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A new, model dependent way of uncovering some of the values of the underlying GMSB parameters is proposed. This method is faster than the existing procedures and once enough luminosity is available, can be used to check the consistency of…
Linear structural equation models, which relate random variables via linear interdependencies and Gaussian noise, are a popular tool for modeling multivariate joint distributions. These models correspond to mixed graphs that include both…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
Identifiability describes the possibility of determining the values of the unknown parameters that characterize a dynamic system from the knowledge of its inputs and outputs. This paper finds the general analytical condition that fully…
The data drawn from biological, economic, and social systems are often confounded due to the presence of unmeasured variables. Prior work in causal discovery has focused on discrete search procedures for selecting acyclic directed mixed…
Misspecifications (i.e. errors on the parameters) of state space models lead to incorrect inference of the hidden states. This paper studies weakly nonlin-ear state space models with additive Gaussian noises and proposes a method for…
Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer most times from paucity of data, while they may…
Poyiadjis et al. (2011) show how particle methods can be used to estimate both the score and the observed information matrix for state space models. These methods either suffer from a computational cost that is quadratic in the number of…
Mathematical modelling is a widely used approach to understand and interpret clinical trial data. This modelling typically involves fitting mechanistic mathematical models to data from individual trial participants. Despite the widespread…
In this paper, we present a simple non-parametric method for learning the structure of undirected graphs from data that drawn from an underlying unknown distribution. We propose to use Brownian distance covariance to estimate the…
Structural identifiability is an important property of parametric ODE models. When conducting an experiment and inferring the parameter value from the time-series data, we want to know if the value is globally, locally, or non-identifiable.…
Modern distributed cyber-physical systems (CPSs) encounter a large variety of physical faults and cyber anomalies and in many cases, they are vulnerable to catastrophic fault propagation scenarios due to strong connectivity among the…
This paper is concerned with black-box identification of nonlinear state space models. By using a basis function expansion within the state space model, we obtain a flexible structure. The model is identified using an expectation…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…
We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…
We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal…
Algebraic statistics is a recently evolving field, where one would treat statistical models as algebraic objects and thereby use tools from computational commutative algebra and algebraic geometry in the analysis and computation of…
Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical…
Physics models typically contain adjustable parameters to reproduce measured data. While some parameters correspond directly to measured features in the data, others are unobservable. These unobservables can, in some cases, cause…
This paper proposes an information-based inference method for partially identified parameters in incomplete models that is valid both when the model is correctly specified and when it is misspecified. Key features of the method are: (i) it…