Page 680 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 680
STATISTICS AND FINANCIAL MATHEMATICS
On change estimation in stochastic intensity-driven continuous time point
processes through multiple testing
Moinak Bhaduri, mbhaduri@bentley.edu
Bentley University, United States
Point processes stand as convenient instruments to model count data, and the relevance of
observation-reliant underlying intensities remains undeniable even in the face of seemingly
tempting alternatives. Hawkes processes offer a sterling example, often leading to a branch-
ing process framework. We posit a genre of change detection algorithms, engineered through
permutations of trend-switched statistics and a judicious application of false discovery rate con-
trol. Quick, accurate change detection on both the immigrant and offspring kernels, coupled
with the scarcity of false positives are a few optimal properties. Certain members of this family
that remain asymptotically consistent and close to the ground truth (evidenced through some
Hausdorff-similarity) are isolated to pinpoint estimated change locations. Efficient forecasting
proves to be a natural corollary.
Keywords: Point process, change detection, self-exciting intensity, Hawkes process, oceanog-
raphy, global terrorism, economic announcements
Consistency of Bayesian inference with Gaussian priors in an elliptic
nonlinear inverse problem
Matteo Giordano, mg846@cam.ac.uk
University of Cambridge, United Kingdom
We consider nonparametric Bayesian inference for nonlinear inverse problems based on Gaus-
sian process priors. We present posterior consistency results for the problem of recovering the
unknown conductivity in an elliptic PDE in divergence form from noisy discrete observations of
its solution, and give a convergence rate for the reconstruction error of the associated posterior
mean estimator. The analysis is based on a contraction rates theory for the induced regression
problem, combined with a stability estimate for the solution map of the PDE.
Ranking of Baltic States II pillar pension funds by stochastic dominance
ratio
Audrius Kabašinskas, audkaba@ktu.lt
Kaunas University of Technology, Lithuania
Coauthors: Miloš Kopa, Kristina Šutiene˙
In this presentation we will introduce results of ranking of Lithuanian, Latvian and Estonian
II pillar pension funds by Stochastic Dominance (SD) ratio. Insights of how to select non-
dominated pension fund will be provided, comparison of pension systems and performance of
fund managers will be discussed too. First, second and third order SD are used in this research.
Pairwise SD is numerically computed using non-parametric and parametric approaches. The
later one covers α-stable, hyperbolic, NIG and Student t probability distributions, while empir-
ical SD is assumed to be non-parametric one.
678
On change estimation in stochastic intensity-driven continuous time point
processes through multiple testing
Moinak Bhaduri, mbhaduri@bentley.edu
Bentley University, United States
Point processes stand as convenient instruments to model count data, and the relevance of
observation-reliant underlying intensities remains undeniable even in the face of seemingly
tempting alternatives. Hawkes processes offer a sterling example, often leading to a branch-
ing process framework. We posit a genre of change detection algorithms, engineered through
permutations of trend-switched statistics and a judicious application of false discovery rate con-
trol. Quick, accurate change detection on both the immigrant and offspring kernels, coupled
with the scarcity of false positives are a few optimal properties. Certain members of this family
that remain asymptotically consistent and close to the ground truth (evidenced through some
Hausdorff-similarity) are isolated to pinpoint estimated change locations. Efficient forecasting
proves to be a natural corollary.
Keywords: Point process, change detection, self-exciting intensity, Hawkes process, oceanog-
raphy, global terrorism, economic announcements
Consistency of Bayesian inference with Gaussian priors in an elliptic
nonlinear inverse problem
Matteo Giordano, mg846@cam.ac.uk
University of Cambridge, United Kingdom
We consider nonparametric Bayesian inference for nonlinear inverse problems based on Gaus-
sian process priors. We present posterior consistency results for the problem of recovering the
unknown conductivity in an elliptic PDE in divergence form from noisy discrete observations of
its solution, and give a convergence rate for the reconstruction error of the associated posterior
mean estimator. The analysis is based on a contraction rates theory for the induced regression
problem, combined with a stability estimate for the solution map of the PDE.
Ranking of Baltic States II pillar pension funds by stochastic dominance
ratio
Audrius Kabašinskas, audkaba@ktu.lt
Kaunas University of Technology, Lithuania
Coauthors: Miloš Kopa, Kristina Šutiene˙
In this presentation we will introduce results of ranking of Lithuanian, Latvian and Estonian
II pillar pension funds by Stochastic Dominance (SD) ratio. Insights of how to select non-
dominated pension fund will be provided, comparison of pension systems and performance of
fund managers will be discussed too. First, second and third order SD are used in this research.
Pairwise SD is numerically computed using non-parametric and parametric approaches. The
later one covers α-stable, hyperbolic, NIG and Student t probability distributions, while empir-
ical SD is assumed to be non-parametric one.
678
