36,541 research outputs found
Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis
In performing a Bayesian analysis of astronomical data, two difficult
problems often emerge. First, in estimating the parameters of some model for
the data, the resulting posterior distribution may be multimodal or exhibit
pronounced (curving) degeneracies, which can cause problems for traditional
MCMC sampling methods. Second, in selecting between a set of competing models,
calculation of the Bayesian evidence for each model is computationally
expensive. The nested sampling method introduced by Skilling (2004), has
greatly reduced the computational expense of calculating evidences and also
produces posterior inferences as a by-product. This method has been applied
successfully in cosmological applications by Mukherjee et al. (2006), but their
implementation was efficient only for unimodal distributions without pronounced
degeneracies. Shaw et al. (2007), recently introduced a clustered nested
sampling method which is significantly more efficient in sampling from
multimodal posteriors and also determines the expectation and variance of the
final evidence from a single run of the algorithm, hence providing a further
increase in efficiency. In this paper, we build on the work of Shaw et al. and
present three new methods for sampling and evidence evaluation from
distributions that may contain multiple modes and significant degeneracies; we
also present an even more efficient technique for estimating the uncertainty on
the evaluated evidence. These methods lead to a further substantial improvement
in sampling efficiency and robustness, and are applied to toy problems to
demonstrate the accuracy and economy of the evidence calculation and parameter
estimation. Finally, we discuss the use of these methods in performing Bayesian
object detection in astronomical datasets.Comment: 14 pages, 11 figures, submitted to MNRAS, some major additions to the
previous version in response to the referee's comment
Approximate Two-Party Privacy-Preserving String Matching with Linear Complexity
Consider two parties who want to compare their strings, e.g., genomes, but do
not want to reveal them to each other. We present a system for
privacy-preserving matching of strings, which differs from existing systems by
providing a deterministic approximation instead of an exact distance. It is
efficient (linear complexity), non-interactive and does not involve a third
party which makes it particularly suitable for cloud computing. We extend our
protocol, such that it mitigates iterated differential attacks proposed by
Goodrich. Further an implementation of the system is evaluated and compared
against current privacy-preserving string matching algorithms.Comment: 6 pages, 4 figure
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