Related papers: Reformulating Confidence as Extended Likelihood
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
The geometric formulation of fiducial probability employed in this paper is an improvement over the usual pivotal quantity formulation. For a single parameter and single observation, the new formulation is based on the geometric properties…
Critical exponent $\eta$ for three-dimensional systems with $n$-vector order parameter is evaluated in the frame of pseudo-$\epsilon$ expansion approach. Pseudo-$\epsilon$ expansion ($\tau$-series) for $\eta$ found up to $\tau^7$ term for…
Bayesian, frequentist and fiducial (BFF) inferences are much more congruous than they have been perceived historically in the scientific community (cf., Reid and Cox 2015; Kass 2011; Efron 1998). Most practitioners are probably more…
Don Fraser has given an interesting account of the agreements and disagreements between Bayesian posterior probabilities and confidence levels. In this comment I discuss some cases where the lack of such agreement is extreme. I then discuss…
Fisher's exact test is often a preferred method to estimate the significance of statistical dependence. However, in large data sets the test is usually too worksome to be applied, especially in an exhaustive search (data mining). The…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
Confidence sets based on sparse estimators are shown to be large compared to more standard confidence sets, demonstrating that sparsity of an estimator comes at a substantial price in terms of the quality of the estimator. The results are…
We propose a rigorous decomposition of predictive error, highlighting that not all 'irreducible' error is genuinely immutable. Many domains stand to benefit from iterative enhancements in measurement, construct validity, and modeling. Our…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
In an earlier paper [Rational choice and AGM belief revision, Artificial Intelligence, 2009] a correspondence was established between the choice structures of revealed-preference theory (developed in economics) and the syntactic belief…
The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…
In this paper, we develop an approach for optimizing the explicit binomial confidence interval recently derived by Chen et al. The optimization reduces conservativeness while guaranteeing prescribed coverage probability.
Belief revision is an operation that aims at modifying old beliefs so that they become consistent with new ones. The issue of belief revision has been studied in various formalisms, in particular, in qualitative algebras (QAs) in which the…
This article extends the scope of empirical likelihood methodology in three directions: to allow for plug-in estimates of nuisance parameters in estimating equations, slower than $\sqrt{n}$-rates of convergence, and settings in which there…
I proposed (8, 1, 3) that p values should be supplemented by an estimate of the false positive risk (FPR). FPR was defined as the probability that, if you claim that there is a real effect on the basis of p value from a single unbiased…
First a few reformulations of Frankl's conjecture are given, in terms of reduced families or matrices, or analogously in terms of lattices. These lead naturally to a stronger conjecture with a neat formulation which might be easier to…
A new method is proposed for the correction of confidence intervals when the original interval does not have the correct nominal coverage probabilities in the frequentist sense. The proposed method is general and does not require any…
Traditional logic-based belief revision research focuses on designing rules to constrain the behavior of revision operators. Frameworks have been proposed to characterize iterated revision rules, but they are often too loose, leading to…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…