Related papers: Lower Bounds on the Bayesian Risk via Information …
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…
We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…
Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…
Boosting methods are widely used in statistical learning to deal with high-dimensional data due to their variable selection feature. However, those methods lack straightforward ways to construct estimators for the precision of the…
We address the problem of integrating data from multiple, possibly biased, observational and interventional studies, to eventually compute counterfactuals in structural causal models. We start from the case of a single observational dataset…
Analysis of competing risks data plays an important role in the lifetime data analysis. Recently Feizjavadian and Hashemi (Computational Statistics and Data Analysis, vol. 82, 19-34, 2015) provided a classical inference of a competing risks…
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…
The aim of this article is to make a contribution to the Bayesian procedure of testing precise hypotheses for parametric models. For this purpose, we define the Bayesian Discrepancy Measure that allows one to evaluate the suitability of a…
We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But in contrast to mutual…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
We propose a new method for parameter learning in Bayesian networks with qualitative influences. This method extends our previous work from networks of binary variables to networks of discrete variables with ordered values. The specified…
The problem how to approximately determine the absolute value of the Fisher information measure for a general parametric probabilistic system is considered. Having available the first and second moment of the system output in a parametric…
Experiments on decision making under uncertainty are known to display a classical pattern of risk aversion and risk seeking referred to as "fourfold pattern" (or "reflection effect") , but recent experiments varying the speed and order of…
We revisit the problem of asymmetric binary hypothesis testing against a composite alternative hypothesis. We introduce a general framework to treat such problems when the alternative hypothesis adheres to certain axioms. In this case we…
Accurately estimating the informativeness of individual samples in a dataset is an important objective in deep learning, as it can guide sample selection, which can improve model efficiency and accuracy by removing redundant or potentially…
A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences…
In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar…
Ideally, a meta-analysis will summarize data from several unbiased studies. Here we consider the less than ideal situation in which contributing studies may be compromised by measurement error. Measurement error affects every study design,…
The mutual information between two jointly distributed random variables $X$ and $Y$ is a functional of the joint distribution $P_{XY},$ which is sometimes difficult to handle or estimate. A coarser description of the statistical behavior of…
Randomized benchmarking (RB) protocols are standard tools for characterizing quantum devices. Prior analyses of RB protocols have not provided a complete method for analyzing realistic data, resulting in a variety of ad-hoc methods. The…