Search results for "Dual analysis"

showing 3 items of 13 documents

Local inhomogeneous second-order characteristics for spatio-temporal point processes occurring on linear networks

2022

AbstractPoint processes on linear networks are increasingly being considered to analyse events occurring on particular network-based structures. In this paper, we extend Local Indicators of Spatio-Temporal Association (LISTA) functions to the non-Euclidean space of linear networks, allowing to obtain information on how events relate to nearby events. In particular, we propose the local version of two inhomogeneous second-order statistics for spatio-temporal point processes on linear networks, the K- and the pair correlation functions. We put particular emphasis on the local K-functions, deriving come theoretical results which enable us to show that these LISTA functions are useful for diagn…

Statistics and ProbabilityLocal Indicators of Spatio-Temporal Associationlocal propertiessecond-order characteristicsresidual analysislinear networksspatio-temporal point patternsStatistics Probability and UncertaintySettore SECS-S/01 - StatisticaLinear networks Local Indicators of Spatio-temporal Association Local properties Residual analysis Second-order characteristics Spatio-temporal point patterns
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Point process diagnostics based on weighted second-order statistics and their asymptotic properties

2008

A new approach for point process diagnostics is presented. The method is based on extending second-order statistics for point processes by weighting each point by the inverse of the conditional intensity function at the point’s location. The result is generalized versions of the spectral density, R/S statistic, correlation integral and K-function, which can be used to test the fit of a complex point process model with an arbitrary conditional intensity function, rather than a stationary Poisson model. Asymptotic properties of these generalized second-order statistics are derived, using an approach based on martingale theory.

Statistics and ProbabilityMathematical optimizationSpectral densityInverseResidual analysis point process second-order analysis conditional intensity functionResidualPoint processWeightingCorrelation integralApplied mathematicsPoint (geometry)Settore SECS-S/01 - StatisticaStatisticMathematicsAnnals of the Institute of Statistical Mathematics
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GAMLSS for high-variability data: an application to liver fibrosis case

2020

In this paper, we propose management of the problem caused by overdispersed data by applying the generalized additive model for location, scale and shape framework (GAMLSS) as introduced by Rigby and Stasinopoulos (2005). The idea of using a GAMLSS approach for handling our problem comes from the idea of Aitkin (1996) consisting in the use of an EM maximum likelihood estimation algorithm (Dempster, Laird, and Rubin, 1977) to deal with overdispersed generalized linear models (GLM). As in the GLM case, the algorithm is initially derived as a form of Gaussian quadrature assuming a normal mixing distribution. The GAMLSS specification allows the extension of the Aitkin algorithm to probability d…

Statistics and Probabilitymixture models worm plot residual analysis liver diseasesScale (ratio)Generalized additive modelliver diseases mixture models residual analysis worm plotStatistical modelProbability and statisticsGeneral MedicineVariance (accounting)ResidualMixture model01 natural sciences030218 nuclear medicine & medical imaging010104 statistics & probability03 medical and health sciences0302 clinical medicineOverdispersionEconometrics0101 mathematicsStatistics Probability and UncertaintyThe International Journal of Biostatistics
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