keyword(s):  
Approximation Methods ◽  
Cox Process ◽  
Normalization Constant ◽  
Log Gaussian Cox Process

scholarly journals Bayesian log‐Gaussian Cox process regression: applications to meta‐analysis of neuroimaging working memory studies

2018 ◽  
Vol 68 (1) ◽  
pp. 217-234 ◽  
Author(s):  
Pantelis Samartsidis ◽  
Claudia R. Eickhoff ◽  
Simon B. Eickhoff ◽  
Tor D. Wager ◽  
Lisa Feldman Barrett ◽  
...  
Keyword(s):  
Working Memory ◽  
Meta Analysis ◽  
Memory Studies ◽  
Cox Process ◽  
Log Gaussian Cox Process

scholarly journals Hierarchical log Gaussian Cox process for regeneration in uneven-aged forests

2021 ◽  
Author(s):  
Mikko Kuronen ◽  
Aila Särkkä ◽  
Matti Vihola ◽  
Mari Myllymäki
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Gaussian Field ◽  
Cox Process ◽  
Observation Window ◽  
Point Patterns ◽  
Proposed Model ◽  
Large Trees ◽  
Log Gaussian Cox Process ◽  
Set Of Points

AbstractWe propose a hierarchical log Gaussian Cox process (LGCP) for point patterns, where a set of points $$\varvec{x}$$ x affects another set of points $$\varvec{y}$$ y but not vice versa. We use the model to investigate the effect of large trees on the locations of seedlings. In the model, every point in $$\varvec{x}$$ x has a parametric influence kernel or signal, which together form an influence field. Conditionally on the parameters, the influence field acts as a spatial covariate in the intensity of the model, and the intensity itself is a non-linear function of the parameters. Points outside the observation window may affect the influence field inside the window. We propose an edge correction to account for this missing data. The parameters of the model are estimated in a Bayesian framework using Markov chain Monte Carlo where a Laplace approximation is used for the Gaussian field of the LGCP model. The proposed model is used to analyze the effect of large trees on the success of regeneration in uneven-aged forest stands in Finland.

Algorithmically deconstructing shot locations as a method for shot quality in hockey

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Devan G. Becker ◽  
Douglas G. Woolford ◽  
Charmaine B. Dean
Keyword(s):  
Point Process ◽  
Process Model ◽  
Point Processes ◽  
Learning Algorithm ◽  
Basis Functions ◽  
Cox Process ◽  
Spatial Point Processes ◽  
Professional Basketball ◽  
Spatial Point ◽  
Log Gaussian Cox Process

AbstractSpatial point processes have been successfully used to model the relative efficiency of shot locations for each player in professional basketball games. Those analyses were possible because each player makes enough baskets to reliably fit a point process model. Goals in hockey are rare enough that a point process cannot be fit to each player’s goal locations, so novel techniques are needed to obtain measures of shot efficiency for each player. A Log-Gaussian Cox Process (LGCP) is used to model all shot locations, including goals, of each NHL player who took at least 500 shots during the 2011–2018 seasons. Each player’s LGCP surface is treated as an image and these images are then used in an unsupervised statistical learning algorithm that decomposes the pictures into a linear combination of spatial basis functions. The coefficients of these basis functions are shown to be a very useful tool to compare players. To incorporate goals, the locations of all shots that resulted in a goal are treated as a “perfect player” and used in the same algorithm (goals are further split into perfect forwards, perfect centres and perfect defence). These perfect players are compared to other players as a measure of shot efficiency. This analysis provides a map of common shooting locations, identifies regions with the most goals relative to the number of shots and demonstrates how each player’s shot location differs from scoring locations.

scholarly journals How does the community COVID-19 level of risk impact on that of a care home?

PLoS ONE ◽  
2021 ◽  
Vol 16 (12) ◽  
pp. e0260051
Author(s):  
Glenna Nightingale ◽  
Megan Laxton ◽  
Janine B. Illian
Keyword(s):  
Care Home ◽  
Community Level ◽  
Process Models ◽  
Care Homes ◽  
Cox Process ◽  
Two Stage ◽  
Modeling Process ◽  
Community Risk ◽  
Log Gaussian Cox Process ◽  
The Impact

Objectives To model the risk of COVID-19 mortality in British care homes conditional on the community level risk. Methods A two stage modeling process (“doubly latent”) which includes a Besag York Mollie model (BYM) and a Log Gaussian Cox Process. The BYM is adopted so as to estimate the community level risks. These are incorporated in the Log Gaussian Cox Process to estimate the impact of these risks on that in care homes. Results For an increase in the risk at the community level, the number of COVID-19 related deaths in the associated care home would be increased by exp (0.833), 2. This is based on a simulated dataset. In the context of COVID-19 related deaths, this study has illustrated the estimation of the risk to care homes in the presence of background community risk. This approach will be useful in facilitating the identification of the most vulnerable care homes and in predicting risk to new care homes. Conclusions The modeling of two latent processes have been shown to be successfully facilitated by the use of the BYM and Log Gaussian Cox Process Models. Community COVID-19 risks impact on that of the care homes embedded in these communities.

scholarly journals Tornado Occurrences in the United States: A Spatio-Temporal Point Process Approach

Econometrics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 25
Author(s):  
Fernanda Valente ◽  
Márcio Laurini
Keyword(s):  
United States ◽  
Point Process ◽  
Temporal Distribution ◽  
The United States ◽  
Cox Process ◽  
Spatial Effects ◽  
Dynamic Representation ◽  
Log Gaussian Cox Process ◽  
Spatio Temporal ◽  
Unites States

In this paper, we analyze the tornado occurrences in the Unites States. To perform inference procedures for the spatio-temporal point process we adopt a dynamic representation of Log-Gaussian Cox Process. This representation is based on the decomposition of intensity function in components of trend, cycles, and spatial effects. In this model, spatial effects are also represented by a dynamic functional structure, which allows analyzing the possible changes in the spatio-temporal distribution of the occurrence of tornadoes due to possible changes in climate patterns. The model was estimated using Bayesian inference through the Integrated Nested Laplace Approximations. We use data from the Storm Prediction Center’s Severe Weather Database between 1954 and 2018, and the results provided evidence, from new perspectives, that trends in annual tornado occurrences in the United States have remained relatively constant, supporting previously reported findings.

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