相关论文: Directionally collapsible parameterizations of mul…

We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study…

The standard odds ratio of logistic regression is foundational but limited to individual explanatory variables. This work derives a multivariable odds ratio that applies to all the explanatory variables in all their combinations.

The two envelopes paradox is discussed. By calculating the conditional probability, we arrive at a conditional expectations which differs from existing results.

The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open…

Unmeasured confounding is a threat to causal inference and gives rise to biased estimates. In this article, we consider the problem of individualized decision-making under partial identification. Firstly, we argue that when faced with…

For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…

We obtain an analytic expression for the full distribution of conductance for a strongly disordered three dimensional conductor within a perturbative approach based on the transfer-matrix formulation. Our results confirm numerical evidence…

Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…

Many existing approaches for estimating parameters in settings with distributional shifts operate under an invariance assumption. For example, under covariate shift, it is assumed that $p(y|x)$ remains invariant. We refer to such…

It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals.…

Causal parameters may not be point identified in the presence of unobserved confounding. However, information about non-identified parameters, in the form of bounds, may still be recovered from the observed data in some cases. We develop a…

We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…

In this pedagogical text aimed at those wanting to start thinking about or brush up on probabilistic inference, I review the rules by which probability distribution functions can (and cannot) be combined. I connect these rules to the…

Let F be a field of characteristic p. We define and investigate nonassociative differential extensions of F and of a central simple division algebra over F and give a criterium for these algebras to be division. As special cases, we obtain…

We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…

Bidirectional causal relationships arising from mutual interactions between variables are commonly observed within biomedical, econometrical, and social science contexts. When such relationships are further complicated by unobserved…

Distinguishing between uniform and non-uniform sample distributions is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. By merging directional statistics…

Changes of variables giving the dual model are constructed explicitly for sigma-models without isotropy. In particular, the jacobian is calculated to give the known results. The global aspects of the abelian case as well as some of those of…

An explanation to Lord's paradox using ordinary least square regression models is given. It is not a paradox at all, if the regression parameters are interpreted as predictive or as causal with stricter conditions and be aware of laws of…

We consider in this paper the semiparametric mixture of two distributions equal up to a shift parameter. The model is said to be semiparametric in the sense that the mixed distribution is not supposed to belong to a parametric family. In…