3,174 research outputs found
Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models
We propose a new class of filtering and smoothing methods for inference in
high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models.
The main idea is to combine the ensemble Kalman filter and smoother, developed
in the geophysics literature, with state-space algorithms from the statistics
literature. Our algorithms address a variety of estimation scenarios, including
on-line and off-line state and parameter estimation. We take a Bayesian
perspective, for which the goal is to generate samples from the joint posterior
distribution of states and parameters. The key benefit of our approach is the
use of ensemble Kalman methods for dimension reduction, which allows inference
for high-dimensional state vectors. We compare our methods to existing ones,
including ensemble Kalman filters, particle filters, and particle MCMC. Using a
real data example of cloud motion and data simulated under a number of
nonlinear and non-Gaussian scenarios, we show that our approaches outperform
these existing methods
Statistical Inference for Time-changed Brownian Motion Credit Risk Models
We consider structural credit modeling in the important special case where
the log-leverage ratio of the firm is a time-changed Brownian motion (TCBM)
with the time-change taken to be an independent increasing process. Following
the approach of Black and Cox, one defines the time of default to be the first
passage time for the log-leverage ratio to cross the level zero. Rather than
adopt the classical notion of first passage, with its associated numerical
challenges, we accept an alternative notion applicable for TCBMs called "first
passage of the second kind". We demonstrate how statistical inference can be
efficiently implemented in this new class of models. This allows us to compare
the performance of two versions of TCBMs, the variance gamma (VG) model and the
exponential jump model (EXP), to the Black-Cox model. When applied to a 4.5
year long data set of weekly credit default swap (CDS) quotes for Ford Motor
Co, the conclusion is that the two TCBM models, with essentially one extra
parameter, can significantly outperform the classic Black-Cox model.Comment: 21 pages, 3 figures, 2 table
Affine Invariant Ensemble Transform Methods to Improve Predictive Uncertainty in ReLU Networks
We consider the problem of performing Bayesian inference for logistic
regression using appropriate extensions of the ensemble Kalman filter. Two
interacting particle systems are proposed that sample from an approximate
posterior and prove quantitative convergence rates of these interacting
particle systems to their mean-field limit as the number of particles tends to
infinity. Furthermore, we apply these techniques and examine their
effectiveness as methods of Bayesian approximation for quantifying predictive
uncertainty in ReLU networks
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