8,146 research outputs found
On the Estimation of Nonrandom Signal Coefficients from Jittered Samples
This paper examines the problem of estimating the parameters of a bandlimited
signal from samples corrupted by random jitter (timing noise) and additive iid
Gaussian noise, where the signal lies in the span of a finite basis. For the
presented classical estimation problem, the Cramer-Rao lower bound (CRB) is
computed, and an Expectation-Maximization (EM) algorithm approximating the
maximum likelihood (ML) estimator is developed. Simulations are performed to
study the convergence properties of the EM algorithm and compare the
performance both against the CRB and a basic linear estimator. These
simulations demonstrate that by post-processing the jittered samples with the
proposed EM algorithm, greater jitter can be tolerated, potentially reducing
on-chip ADC power consumption substantially.Comment: 11 pages, 8 figure
Fisher Information for Inverse Problems and Trace Class Operators
This paper provides a mathematical framework for Fisher information analysis
for inverse problems based on Gaussian noise on infinite-dimensional Hilbert
space. The covariance operator for the Gaussian noise is assumed to be trace
class, and the Jacobian of the forward operator Hilbert-Schmidt. We show that
the appropriate space for defining the Fisher information is given by the
Cameron-Martin space. This is mainly because the range space of the covariance
operator always is strictly smaller than the Hilbert space. For the Fisher
information to be well-defined, it is furthermore required that the range space
of the Jacobian is contained in the Cameron-Martin space. In order for this
condition to hold and for the Fisher information to be trace class, a
sufficient condition is formulated based on the singular values of the Jacobian
as well as of the eigenvalues of the covariance operator, together with some
regularity assumptions regarding their relative rate of convergence. An
explicit example is given regarding an electromagnetic inverse source problem
with "external" spherically isotropic noise, as well as "internal" additive
uncorrelated noise.Comment: Submitted to Journal of Mathematical Physic
Coherent frequentism
By representing the range of fair betting odds according to a pair of
confidence set estimators, dual probability measures on parameter space called
frequentist posteriors secure the coherence of subjective inference without any
prior distribution. The closure of the set of expected losses corresponding to
the dual frequentist posteriors constrains decisions without arbitrarily
forcing optimization under all circumstances. This decision theory reduces to
those that maximize expected utility when the pair of frequentist posteriors is
induced by an exact or approximate confidence set estimator or when an
automatic reduction rule is applied to the pair. In such cases, the resulting
frequentist posterior is coherent in the sense that, as a probability
distribution of the parameter of interest, it satisfies the axioms of the
decision-theoretic and logic-theoretic systems typically cited in support of
the Bayesian posterior. Unlike the p-value, the confidence level of an interval
hypothesis derived from such a measure is suitable as an estimator of the
indicator of hypothesis truth since it converges in sample-space probability to
1 if the hypothesis is true or to 0 otherwise under general conditions.Comment: The confidence-measure theory of inference and decision is explicitly
extended to vector parameters of interest. The derivation of upper and lower
confidence levels from valid and nonconservative set estimators is formalize
Statistical applications of the multivariate skew-normal distribution
Azzalini & Dalla Valle (1996) have recently discussed the multivariate
skew-normal distribution which extends the class of normal distributions by the
addition of a shape parameter. The first part of the present paper examines
further probabilistic properties of the distribution, with special emphasis on
aspects of statistical relevance. Inferential and other statistical issues are
discussed in the following part, with applications to some multivariate
statistics problems, illustrated by numerical examples. Finally, a further
extension is described which introduces a skewing factor of an elliptical
density.Comment: full-length version of the published paper, 32 pages, with 7 figures,
uses psfra
Bayesian model comparison in cosmology with Population Monte Carlo
We use Bayesian model selection techniques to test extensions of the standard
flat LambdaCDM paradigm. Dark-energy and curvature scenarios, and primordial
perturbation models are considered. To that end, we calculate the Bayesian
evidence in favour of each model using Population Monte Carlo (PMC), a new
adaptive sampling technique which was recently applied in a cosmological
context. The Bayesian evidence is immediately available from the PMC sample
used for parameter estimation without further computational effort, and it
comes with an associated error evaluation. Besides, it provides an unbiased
estimator of the evidence after any fixed number of iterations and it is
naturally parallelizable, in contrast with MCMC and nested sampling methods. By
comparison with analytical predictions for simulated data, we show that our
results obtained with PMC are reliable and robust. The variability in the
evidence evaluation and the stability for various cases are estimated both from
simulations and from data. For the cases we consider, the log-evidence is
calculated with a precision of better than 0.08.
Using a combined set of recent CMB, SNIa and BAO data, we find inconclusive
evidence between flat LambdaCDM and simple dark-energy models. A curved
Universe is moderately to strongly disfavoured with respect to a flat
cosmology. Using physically well-motivated priors within the slow-roll
approximation of inflation, we find a weak preference for a running spectral
index. A Harrison-Zel'dovich spectrum is weakly disfavoured. With the current
data, tensor modes are not detected; the large prior volume on the
tensor-to-scalar ratio r results in moderate evidence in favour of r=0.
[Abridged]Comment: 11 pages, 6 figures. Matches version accepted for publication by
MNRA
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