Related papers: Data-dependent probability matching priors for emp…
We generalize the notion of consequence relation standard in abstract treatments of logic to accommodate intuitions of relevance. The guiding idea follows the \emph{use criterion}, according to which in order for some premises to have some…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical…
The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
For many interesting tasks, such as medical diagnosis and web page classification, a learner only has access to some positively labeled examples and many unlabeled examples. Learning from this type of data requires making assumptions about…
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
By probabilistic logic I mean a normative theory of belief that explains how a body of evidence affects one's degree of belief in a possible hypothesis. A new axiomatization of such a theory is presented which avoids a finite additivity…
Randomization tests are based on a re-randomization of existing data to gain data-dependent critical values that lead to exact hypothesis tests under special circumstances. However, it is not always possible to re-randomize data in…
An agent often has a number of hypotheses, and must choose among them based on observations, or outcomes of experiments. Each of these observations can be viewed as providing evidence for or against various hypotheses. All the attempts to…
Maximum likelihood estimation has been extensively used in the joint analysis of repeated measurements and survival time. However, there is a lack of theoretical justification of the asymptotic properties for the maximum likelihood…
In an empirical Bayesian setting, we provide a new multiple testing method, useful when an additional covariate is available, that influences the probability of each null hypothesis being true. We measure the posterior significance of each…
In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…
In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…
An informative sampling design leads to unit inclusion probabilities that are correlated with the response variable of interest. However, multistage sampling designs may also induce higher order dependencies, which are typically ignored in…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
Two data-dependent information metrics are developed to quantify the information of the prior and likelihood functions within a parametric Bayesian model, one of which is closely related to the reference priors from Berger, Bernardo, and…
In this paper we use e-values in the context of multiple hypothesis testing assuming that the base tests produce independent, or sequential, e-values. Our simulation and empirical studies and theoretical considerations suggest that, under…
Identifying causal relationships from observation data is difficult, in large part, due to the presence of hidden common causes. In some cases, where just the right patterns of conditional independence and dependence lie in the data---for…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…