46,356 research outputs found
On the Measurement of Privacy as an Attacker's Estimation Error
A wide variety of privacy metrics have been proposed in the literature to
evaluate the level of protection offered by privacy enhancing-technologies.
Most of these metrics are specific to concrete systems and adversarial models,
and are difficult to generalize or translate to other contexts. Furthermore, a
better understanding of the relationships between the different privacy metrics
is needed to enable more grounded and systematic approach to measuring privacy,
as well as to assist systems designers in selecting the most appropriate metric
for a given application.
In this work we propose a theoretical framework for privacy-preserving
systems, endowed with a general definition of privacy in terms of the
estimation error incurred by an attacker who aims to disclose the private
information that the system is designed to conceal. We show that our framework
permits interpreting and comparing a number of well-known metrics under a
common perspective. The arguments behind these interpretations are based on
fundamental results related to the theories of information, probability and
Bayes decision.Comment: This paper has 18 pages and 17 figure
A Method for Individual Source Brightness Estimation in Single- and Multi-band Data
We present a method of reliably extracting the flux of individual sources
from sky maps in the presence of noise and a source population in which number
counts are a steeply falling function of flux. The method is an extension of a
standard Bayesian procedure in the millimeter/submillimeter literature. As in
the standard method, the prior applied to source flux measurements is derived
from an estimate of the source counts as a function of flux, dN/dS. The key
feature of the new method is that it enables reliable extraction of properties
of individual sources, which previous methods in the literature do not. We
first present the method for extracting individual source fluxes from data in a
single observing band, then we extend the method to multiple bands, including
prior information about the spectral behavior of the source population(s). The
multi-band estimation technique is particularly relevant for classifying
individual sources into populations according to their spectral behavior. We
find that proper treatment of the correlated prior information between
observing bands is key to avoiding significant biases in estimations of
multi-band fluxes and spectral behavior, biases which lead to significant
numbers of misclassified sources. We test the single- and multi-band versions
of the method using simulated observations with observing parameters similar to
that of the South Pole Telescope data used in Vieira, et al. (2010).Comment: 11 emulateapj pages, 3 figures, revised to match published versio
Cosmological parameter inference with Bayesian statistics
Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found
their place in the field of Cosmology. They have become important mathematical
and numerical tools, especially in parameter estimation and model comparison.
In this paper, we review some fundamental concepts to understand Bayesian
statistics and then introduce MCMC algorithms and samplers that allow us to
perform the parameter inference procedure. We also introduce a general
description of the standard cosmological model, known as the CDM
model, along with several alternatives, and current datasets coming from
astrophysical and cosmological observations. Finally, with the tools acquired,
we use an MCMC algorithm implemented in python to test several cosmological
models and find out the combination of parameters that best describes the
Universe.Comment: 30 pages, 17 figures, 5 tables; accepted for publication in Universe;
references adde
-Decay Spectrum, Response Function and Statistical Model for Neutrino Mass Measurements with the KATRIN Experiment
The objective of the Karlsruhe Tritium Neutrino (KATRIN) experiment is to
determine the effective electron neutrino mass with an
unprecedented sensitivity of (90\% C.L.) by precision electron
spectroscopy close to the endpoint of the decay of tritium. We present
a consistent theoretical description of the electron energy spectrum in
the endpoint region, an accurate model of the apparatus response function, and
the statistical approaches suited to interpret and analyze tritium
decay data observed with KATRIN with the envisaged precision. In addition to
providing detailed analytical expressions for all formulae used in the
presented model framework with the necessary detail of derivation, we discuss
and quantify the impact of theoretical and experimental corrections on the
measured . Finally, we outline the statistical methods for
parameter inference and the construction of confidence intervals that are
appropriate for a neutrino mass measurement with KATRIN. In this context, we
briefly discuss the choice of the energy analysis interval and the
distribution of measuring time within that range.Comment: 27 pages, 22 figures, 2 table
Median Statistics, H_0, and the Accelerating Universe
(Abridged) We develop median statistics that provide powerful alternatives to
chi-squared likelihood methods and require fewer assumptions about the data.
Applying median statistics to Huchra's compilation of nearly all estimates of
the Hubble constant, we find a median value H_0=67 km/s/Mpc. Median statistics
assume only that the measurements are independent and free of systematic
errors. This estimate is arguably the best summary of current knowledge because
it uses all available data and, unlike other estimates, makes no assumption
about the distribution of measurement errors. The 95% range of purely
statistical errors is +/- 2 km/s/Mpc. The statistical precision of this result
leads us to analyze the range of possible systematic errors in the median,
which we estimate to be roughly +/- 5 km/s/Mpc (95% limits), dominating over
the statistical errors. A Bayesian median statistics treatment of high-redshift
Type Ia supernovae (SNe Ia) apparent magnitude versus redshift data from Riess
et al. yields a posterior probability that the cosmological constant Lambda > 0
of 70 or 89%, depending on the prior information used. The posterior
probability of an open universe is about 47%. Analysis of the Perlmutter et al.
high-redshift SNe Ia data show the best-fit flat-Lambda model favored over the
best-fit Lambda = 0 open model by odds of 366:1; corresponding Riess et al.
odds are 3:1 (assuming prior odds of 1:1).Median statistics analyses of the SNe
Ia data do not rule out a time-variable Lambda model, and may even favor it
over a time-independent Lambda and a Lambda = 0 open model.Comment: Significant revisions include discussion of systematic errors in the
median of H_0. Accepted for publication in The Astrophysical Journal, v548,
February 20, 2001 issue. 47 pages incl. figures and table
Estimation of Upper Limits Using a Poisson Statistic
Bayesian, classical, and extended maximum likelihood approaches to estimation
of upper limits in experiments with small numbers of signal events are
surveyed. The discussion covers only experiments whose outcomes are well
described by a Poisson statistic. A new approach, based on the statistical
significance of a signal rather than on the number of events in the signal
region, is proposed. A toy model and an example of a recent search for the
lepton number violating decay are used to illustrate
application of the discussed techniques.Comment: 24 pages, 7 figure
- …