Related papers: Parameter identifiability and input-output equatio…
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…
Mechanistic mathematical models of biological systems usually contain a number of unknown parameters whose values need to be estimated from available experimental data in order for the models to be validated and used to make quantitative…
How to make a dynamic system unidentifiable is an important but still open issue. It not only requires that the parameters of the systems but also the equivalent systems cannot be identified by any identification approaches. Thus, it is a…
In this note, we propose a novel approach for a class of autonomous dynamical systems that allows, given some observations of the solutions, to identify its parameters and reconstruct the state vector. This approach relies on proving the…
The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…
The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices. For infinite state systems, however, the situation is different: in…
The paper is concerned with inference for a parameter of interest in models that share a common interpretation for that parameter but that may differ appreciably in other respects. We study the general structure of models under which the…
An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable,…
Existing methods for differentiable structure learning in discrete data typically assume that the data are generated from specific structural equation models. However, these assumptions may not align with the true data-generating process,…
The paper gives an overview of recent advances in structural equation modeling. A structural equation model is a multivariate statistical model that is determined by a mixed graph, also known as a path diagram. Our focus is on the…
This paper establishes fundamental results for statistical inference of diagnostic classification models (DCM). The results are developed at a high level of generality, applicable to essentially all diagnostic classification models. In…
Choosing a suitable model and determining its associated parameters from fitting to experimental data is fundamental for many problems in biomechanics. Models of shear-thinning complex fluids, dating from the work of Bird, Carreau, Cross…
Mathematical models are invaluable for understanding and predicting how biological systems behave, although their construction requires specifying mechanisms and relationships that are often not perfectly known. In the presence of multiple…
The problem of identifiability of finite mixtures of finite product measures is studied. A mixture model with $K$ mixture components and $L$ observed variables is considered, where each variable takes its value in a finite set with…
Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
The outlying property detection problem is the problem of discovering the properties distinguishing a given object, known in advance to be an outlier in a database, from the other database objects. In this paper, we analyze the problem…
Structural and practical parameter non-identifiability issues are common when mathematical models are used to interpret data. Such issues motivate model reparameterisation and reduction methods. Here, we consider Invariant Image…
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 missing-data mechanism is NMAR or non-ignorable, missingness is itself vital information and it must be taken into the likelihood, which, however, needs to introduce additional parameters to be estimated. The incompleteness of the…