5,137 research outputs found
A nonparametric ensemble transform method for Bayesian inference
Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables.
© 2013, Society for Industrial and Applied Mathematic
Bayesian Nonparametric Calibration and Combination of Predictive Distributions
We introduce a Bayesian approach to predictive density calibration and
combination that accounts for parameter uncertainty and model set
incompleteness through the use of random calibration functionals and random
combination weights. Building on the work of Ranjan, R. and Gneiting, T. (2010)
and Gneiting, T. and Ranjan, R. (2013), we use infinite beta mixtures for the
calibration. The proposed Bayesian nonparametric approach takes advantage of
the flexibility of Dirichlet process mixtures to achieve any continuous
deformation of linearly combined predictive distributions. The inference
procedure is based on Gibbs sampling and allows accounting for uncertainty in
the number of mixture components, mixture weights, and calibration parameters.
The weak posterior consistency of the Bayesian nonparametric calibration is
provided under suitable conditions for unknown true density. We study the
methodology in simulation examples with fat tails and multimodal densities and
apply it to density forecasts of daily S&P returns and daily maximum wind speed
at the Frankfurt airport.Comment: arXiv admin note: text overlap with arXiv:1305.2026 by other author
A Stein variational Newton method
Stein variational gradient descent (SVGD) was recently proposed as a general
purpose nonparametric variational inference algorithm [Liu & Wang, NIPS 2016]:
it minimizes the Kullback-Leibler divergence between the target distribution
and its approximation by implementing a form of functional gradient descent on
a reproducing kernel Hilbert space. In this paper, we accelerate and generalize
the SVGD algorithm by including second-order information, thereby approximating
a Newton-like iteration in function space. We also show how second-order
information can lead to more effective choices of kernel. We observe
significant computational gains over the original SVGD algorithm in multiple
test cases.Comment: 18 pages, 7 figure
- …