2,024 research outputs found
Semiparametric posterior limits
We review the Bayesian theory of semiparametric inference following Bickel
and Kleijn (2012) and Kleijn and Knapik (2013). After an overview of efficiency
in parametric and semiparametric estimation problems, we consider the
Bernstein-von Mises theorem (see, e.g., Le Cam and Yang (1990)) and generalize
it to (LAN) regular and (LAE) irregular semiparametric estimation problems. We
formulate a version of the semiparametric Bernstein-von Mises theorem that does
not depend on least-favourable submodels, thus bypassing the most restrictive
condition in the presentation of Bickel and Kleijn (2012). The results are
applied to the (regular) estimation of the linear coefficient in partial linear
regression (with a Gaussian nuisance prior) and of the kernel bandwidth in a
model of normal location mixtures (with a Dirichlet nuisance prior), as well as
the (irregular) estimation of the boundary of the support of a monotone family
of densities (with a Gaussian nuisance prior).Comment: 47 pp., 1 figure, submitted for publication. arXiv admin note:
substantial text overlap with arXiv:1007.017
Recovery, detection and confidence sets of communities in a sparse stochastic block model
Posterior distributions for community assignment in the planted bi-section
model are shown to achieve frequentist exact recovery and detection under sharp
lower bounds on sparsity. Assuming posterior recovery (or detection), one may
interpret credible sets (or enlarged credible sets) as consistent confidence
sets. If credible levels grow to one quickly enough, credible sets can be
interpreted as frequentist confidence sets without conditions on the
parameters. In the regime where within-class and between-class
edge-probabilities are very close, credible sets may be enlarged to achieve
frequentist asymptotic coverage. The diameters of credible sets are controlled
and match rates of posterior convergence.Comment: 22 pp., 2 fi
The semiparametric Bernstein-von Mises theorem
In a smooth semiparametric estimation problem, the marginal posterior for the
parameter of interest is expected to be asymptotically normal and satisfy
frequentist criteria of optimality if the model is endowed with a suitable
prior. It is shown that, under certain straightforward and interpretable
conditions, the assertion of Le Cam's acclaimed, but strictly parametric,
Bernstein-von Mises theorem [Univ. California Publ. Statist. 1 (1953) 277-329]
holds in the semiparametric situation as well. As a consequence, Bayesian
point-estimators achieve efficiency, for example, in the sense of H\'{a}jek's
convolution theorem [Z. Wahrsch. Verw. Gebiete 14 (1970) 323-330]. The model is
required to satisfy differentiability and metric entropy conditions, while the
nuisance prior must assign nonzero mass to certain Kullback-Leibler
neighborhoods [Ghosal, Ghosh and van der Vaart Ann. Statist. 28 (2000)
500-531]. In addition, the marginal posterior is required to converge at
parametric rate, which appears to be the most stringent condition in examples.
The results are applied to estimation of the linear coefficient in partial
linear regression, with a Gaussian prior on a smoothness class for the
nuisance.Comment: Published in at http://dx.doi.org/10.1214/11-AOS921 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
The Bayesian Analysis of Complex, High-Dimensional Models: Can It Be CODA?
We consider the Bayesian analysis of a few complex, high-dimensional models
and show that intuitive priors, which are not tailored to the fine details of
the model and the estimated parameters, produce estimators which perform poorly
in situations in which good, simple frequentist estimators exist. The models we
consider are: stratified sampling, the partial linear model, linear and
quadratic functionals of white noise and estimation with stopping times. We
present a strong version of Doob's consistency theorem which demonstrates that
the existence of a uniformly -consistent estimator ensures that the
Bayes posterior is -consistent for values of the parameter in subsets
of prior probability 1. We also demonstrate that it is, at least, in principle,
possible to construct Bayes priors giving both global and local minimax rates,
using a suitable combination of loss functions. We argue that there is no
contradiction in these apparently conflicting findings.Comment: Published in at http://dx.doi.org/10.1214/14-STS483 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Analysis and improvement of the vector quantization in SELP (Stochastically Excited Linear Prediction)
The Stochastically Excited Linear Prediction (SELP) algorithm is described as a speech coding method employing a two-stage vector quantization. The first stage uses an adaptive codebook which efficiently encodes the periodicity of voiced speech, and the second stage uses a stochastic codebook to encode the remainder of the excitation signal. The adaptive codebook performs well when the pitch period of the speech signal is larger than the frame size. An extension is introduced, which increases its performance for the case that the frame size is longer than the pitch period. The performance of the stochastic stage, which improves with frame length, is shown to be best in those sections of the speech signal where a high level of short-term correlations is present. It can be concluded that the SELP algorithm performs best during voiced speech where the pitch period is longer than the frame length
Dependencies and Simultaneity in Membrane Systems
Membrane system computations proceed in a synchronous fashion: at each step
all the applicable rules are actually applied. Hence each step depends on the
previous one. This coarse view can be refined by looking at the dependencies
among rule occurrences, by recording, for an object, which was the a rule that
produced it and subsequently (in a later step), which was the a rule that
consumed it. In this paper we propose a way to look also at the other main
ingredient in membrane system computations, namely the simultaneity in the rule
applications. This is achieved using zero-safe nets that allows to synchronize
transitions, i.e., rule occurrences. Zero-safe nets can be unfolded into
occurrence nets in a classical way, and to this unfolding an event structure
can be associated. The capability of capturing simultaneity of zero-safe nets
is transferred on the level of event structure by adding a way to express which
events occur simultaneously
The Horseshoe Estimator: Posterior Concentration around Nearly Black Vectors
We consider the horseshoe estimator due to Carvalho, Polson and Scott (2010)
for the multivariate normal mean model in the situation that the mean vector is
sparse in the nearly black sense. We assume the frequentist framework where the
data is generated according to a fixed mean vector. We show that if the number
of nonzero parameters of the mean vector is known, the horseshoe estimator
attains the minimax risk, possibly up to a multiplicative constant. We
provide conditions under which the horseshoe estimator combined with an
empirical Bayes estimate of the number of nonzero means still yields the
minimax risk. We furthermore prove an upper bound on the rate of contraction of
the posterior distribution around the horseshoe estimator, and a lower bound on
the posterior variance. These bounds indicate that the posterior distribution
of the horseshoe prior may be more informative than that of other one-component
priors, including the Lasso.Comment: This version differs from the final published version in pagination
and typographical detail; Available at
http://projecteuclid.org/euclid.ejs/141813426
Codebook-based Bayesian speech enhancement for nonstationary environments
In this paper, we propose a Bayesian minimum mean squared error approach for the joint estimation of the short-term predictor parameters of speech and noise, from the noisy observation. We use trained codebooks of speech and noise linear predictive coefficients to model the a priori information required by the Bayesian scheme. In contrast to current Bayesian estimation approaches that consider the excitation variances as part of the a priori information, in the proposed method they are computed online for each short-time segment, based on the observation at hand. Consequently, the method performs well in nonstationary noise conditions. The resulting estimates of the speech and noise spectra can be used in a Wiener filter or any state-of-the-art speech enhancement system. We develop both memoryless (using information from the current frame alone) and memory-based (using information from the current and previous frames) estimators. Estimation of functions of the short-term predictor parameters is also addressed, in particular one that leads to the minimum mean squared error estimate of the clean speech signal. Experiments indicate that the scheme proposed in this paper performs significantly better than competing method
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