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Register a new userConstraining subglacial processes from surface velocity observations using surrogate-based Bayesian inference
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Basal motion is the primary mechanism for ice flux outside Antarctica, yet a widely applicable model for predicting it in the absence of retrospective observations remains elusive. This is due to the difficulty in both observing small-scale bed properties and predicting a time-varying water pressure on which basal motion putatively depends. We take a Bayesian approach to these problems by coupling models of ice dynamics and subglacial hydrology and conditioning on observations of surface velocity in southwestern Greenland to infer the posterior probability distributions for eight spatially and temporally constant parameters governing the behavior of both the sliding law and hydrologic model. Because the model is computationally expensive, classical MCMC sampling is intractable. We skirt this issue by training a neural network as a surrogate that approximates the model at a sliver of the computational cost. We find that surface velocity observations establish strong constraints on model parameters relative to a prior distribution and also elucidate correlations, while the model explains 60% of observed variance. However, we also find that several distinct configurations of the hydrologic system and stress regime are consistent with observations, underscoring the need for continued data collection and model development.
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Bayesian inference applied to microseismic activity monitoring allows for principled estimation of the coordinates of microseismic events from recorded seismograms, and their associated uncertainties. However, forward modelling of these microseismic events, necessary to perform Bayesian source inversion, can be prohibitively expensive in terms of computational resources. A viable solution is to train a surrogate model based on machine learning techniques, to emulate the forward model and thus accelerate Bayesian inference. In this paper, we improve on previous work, which considered only sources with isotropic moment tensor. We train a machine learning algorithm on the power spectrum of the recorded pressure wave and show that the trained emulator allows for the complete and fast retrieval of the event coordinates for $textit{any}$ source mechanism. Moreover, we show that our approach is computationally inexpensive, as it can be run in less than 1 hour on a commercial laptop, while yielding accurate results using less than $10^4$ training seismograms. We additionally demonstrate how the trained emulators can be used to identify the source mechanism through the estimation of the Bayesian evidence. This work lays the foundations for the efficient localisation and characterisation of any recorded seismogram, thus helping to quantify human impact on seismic activity and mitigate seismic hazard.
Extreme mass ratio inspirals (EMRIs) are thought to be one of the most exciting gravitational wave sources to be detected with LISA. Due to their complicated nature and weak amplitudes the detection and parameter estimation of such sources is a challenging task. In this paper we present a statistical methodology based on Bayesian inference in which the estimation of parameters is carried out by advanced Markov chain Monte Carlo (MCMC) algorithms such as parallel tempering MCMC. We analysed high and medium mass EMRI systems that fall well inside the low frequency range of LISA. In the context of the Mock LISA Data Challenges, our investigation and results are also the first instance in which a fully Markovian algorithm is applied for EMRI searches. Results show that our algorithm worked well in recovering EMRI signals from different (simulated) LISA data sets having single and multiple EMRI sources and holds great promise for posterior computation under more realistic conditions. The search and estimation methods presented in this paper are general in their nature, and can be applied in any other scenario such as AdLIGO, AdVIRGO and Einstein Telescope with their respective response functions.
We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian Structural Inference (BSI) relies on a set of candidate unifilar HMM (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological epsilon-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be epsilon-machines, irrespective of estimated transition probabilities. Properties of epsilon-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSIs effectiveness in estimating a processs randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.
The effectiveness of Bayesian Additive Regression Trees (BART) has been demonstrated in a variety of contexts including non parametric regression and classification. Here we introduce a BART scheme for estimating the intensity of inhomogeneous Poisson Processes. Poisson intensity estimation is a vital task in various applications including medical imaging, astrophysics and network traffic analysis. Our approach enables full posterior inference of the intensity in a nonparametric regression setting. We demonstrate the performance of our scheme through simulation studies on synthetic and real datasets in one and two dimensions, and compare our approach to alternative approaches.
Accurate phase diagram calculation from molecular dynamics requires systematic treatment and convergence of statistical averages. In this work we propose a Gaussian process regression based framework for reconstructing the free energy functions using data of various origin. Our framework allows for propagating statistical uncertainty from finite molecular dynamics trajectories to the phase diagram and automatically performing convergence with respect to simulation parameters. Furthermore, our approach provides a way for automatic optimal sampling in the simulation parameter space based on Bayesian optimization approach. We validate our methodology by constructing phase diagrams of two model systems, the Lennard-Jones and soft-core potential, and compare the results with existing works studies and our coexistence simulations. Finally, we construct the phase diagram of lithium at temperatures above 300 K and pressures below 30 GPa from a machine-learning potential trained on ab initio data. Our approach performs well when compared to coexistence simulations and experimental results.
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