Related papers: Sensitivity analysis, multilinearity and beyond
The number of modes in a probability density function is representative of the complexity of a model and can also be viewed as the number of subpopulations. Despite its relevance, there has been limited research in this area. A novel…
Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…
In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a…
Matching is one of the most widely used study designs for adjusting for measured confounders in observational studies. However, unmeasured confounding may exist and cannot be removed by matching. Therefore, a sensitivity analysis is…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…
This paper considers the problem of learning the parameters in Bayesian networks of discrete variables with known structure and hidden variables. Previous approaches in these settings typically use expectation maximization; when the network…
This paper presents a Bayesian parameter estimation approach and identifiability analysis for a lithium-ion battery model, to determine the uniqueness, evaluate the sensitivity and quantify the uncertainty of a subset of the model…
Sensitivity analysis is an important part of a mathematical modeller's toolbox for model analysis. In this review paper, we describe the most frequently used sensitivity techniques, discussing their advantages and limitations, before…
Parameter sensitivity analysis is a powerful tool in the building and analysis of biochemical network models. For stochastic simulations, parameter sensitivity analysis can be computationally expensive, requiring multiple simulations for…
We show an alternative way of representing a Bayesian belief network by sensitivities and probability distributions. This representation is equivalent to the traditional representation by conditional probabilities, but makes dependencies…
Sensitivity analysis is popular in dealing with missing data problems particularly for non-ignorable missingness. It analyses how sensitively the conclusions may depend on assumptions about missing data e.g. missing data mechanism (MDM). We…
Sensitivity analysis is concerned with understanding how the model output depends on uncertainties (variances) in inputs and then identifies which inputs are important in contributing to the prediction imprecision. Uncertainty determination…
In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
We present an exact approach to analyze and quantify the sensitivity of higher moments of probabilistic loops with symbolic parameters, polynomial arithmetic and potentially uncountable state spaces. Our approach integrates methods from…
We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…
Despite their theoretical importance, dynamic Bayesian networks associated with quantum processes are currently not accessible experimentally. We here describe a general scheme to determine the multi-time path probability of a Bayesian…
A Bayesian belief network models a joint distribution with an directed acyclic graph representing dependencies among variables and network parameters characterizing conditional distributions. The parameters are viewed as random variables to…