Related papers: Information Criteria Fail for Dynamical Systems: S…
Many statistical models are given in the form of non-normalized densities with an intractable normalization constant. Since maximum likelihood estimation is computationally intensive for these models, several estimation methods have been…
A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…
We formulate and analyze a general class of stochastic dynamic games with asymmetric information arising in dynamic systems. In such games, multiple strategic agents control the system dynamics and have different information about the…
We propose information criteria that measure the prediction risk of a predictive density based on the Bayesian marginal likelihood from a frequentist point of view. We derive criteria for selecting variables in linear regression models,…
Uncertainty around multimodel ensemble forecasts of changes in future climate reduces the accuracy of those forecasts. For very uncertain forecasts this effect may mean that the forecasts should not be used. We investigate the use of the…
Accurate model selection is a fundamental requirement for statistical analysis. In many real-world applications of graphical modelling, correct model structure identification is the ultimate objective. Standard model validation procedures…
Model selection is crucial to high-dimensional learning and inference for contemporary big data applications in pinpointing the best set of covariates among a sequence of candidate interpretable models. Most existing work assumes implicitly…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
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…
In a Gaussian graphical model, the conditional independence between two variables are characterized by the corresponding zero entries in the inverse covariance matrix. Maximum likelihood method using the smoothly clipped absolute deviation…
Efficient and accurate learning of constitutive laws is crucial for accurately predicting the mechanical behavior of materials under complex loading conditions. Accurate model calibration hinges on a delicate interplay between the…
The Bayesian measure of sample information about the parameter, known as Lindley's measure, is widely used in various problems such as developing prior distributions, models for the likelihood functions and optimal designs. The predictive…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
AI systems are often used to make or contribute to important decisions in a growing range of applications, including criminal justice, hiring, and medicine. Since these decisions impact human lives, it is important that the AI systems act…
To determine the exact shape of the luminosity function (LF) of galaxies is one of the central problems in galactic astronomy and observational cosmology. The most popular method to estimate the LF is maximum likelihood, which is clearly…
The purpose of this article is to look at how information criteria, such as AIC and BIC, relate to the g%SD fit criterion derived in Waddell et al. (2007, 2010a). The g%SD criterion measures the fit of data to model based on a normalized…
This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…
Models with fewer parameters are often easier to interpret and more robust. Parsimony can be achieved through optimizing objectives like the AIC or BIC, which are functions of the the number of free parameters in the model. Optimizing this…
We investigate a selection-mutation model for the dynamics of technological innovation,a special case of reaction-diffusion equations. Although mutations are assumed to increase the variety of technologies, not their average success…
Complex dynamical systems, from macromolecules to ecosystems, are often modeled by stochastic differential equations. To learn such models from data, a common approach involves sparse selection among a large function library. However, we…