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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…
In statistical exercises where there are several candidate models, the traditional approach is to select one model using some data driven criterion and use that model for estimation, testing and other purposes, ignoring the variability of…
Frequentist statistical methods, such as hypothesis testing, are standard practice in papers that provide benchmark comparisons. Unfortunately, these methods have often been misused, e.g., without testing for their statistical test…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
While there have been a lot of recent developments in the context of Bayesian model selection and variable selection for high dimensional linear models, there is not much work in the presence of change point in literature, unlike the…
The long duration of the COVID-19 pandemic allowed for multiple bursts in the infection and death rates, the so-called epidemic waves. This complex behavior is no longer tractable by simple compartmental model and requires more…
We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general…
We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…
Evidence accumulation models (EAMs) are an important class of cognitive models used to analyze both response time and response choice data recorded from decision-making tasks. Developments in estimation procedures have helped EAMs become…
The use of moving averages is pervasive in macroeconomic monitoring, particularly for tracking noisy series such as inflation. The choice of the look-back window is crucial. Too long of a moving average is not timely enough when faced with…
The Drift-Diffusion Model (DDM) is widely used in neuropsychological studies to understand the decision process by incorporating both reaction times and subjects' responses. Various models have been developed to estimate DDM parameters,…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from…
The Bayesian statistical paradigm provides a principled and coherent approach to probabilistic forecasting. Uncertainty about all unknowns that characterize any forecasting problem -- model, parameters, latent states -- is able to be…
Mathematical modeling with Ordinary Differential Equations (ODEs) has proven to be extremely successful in a variety of fields, including biology. However, these models are completely deterministic given a certain set of initial conditions.…
The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…
Agent-Based Models (ABM) are computational scenario-generators, which can be used to predict the possible future outcomes of the complex system they represent. To better understand the robustness of these predictions, it is necessary to…
Insurance products frequently cover significant claims arising from a variety of sources. To model losses from these products accurately, actuarial models must account for high-severity claims. A widely used strategy is to apply a mixture…
The posterior in probabilistic programs with stochastic support decomposes as a weighted sum of the local posterior distributions associated with each possible program path. We show that making predictions with this full posterior…
When sample data are governed by an unknown sequence of independent but possibly non-identical distributions, the data-generating process (DGP) in general cannot be perfectly identified from the data. For making decisions facing such…