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The conditionality principle $C$ plays a key role in attempts to characterize the concept of statistical evidence. The standard version of $C$ considers a model and a derived conditional model, formed by conditioning on an ancillary…
We consider a simple approach for approximating detailed information about the conditional distribution of a real-valued response variable, given values for its covariates, using only the outputs from a standard regression model. We…
Prediction models trained under the source distribution do not generalize well to a different target distribution. A valid inference about an unseen data distribution must be anchored by the invariance of certain causal mechanisms that…
Let $\exp[x_0,x_1,\dots,x_n]$ denote the divided difference of the exponential function. (i) We prove that exponential divided differences are log-submodular. (ii) We establish the four-point inequality $…
Motivated by investigating spatio-temporal patterns of the distribution of continuous variables, we consider describing the conditional distribution function of the response variable incorporating spatio-temporal components given…
In multiple classification, one aims to determine whether a testing sequence is generated from the same distribution as one of the M training sequences or not. Unlike most of existing studies that focus on discrete-valued sequences with…
The Weibull distribution is a very applicable model for the lifetime data. In this paper, we have investigated inference on the parameters of Weibull distribution based on record values. We first propose a simple and exact test and a…
We consider inference on a scalar regression coefficient under a constraint on the magnitude of the control coefficients. A class of estimators based on a regularized propensity score regression is shown to exactly solve a tradeoff between…
One goal of statistical privacy research is to construct a data release mechanism that protects individual privacy while preserving information content. An example is a {\em random mechanism} that takes an input database $X$ and outputs a…
A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…
We examine the extent to which sublinear-sample property testing and estimation apply to settings where samples are independently but not identically distributed. Specifically, we consider the following distributional property testing…
Large-scale datasets are increasingly being used to inform decision making. While this effort aims to ground policy in real-world evidence, challenges have arisen as selection bias and other forms of distribution shifts often plague…
Bayes factors are characterized by both the powerful mathematical framework of Bayesian statistics and the useful interpretation as evidence quantification. Former requires a parameter distribution that changes by seeing the data, latter…
In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function.…
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…
In the setting of dominated statistical models, we provide conditions yielding strong continuity of the posterior distribution with respect to the observed data. We show some applications, with special focus on exponential models.
A random variable is equi-dispersed if its mean equals its variance. A Poisson distribution is a classical example of this phenomenon. However, a less well-known fact is that the class of normal densities that are equi-dispersed constitutes…
In this paper we study the exponential decay of posterior probability of a set of sources and conditioning by rare sources for both uniform and general prior distributions of sources. The decay rate is determined by $L$-divergence and rare…
The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting…
Model diagnostics and forecast evaluation are two sides of the same coin. A common principle is that fitted or predicted distributions ought to be calibrated or reliable, ideally in the sense of auto-calibration, where the outcome is a…