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Recently, several researchers have claimed that conclusions obtained from a Bayes factor (or the posterior odds) may contradict those obtained from Bayesian posterior estimation. In this short paper, we wish to point out that no such…

Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The…

In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen at…

Causal inference is widely used in various fields, such as biology, psychology and economics, etc. In observational studies, we need to balance the covariates before estimating causal effect. This study extends the one-dimensional entropy…

The problem of individualization is recognized as crucial in almost every field. Identifying causes of effects in specific events is likewise essential for accurate decision making. However, such estimates invoke counterfactual…

Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only…

Causal models communicate our assumptions about causes and effects in real-world phe- nomena. Often the interest lies in the identification of the effect of an action which means deriving an expression from the observed probability…

The bifactor model and its extensions are multidimensional latent variable models, under which each item measures up to one subdimension on top of the primary dimension(s). Despite their wide applications to educational and psychological…

This study presents a mathematical model formulated as a system of first-order non-linear ordinary differential equations, aimed at examining the effects of different factors, classified as local and systemic factors on a wound healing…

In social science researches, causal inference regarding peer effects often faces significant challenges due to homophily bias and contextual confounding. For example, unmeasured health conditions (e.g., influenza) and psychological states…

Observational studies of causal effects require adjustment for confounding factors. In the tabular setting, where these factors are well-defined, separate random variables, the effect of confounding is well understood. However, in public…

We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case-control studies. Graphical models represent assumptions about the…

Learning about cause and effect is arguably the main goal in applied econometrics. In practice, the validity of these causal inferences is contingent on a number of critical assumptions regarding the type of data that has been collected and…

Estimating causal effects from observational data (at either an individual -- or a population -- level) is critical for making many types of decisions. One approach to address this task is to learn decomposed representations of the…

We investigate the estimation of the causal effect of a treatment variable on an outcome in the presence of a latent confounder. We first show that the causal effect is identifiable under certain conditions when data is available from…

We study the informational content of factor structures in discrete triangular systems. Factor structures have been employed in a variety of settings in cross sectional and panel data models, and in this paper we formally quantify their…

Understanding the relationship between brain activity and behavior is a central goal of neuroscience. Despite significant advances, a fundamental dichotomy persists: neural activity manifests as both discrete spikes of individual neurons…

We show that it is possible to understand and identify a decision maker's subjective causal judgements by observing her preferences over interventions. Following Pearl [2000], we represent causality using causal models (also called…

We consider the problem of assessing whether, in an individual case, there is a causal relationship between an observed exposure and a response variable. When data are available on similar individuals we may be able to estimate prospective…

Factor analysis models explain dependence among observed variables by a smaller number of unobserved factors. A main challenge in confirmatory factor analysis is determining whether the factor loading matrix is identifiable from the…