Estimating the concentration of the Langevin distribution

1990 ◽  
Vol 18 (2) ◽  
pp. 163-169 ◽  
Author(s):  
Gilles R. Ducharme ◽  
Philip Milasevic
Keyword(s):  
Langevin Distribution

scholarly journals Conjugate Priors and Posterior Inference for the Matrix Langevin Distribution on the Stiefel Manifold

2020 ◽  
Vol 15 (3) ◽  
pp. 871-908
Author(s):  
Subhadip Pal ◽  
Subhajit Sengupta ◽  
Riten Mitra ◽  
Arunava Banerjee
Keyword(s):  
Stiefel Manifold ◽  
Conjugate Priors ◽  
Posterior Inference ◽  
The Matrix ◽  
Langevin Distribution

scholarly journals Seismic moment tensor event screening

2020 ◽  
Vol 221 (1) ◽  
pp. 77-88
Author(s):  
Sean R Ford ◽  
Gordon D Kraft ◽  
Gene A Ichinose
Keyword(s):  
Seismic Moment ◽  
Moment Tensor ◽  
Test Site ◽  
Seismic Moment Tensor ◽  
Data Set ◽  
New Approach ◽  
Moment Tensors ◽  
Explosion Monitoring ◽  
Langevin Distribution ◽  
Monitoring Practice

SUMMARY Event screening is an explosion monitoring practice that aims to identify an event as an explosion (‘screened in’) or not (‘screened out’). Confidence in event screening can be increased if multiple independent approaches are used. We describe a new approach to event screening using the seismic moment tensor and its representation on the hypersphere, specifically the 5-sphere of 6-degree unit vectors representing the normalized symmetric moment tensor. The sample of moment tensors from an explosion data set is unimodal on the 5-sphere and can be parametrized by the Langevin distribution, which is sometimes referred to as the Normal distribution on the hypersphere. Screening is then accomplished by finding the angle from the explosion population mean to any newly measured moment tensor and testing if that angle is in the tail of the Langevin distribution (conservatively quantified as greater than 99.9 per cent of the cumulative density). We apply the screen to a sample of earthquakes from the Western USA and the September 2017 explosion and subsequent collapse at the Pungyye-Ri Test Site in North Korea. All the earthquakes and the collapse screen out, but the explosion does not.

scholarly journals State-Space Models on the Stiefel Manifold with a New Approach to Nonlinear Filtering

Econometrics ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 48
Author(s):  
Yukai Yang ◽  
Luc Bauwens
Keyword(s):  
State Space ◽  
Nonlinear Filtering ◽  
State Space Models ◽  
Stiefel Manifold ◽  
Dynamic Factor ◽  
New Approach ◽  
Vector Error Correction ◽  
Vector Error ◽  
Langevin Distribution ◽  
Vector Error Correction Models

We develop novel multivariate state-space models wherein the latent states evolve on the Stiefel manifold and follow a conditional matrix Langevin distribution. The latent states correspond to time-varying reduced rank parameter matrices, like the loadings in dynamic factor models and the parameters of cointegrating relations in vector error-correction models. The corresponding nonlinear filtering algorithms are developed and evaluated by means of simulation experiments.

Sign in / Sign up

Export Citation Format

Share Document