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Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean-shift model, we introduce a…
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
We describe a Bayesian framework for estimating the time-domain noise covariance of CMB observations, typically parametrized in terms of a 1/f frequency profile. This framework is based on the Gibbs sampling algorithm, which allows for…
Compressed sensing (CS) is on recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior and digital quantization of the measurement data is inevitable in practical implementation of CS…
The problem of estimating the support of a distribution is of great importance in many areas of machine learning, computer science, physics and biology. Most of the existing work in this domain has focused on settings that assume perfectly…
This paper investigates the accuracy of bootstrap-based bias correction of persistence measures for long memory fractionally integrated processes. The bootstrap method is based on the semi-parametric sieve approach, with the dynamics in the…
This article explores combinations of weighted bootstraps, like the Bayesian bootstrap, with the bootstrap $t$ method for setting approximate confidence intervals for the mean of a random variable in small samples. For this problem the…
We show that, when the double bootstrap is used to improve performance of bootstrap methods for bias correction, techniques based on using a single double-bootstrap sample for each single-bootstrap sample can be particularly effective. In…
We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…
Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators.…
Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample…
Parametric empirical Bayes (EB) estimators have been widely used in variety of fields including small area estimation, disease mapping. Since EB estimator is constructed by plugging in the estimator of parameters in prior distributions, it…
The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…
Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…
Sparse model identification enables nonlinear dynamical system discovery from data. However, the control of false discoveries for sparse model identification is challenging, especially in the low-data and high-noise limit. In this paper, we…
Machine learning models achieve state-of-the-art performance on many supervised learning tasks. However, prior evidence suggests that these models may learn to rely on shortcut biases or spurious correlations (intuitively, correlations that…
A new computation method of frequentist $p$-values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is…
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…
Statistical multispecies models of multiarea marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance…