Statistical Inference in Bernoulli Trials with Dependence

Klotz, Jerome

doi:10.1214/aos/1176342377

Cited by 105 publications

(67 citation statements)

References 7 publications

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“…However, this assumption breaks down as correlations will develop between the status of neighbouring nodes, as new infections are bound to be the neighbours of their infectors. [18]. This explanation makes it much easier to see which kinds of network structure are assumed during momemt closure, and how different closures are related to each other.…”

Section: Moment Closuresmentioning

confidence: 99%

From Markovian to pairwise epidemic models and the performance of moment closure approximations

et al. 2011

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Many if not all models of disease transmission on networks can be linked to the exact state-based Markovian formulation. However the large number of equations for any system of realistic size limits their applicability to small populations. As a result, most modelling work relies on simulation and pairwise models. In this paper, for a simple SIS dynamics on an arbitrary network, we formalise the link between a well known pairwise model and the exact Markovian formulation. This involves the rigorous derivation of the exact ODE model at the level of pairs in terms of the expected number of pairs and triples. The exact system is then closed using two different closures, one well established and one that has been recently proposed. A new interpretation of both closures is presented, which explains several of their previously observed properties. The closed dynamical systems are solved numerically and the results are compared to output from individual-based stochastic simulations. This is done for a range of networks with the same average degree and clustering coefficient but generated using different algorithms. It is shown that the ability of the pairwise system to accurately model an epidemic is fundamentally dependent on the underlying large-scale network structure. We show that the existing pairwise models are a good fit for certain types of network but have to be used with caution as higher-order network structures may compromise their effectiveness.

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Section: Moment Closuresmentioning

confidence: 99%

From Markovian to pairwise epidemic models and the performance of moment closure approximations

et al. 2011

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“…Clustering. To introduce clustering to the trials, we consider the method of Klotz [13] (and the parametrization of Lindqvist [14]) for generation of D m . In this construction, the n individuals canvassed have states fX i g i¼1, .…”

Section: Canvassing Methodsmentioning

confidence: 99%

Modelling behavioural contagion

House

2011

J. R. Soc. Interface.

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The last decade has seen much work on quantitative understanding of human behaviour, with online social interaction offering the possibility of more precise measurement of behavioural phenomena than was previously possible. A parsimonious model is proposed that incorporates several observed features of behavioural contagion not seen in existing epidemic model schemes, leading to metastable behavioural dynamics.

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“…In addition, f corresponds to the mean of Bernoulli trials with Markov dependence. From Klotz (1973), we have that √ n( f − f ) converges in distribution to a centered Gaussian model, and thus √ n( p (F) − p) by the Delta Method, as n → ∞. For more details, see Ferreira (2012).…”

Section: Estimationmentioning

confidence: 99%

Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective

Феррейра

Ferreira

2017

Risks

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Abstract:Pareto processes are suitable to model stationary heavy-tailed data. Here, we consider the auto-regressive Gaver-Lewis Pareto Process and address a study of the tail behavior. We characterize its local and long-range dependence. We will see that consecutive observations are asymptotically tail independent, a feature that is often misevaluated by the most common extremal models and with strong relevance to the tail inference. This also reveals clustering at "penultimate" levels. Linear correlation may not exist in a heavy-tailed context and an alternative diagnostic tool will be presented. The derived properties relate to the auto-regressive parameter of the process and will provide estimators. A comparison of the proposals is conducted through simulation and an application to a real dataset illustrates the procedure.

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Statistical Inference in Bernoulli Trials with Dependence

Cited by 105 publications

References 7 publications

From Markovian to pairwise epidemic models and the performance of moment closure approximations

From Markovian to pairwise epidemic models and the performance of moment closure approximations

Modelling behavioural contagion

Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective

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