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Abstract Bayesian hierarchical models allow ecologists to account for uncertainty and make inference at multiple scales. However, hierarchical models are often computationally intensive to fit, especially with large datasets, and researchers face trade‐offs between capturing ecological complexity in statistical models and implementing these models.We present a recursive Bayesian computing (RB) method that can be used to fit Bayesian models efficiently in sequential MCMC stages to ease computation and streamline hierarchical inference. We also introduce transformation‐assisted RB (TARB) to create unsupervised MCMC algorithms and improve interpretability of parameters. We demonstrate TARB by fitting a hierarchical animal movement model to obtain inference about individual‐ and population‐level migratory characteristics.Our recursive procedure reduced computation time for fitting our hierarchical movement model by half compared to fitting the model with a single MCMC algorithm. We obtained the same inference fitting our model using TARB as we obtained fitting the model with a single algorithm.For complex ecological statistical models, like those for animal movement, multi‐species systems, or large spatial and temporal scales, the computational demands of fitting models with conventional computing techniques can limit model specification, thus hindering scientific discovery. Transformation‐assisted RB is one of the most accessible methods for reducing these limitations, enabling us to implement new statistical models and advance our understanding of complex ecological phenomena.
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Multi-fidelity Monte Carlo: a pseudo-marginal approach
Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in apply- ing MCMC to scientific domains is computation: the target density of interest is often a function of expensive computations, such as a high-fidelity physical simulation, an intractable integral, or a slowly-converging iterative algorithm. Thus, using an MCMC algorithms with an expensive target density becomes impractical, as these expensive computations need to be evaluated at each iteration of the algorithm. In practice, these computations often approximated via a cheaper, low- fidelity computation, leading to bias in the resulting target density. Multi-fidelity MCMC algorithms combine models of varying fidelities in order to obtain an ap- proximate target density with lower computational cost. In this paper, we describe a class of asymptotically exact multi-fidelity MCMC algorithms for the setting where a sequence of models of increasing fidelity can be computed that approximates the expensive target density of interest. We take a pseudo-marginal MCMC approach for multi-fidelity inference that utilizes a cheaper, randomized-fidelity unbiased estimator of the target fidelity constructed via random truncation of a telescoping series of the low-fidelity sequence of models. Finally, we discuss and evaluate the proposed multi-fidelity MCMC approach on several applications, including log-Gaussian Cox process modeling, Bayesian ODE system identification, PDE-constrained optimization, and Gaussian process parameter inference.
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- PAR ID:
- 10470413
- Publisher / Repository:
- Advances in Neural Information Processing Systems (NeurIPS)
- Date Published:
- Format(s):
- Medium: X
- Location:
- New Orleans, LA
- Sponsoring Org:
- National Science Foundation
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