246,822 research outputs found
Standardization of multivariate Gaussian mixture models and background adjustment of PET images in brain oncology
In brain oncology, it is routine to evaluate the progress or remission of the
disease based on the differences between a pre-treatment and a post-treatment
Positron Emission Tomography (PET) scan. Background adjustment is necessary to
reduce confounding by tissue-dependent changes not related to the disease. When
modeling the voxel intensities for the two scans as a bivariate Gaussian
mixture, background adjustment translates into standardizing the mixture at
each voxel, while tumor lesions present themselves as outliers to be detected.
In this paper, we address the question of how to standardize the mixture to a
standard multivariate normal distribution, so that the outliers (i.e., tumor
lesions) can be detected using a statistical test. We show theoretically and
numerically that the tail distribution of the standardized scores is favorably
close to standard normal in a wide range of scenarios while being conservative
at the tails, validating voxelwise hypothesis testing based on standardized
scores. To address standardization in spatially heterogeneous image data, we
propose a spatial and robust multivariate expectation-maximization (EM)
algorithm, where prior class membership probabilities are provided by
transformation of spatial probability template maps and the estimation of the
class mean and covariances are robust to outliers. Simulations in both
univariate and bivariate cases suggest that standardized scores with soft
assignment have tail probabilities that are either very close to or more
conservative than standard normal. The proposed methods are applied to a real
data set from a PET phantom experiment, yet they are generic and can be used in
other contexts
Trimmed Density Ratio Estimation
Density ratio estimation is a vital tool in both machine learning and
statistical community. However, due to the unbounded nature of density ratio,
the estimation procedure can be vulnerable to corrupted data points, which
often pushes the estimated ratio toward infinity. In this paper, we present a
robust estimator which automatically identifies and trims outliers. The
proposed estimator has a convex formulation, and the global optimum can be
obtained via subgradient descent. We analyze the parameter estimation error of
this estimator under high-dimensional settings. Experiments are conducted to
verify the effectiveness of the estimator.Comment: Made minor revisions. Restructured the introductory section
On default priors for robust Bayesian estimation with divergences
This paper presents objective priors for robust Bayesian estimation against
outliers based on divergences. The minimum -divergence estimator is
well-known to work well estimation against heavy contamination. The robust
Bayesian methods by using quasi-posterior distributions based on divergences
have been also proposed in recent years. In objective Bayesian framework, the
selection of default prior distributions under such quasi-posterior
distributions is an important problem. In this study, we provide some
properties of reference and moment matching priors under the quasi-posterior
distribution based on the -divergence. In particular, we show that the
proposed priors are approximately robust under the condition on the
contamination distribution without assuming any conditions on the contamination
ratio. Some simulation studies are also presented.Comment: 22page
The effect of immigration along the distribution of wages
This paper analyses the effect immigration has on wages of native workers. Unlike most previous work, we estimate wage effects along the distribution of wages. We derive a flexible empirical strategy that does not rely on pre-allocating immigrants to particular skill groups. In our empirical analysis, we demonstrate that immigrants downgrade considerably upon arrival. As for the effects on native wages, we find that immigration depresses wages below the 20th percentile of the wage distribution, but leads to slight wage increases in the upper part of the wage
distribution. The overall wage effect of immigration is slightly positive. The positive wage effects we find are, although modest, too large to be explained by an
immigration surplus. We suggest alternative explanations, based on the idea that immigrants are paid less than the value of what they contribute to production, generating therefore a surplus, and we assess the magnitude of these effects
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