Related papers: A general theory of identification
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
Mathematical models are routinely applied to interpret biological data, with common goals that include both prediction and parameter estimation. A challenge in mathematical biology, in particular, is that models are often complex and…
When a machine-learning algorithm makes biased decisions, it can be helpful to understand the sources of disparity to explain why the bias exists. Towards this, we examine the problem of quantifying the contribution of each individual…
The identifiability problem for interventions aims at assessing whether the total effect of some given interventions can be written with a do-free formula, and thus be computed from observational data only. We study this problem,…
Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. While existing approaches analyze these phenomena in…
We introduce a class of linear compartmental models called identifiable path/cycle models which have the property that all of the monomial functions of parameters associated to the directed cycles and paths from input compartments to output…
The degree to which subjects differ from each other with respect to certain properties measured by a set of variables, plays an important role in many statistical methods. For example, classification, clustering, and data visualization…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
Nonparametric item response models provide a flexible framework in psychological and educational measurements. Douglas (2001) established asymptotic identifiability for a class of models with nonparametric response functions for long…
Wigner found unreasonable the "effectiveness of mathematics in the natural sciences". But if the mathematics we use to describe nature is simply a coded expression of our experience then its effectiveness is quite reasonable. Its…
In this review, we recall the concepts of Identifiability and Observability of dynamical systems, and analyse them in the framework of Mathematical Epidemiology. We show that, even for simple and well known models of the literature, these…
Statistical sufficiency formalizes the notion of data reduction. In the decision theoretic interpretation, once a model is chosen all inferences should be based on a sufficient statistic. However, suppose we start with a set of procedures…
Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms.…
Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as…
The random utility model is known to be unidentified, but there are times when the model admits a unique representation. We offer two characterizations for the existence of a unique random utility representation. Our first characterization…
Model theoretic internality provides conditions under which the group of automorphisms of a model over a reduct is itself a definable group. In this paper we formulate a categorical analogue of the condition of internality, and prove an…
Missing data problems arise in many applied research studies. They may jeopardize statistical inference of the model of interest, if the missing mechanism is nonignorable, that is, the missing mechanism depends on the missing values…
Controversy about the significance of underdetermination of theories persists in the philosophy and conduct of science. The issue has practical import when research is used to inform decision making, because scientific uncertainty yields…
Unobserved confounding is a fundamental obstacle to establishing valid causal conclusions from observational data. Two complementary types of approaches have been developed to address this obstacle: obtaining identification using fortuitous…
In designed experiments and surveys, known laws or design feat ures provide checks on the most relevant aspects of a model and identify the target parameters. In contrast, in most observational studies in the health and social sciences, the…