Tail Distribution of the Maximum of Correlated Gaussian Random Variables

Botev, Zdravko I.; Mandjes, Michel; Ridder, Ad

doi:10.2139/ssrn.2703769

Cited by 2 publications

(3 citation statements)

References 13 publications

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“…Let Γ t,w denote the vector of Γ (i) t,w s. To control the upper bound of the false alarm rate, we compute the eq. ( 4.13) with the technique in Botev (2015):…”

Section: False Alarm Rate Of Scan Statistics For a Given Tmentioning

confidence: 99%

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Online Score Statistics for Detecting Clustered Change in Network Point Processes

Zhang¹,

Xie²

2022

Preprint

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We consider online monitoring of the network event data to detect local changes in a cluster when the affected data stream distribution shifts from one point process to another with different parameters. Specifically, we are interested in detecting a change point that causes a shift of the underlying data distribution from a Poisson process to a multivariate Hawkes process with exponential decay temporal kernel, whereby the Hawkes process is considered to account for spatio-temporal between observations. The proposed detection procedure is based on scan score statistics. We derive the asymptotic distribution of the statistic, which enables the self-normalizing property and facilitates the approximation of the false alarm rate and the average run length. Thus, when detecting a change from Poisson to Hawkes process with non-vanishing self-excitation, the procedure does not require estimating the post-change network parameter while assuming the temporal decay parameter. We further present an efficient procedure to accurately determine the false discovery rate via importance sampling, as validated by numerical examples. The good performance of our procedures compared with the benchmarks is tested with numerical experiments with simulated and real stock exchange data.

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“…Let Γ t,w denote the vector of Γ (i) t,w s. To control the upper bound of the false alarm rate, we compute the eq. ( 4.13) with the technique in Botev (2015):…”

Section: False Alarm Rate Of Scan Statistics For a Given Tmentioning

confidence: 99%

“…According to equation (4.7), Γ t,w ∼ N (0, Σ). In Botev (2015), they provide an importance sampling algorithm to estimate the equation (4.14). Σ can be computed with(4.12) according to the network topology and the score statistics in the clusters.…”

Section: False Alarm Rate Of Scan Statistics For a Given Tmentioning

confidence: 99%

Online Score Statistics for Detecting Clustered Change in Network Point Processes

Zhang¹,

Xie²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…However, Y (m) corresponds to the maximum of correlated and differently distributed Gaussian random variables, for which a straightforward, closed form solution does not appear to exist. Instead, numerical solutions are typically considered [35], [36]. Motivated by this, we use the strategy developed by Clark [37] to approximate Y (m) as a normal random variable through a recursive process.…”

Section: A Error Probability Analysismentioning

confidence: 99%

Higher Order Derivatives: Improved Pre-Processing and Receivers for Molecular Communications

Gursoy

Mitra

2020

GLOBECOM 2020 - 2020 IEEE Global Communications Conference

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While molecular communication via diffusion experiences significant inter-symbol interference (ISI), recent work suggests that ISI can be mitigated via time differentiation preprocessing which achieves pulse narrowing. Herein, the approach is generalized to higher order differentiation. The fundamental trade-off between ISI mitigation and noise amplification is characterized, showing the existence of an optimal derivative order that minimizes the bit error rate (BER). Theoretical analyses of the BER and a signal-to-interference-plus-noise ratio are provided, the derivative order optimization problem is posed and solved for threshold-based detectors. For more complex detectors which exploit a window memory, it is shown that derivative pre-processing can strongly reduce the size of the needed window. Extensive numerical results confirm the accuracy of theoretical derivations, the gains in performance via derivative pre-processing over other methods and the impact of the optimal derivative order. Derivative pre-processing offers a low complexity/high-performance method for reducing ISI at the expense of increased transmission power to reduce noise amplification.

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Tail Distribution of the Maximum of Correlated Gaussian Random Variables

Cited by 2 publications

References 13 publications

Online Score Statistics for Detecting Clustered Change in Network Point Processes

Online Score Statistics for Detecting Clustered Change in Network Point Processes

Higher Order Derivatives: Improved Pre-Processing and Receivers for Molecular Communications

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