51,252 research outputs found
Copula Calibration
We propose notions of calibration for probabilistic forecasts of general
multivariate quantities. Probabilistic copula calibration is a natural analogue
of probabilistic calibration in the univariate setting. It can be assessed
empirically by checking for the uniformity of the copula probability integral
transform (CopPIT), which is invariant under coordinate permutations and
coordinatewise strictly monotone transformations of the predictive distribution
and the outcome. The CopPIT histogram can be interpreted as a generalization
and variant of the multivariate rank histogram, which has been used to check
the calibration of ensemble forecasts. Climatological copula calibration is an
analogue of marginal calibration in the univariate setting. Methods and tools
are illustrated in a simulation study and applied to compare raw numerical
model and statistically postprocessed ensemble forecasts of bivariate wind
vectors
Ensemble model output statistics for wind vectors
A bivariate ensemble model output statistics (EMOS) technique for the
postprocessing of ensemble forecasts of two-dimensional wind vectors is
proposed, where the postprocessed probabilistic forecast takes the form of a
bivariate normal probability density function. The postprocessed means and
variances of the wind vector components are linearly bias-corrected versions of
the ensemble means and ensemble variances, respectively, and the conditional
correlation between the wind components is represented by a trigonometric
function of the ensemble mean wind direction. In a case study on 48-hour
forecasts of wind vectors over the North American Pacific Northwest with the
University of Washington Mesoscale Ensemble, the bivariate EMOS density
forecasts were calibrated and sharp, and showed considerable improvement over
the raw ensemble and reference forecasts, including ensemble copula coupling
Multi-path Probabilistic Available Bandwidth Estimation through Bayesian Active Learning
Knowing the largest rate at which data can be sent on an end-to-end path such
that the egress rate is equal to the ingress rate with high probability can be
very practical when choosing transmission rates in video streaming or selecting
peers in peer-to-peer applications. We introduce probabilistic available
bandwidth, which is defined in terms of ingress rates and egress rates of
traffic on a path, rather than in terms of capacity and utilization of the
constituent links of the path like the standard available bandwidth metric. In
this paper, we describe a distributed algorithm, based on a probabilistic
graphical model and Bayesian active learning, for simultaneously estimating the
probabilistic available bandwidth of multiple paths through a network. Our
procedure exploits the fact that each packet train provides information not
only about the path it traverses, but also about any path that shares a link
with the monitored path. Simulations and PlanetLab experiments indicate that
this process can dramatically reduce the number of probes required to generate
accurate estimates
Bayesian optimisation for likelihood-free cosmological inference
Many cosmological models have only a finite number of parameters of interest,
but a very expensive data-generating process and an intractable likelihood
function. We address the problem of performing likelihood-free Bayesian
inference from such black-box simulation-based models, under the constraint of
a very limited simulation budget (typically a few thousand). To do so, we adopt
an approach based on the likelihood of an alternative parametric model.
Conventional approaches to approximate Bayesian computation such as
likelihood-free rejection sampling are impractical for the considered problem,
due to the lack of knowledge about how the parameters affect the discrepancy
between observed and simulated data. As a response, we make use of a strategy
previously developed in the machine learning literature (Bayesian optimisation
for likelihood-free inference, BOLFI), which combines Gaussian process
regression of the discrepancy to build a surrogate surface with Bayesian
optimisation to actively acquire training data. We extend the method by
deriving an acquisition function tailored for the purpose of minimising the
expected uncertainty in the approximate posterior density, in the parametric
approach. The resulting algorithm is applied to the problems of summarising
Gaussian signals and inferring cosmological parameters from the Joint
Lightcurve Analysis supernovae data. We show that the number of required
simulations is reduced by several orders of magnitude, and that the proposed
acquisition function produces more accurate posterior approximations, as
compared to common strategies.Comment: 16+9 pages, 12 figures. Matches PRD published version after minor
modification
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