Patrick Conrad

Patrick Conrad
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Statistics - Methodology (3)
 
Statistics - Applications (2)
 
Statistics - Computation (2)
 
Mathematics - Numerical Analysis (1)
 
Computer Science - Artificial Intelligence (1)
 
Computer Science - Numerical Analysis (1)

Publications Authored By Patrick Conrad

Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of partial differential equations. In recent work [Conrad et al. JASA 2015, arXiv:1402. Read More

In this paper, we present a formal quantification of epistemic uncertainty induced by numerical solutions of ordinary and partial differential equation models. Numerical solutions of differential equations contain inherent uncertainties due to the finite dimensional approximation of an unknown and implicitly defined function. When statistically analysing models based on differential equations describing physical, or other naturally occurring, phenomena, it is therefore important to explicitly account for the uncertainty introduced by the numerical method. Read More

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis-Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler's exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. Read More

This work presents Drake, a dynamic executive for temporal plans with choice. Dynamic plan execution strategies allow an autonomous agent to react quickly to unfolding events, improving the robustness of the agent. Prior work developed methods for dynamically dispatching Simple Temporal Networks, and further research enriched the expressiveness of the plans executives could handle, including discrete choices, which are the focus of this work. Read More

Polynomial approximations of computationally intensive models are central to uncertainty quantification. This paper describes an adaptive method for non-intrusive pseudospectral approximation, based on Smolyak's algorithm with generalized sparse grids. We rigorously analyze and extend the non-adaptive method proposed in [6], and compare it to a common alternative approach for using sparse grids to construct polynomial approximations, direct quadrature. Read More