Related papers: Identifiability of linear compartmental tree model…
In this paper, we address the problem of identifying linear structural equation models. We first extend the edge set half-trek criterion to cover a broader class of models. We then show that any semi-Markovian linear model can be…
Identifiability is a crucial property for a statistical model since distributions in the model uniquely determine the parameters that produce them. In phylogenetics, the identifiability of the tree parameter is of particular interest since…
Inference of evolutionary trees and rates from biological sequences is commonly performed using continuous-time Markov models of character change. The Markov process evolves along an unknown tree while observations arise only from the tips…
Identifiability of the discrete tree parameter is a key property for phylogenetic models since it is necessary for statistically consistent estimation of the tree from sequence data. Algebraic methods have proven to be very effective at…
Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are…
Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the…
Mixtures of ranking models are standard tools for ranking problems. However, even the fundamental question of parameter identifiability is not fully understood: the identifiability of a mixture model with two Bradley-Terry-Luce (BTL)…
In this paper, we consider to what degree the structure of a linear system is determined by the system's input/output behavior. The structure of a linear system is a directed graph where the vertices represent the variables in the system…
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…
By taking into account the nonlinear effect of the cause, the inner noise effect, and the measurement distortion effect in the observed variables, the post-nonlinear (PNL) causal model has demonstrated its excellent performance in…
Hierarchical Latent Attribute Models (HLAMs) are a family of discrete latent variable models that are attracting increasing attention in educational, psychological, and behavioral sciences. The key ingredients of an HLAM include a binary…
What does it mean to say that a quantity is identifiable from the data? Statisticians seem to agree on a definition in the context of parametric statistical models --- roughly, a parameter $\theta$ in a model $\mathcal{P} = \{P_\theta:…
Differential equation models are crucial to scientific processes. The values of model parameters are important for analyzing the behaviour of solutions. A parameter is called globally identifiable if its value can be uniquely determined…
We indicate a way of distinguishing between structures, for which, two structures are said to be separable.Being separable implies being non-isomorphic. We show that for any first order theory $T$ in a countable language, if it has an…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…
In this paper, an original result in terms of a sufficient condition to test identifiability of nonlinear delayed-differential models with constant delays and multi-inputs is given. The identifiability is studied for the linearized system…
Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…
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…
Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node's neighbors, instead of the…