4,607 research outputs found
A Matrix Approach to Nonstationary Chains
1 online resource (PDF, 35 pages
Computer model calibration with large non-stationary spatial outputs: application to the calibration of a climate model
Bayesian calibration of computer models tunes unknown input parameters by
comparing outputs with observations. For model outputs that are distributed
over space, this becomes computationally expensive because of the output size.
To overcome this challenge, we employ a basis representation of the model
outputs and observations: we match these decompositions to carry out the
calibration efficiently. In the second step, we incorporate the non-stationary
behaviour, in terms of spatial variations of both variance and correlations, in
the calibration. We insert two integrated nested Laplace
approximation-stochastic partial differential equation parameters into the
calibration. A synthetic example and a climate model illustration highlight the
benefits of our approach
Bayesian Nonstationary Spatial Modeling for Very Large Datasets
With the proliferation of modern high-resolution measuring instruments
mounted on satellites, planes, ground-based vehicles and monitoring stations, a
need has arisen for statistical methods suitable for the analysis of large
spatial datasets observed on large spatial domains. Statistical analyses of
such datasets provide two main challenges: First, traditional
spatial-statistical techniques are often unable to handle large numbers of
observations in a computationally feasible way. Second, for large and
heterogeneous spatial domains, it is often not appropriate to assume that a
process of interest is stationary over the entire domain.
We address the first challenge by using a model combining a low-rank
component, which allows for flexible modeling of medium-to-long-range
dependence via a set of spatial basis functions, with a tapered remainder
component, which allows for modeling of local dependence using a compactly
supported covariance function. Addressing the second challenge, we propose two
extensions to this model that result in increased flexibility: First, the model
is parameterized based on a nonstationary Matern covariance, where the
parameters vary smoothly across space. Second, in our fully Bayesian model, all
components and parameters are considered random, including the number,
locations, and shapes of the basis functions used in the low-rank component.
Using simulated data and a real-world dataset of high-resolution soil
measurements, we show that both extensions can result in substantial
improvements over the current state-of-the-art.Comment: 16 pages, 2 color figure
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