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1. Predictive Runtime Monitoring of Vehicle Models Using Bayesian Estimation and Reachability Analysis

   https://doi.org/10.1109/IROS45743.2020.9340755  

   Chou, Yi ; Yoon, Hansol ; Sankaranarayanan, Sriram ( October 2020 , 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS))

   null (Ed.)

   We present a predictive runtime monitoring technique for estimating future vehicle positions and the probability of collisions with obstacles. Vehicle dynamics model how the position and velocity change over time as a function of external inputs. They are commonly described by discrete-time stochastic models. Whereas positions and velocities can be measured, the inputs (steering and throttle) are not directly measurable in these models. In our paper, we apply Bayesian inference techniques for real-time estimation, given prior distribution over the unknowns and noisy state measurements. Next, we pre-compute the set-valued reachability analysis to approximate future positions of a vehicle. The pre-computed reachability sets are combined with the posterior probabilities computed through Bayesian estimation to provided a predictive verification framework that can be used to detect impending collisions with obstacles. Our approach is evaluated using the coordinated-turn vehicle model for a UAV using on-board measurement data obtained from a flight test of a Talon UAV. We also compare the results with sampling-based approaches. We find that precomputed reachability analysis can provide accurate warnings up to 6 seconds in advance and the accuracy of the warnings improve as the time horizon is narrowed from 6 to 2 seconds. The approach also outperforms sampling in terms of on-board computation cost and accuracy measures. 

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2. Bayesian function registration with random truncation

   https://doi.org/10.1371/journal.pone.0287734  

   Lu, Yi ; Herbei, Radu ; Kurtek, Sebastian ( July 2023 , PLOS ONE)

   Yang, Junyuan (Ed.)

   In this work, we develop a new set of Bayesian models to perform registration of real-valued functions. A Gaussian process prior is assigned to the parameter space of time warping functions, and a Markov chain Monte Carlo (MCMC) algorithm is utilized to explore the posterior distribution. While the proposed model can be defined on the infinite-dimensional function space in theory, dimension reduction is needed in practice because one cannot store an infinite-dimensional function on the computer. Existing Bayesian models often rely on some pre-specified, fixed truncation rule to achieve dimension reduction, either by fixing the grid size or the number of basis functions used to represent a functional object. In comparison, the new models in this paper randomize the truncation rule. Benefits of the new models include the ability to make inference on the smoothness of the functional parameters, a data-informative feature of the truncation rule, and the flexibility to control the amount of shape-alteration in the registration process. For instance, using both simulated and real data, we show that when the observed functions exhibit more local features, the posterior distribution on the warping functions automatically concentrates on a larger number of basis functions. Supporting materials including code and data to perform registration and reproduce some of the results presented herein are available online. 

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3. Computational techniques for parameter estimation of gravitational wave signals

   https://doi.org/10.1002/wics.1532  

   Meyer, Renate ; Edwards, Matthew C. ; Maturana‐Russel, Patricio ; Christensen, Nelson ( September 2020 , WIREs Computational Statistics)

   Since the very first detection of gravitational waves from the coalescence of two black holes in 2015, Bayesian statistical methods have been routinely applied by LIGO and Virgo to extract the signal out of noisy interferometric measurements, obtain point estimates of the physical parameters responsible for producing the signal, and rigorously quantify their uncertainties. Different computational techniques have been devised depending on the source of the gravitational radiation and the gravitational waveform model used. Prominent sources of gravitational waves are binary black hole or neutron star mergers, the only objects that have been observed by detectors to date. But also gravitational waves from core‐collapse supernovae, rapidly rotating neutron stars, and the stochastic gravitational‐wave background are in the sensitivity band of the ground‐based interferometers and expected to be observable in future observation runs. As nonlinearities of the complex waveforms and the high‐dimensional parameter spaces preclude analytic evaluation of the posterior distribution, posterior inference for all these sources relies on computer‐intensive simulation techniques such as Markov chain Monte Carlo methods. A review of state‐of‐the‐art Bayesian statistical parameter estimation methods will be given for researchers in this cross‐disciplinary area of gravitational wave data analysis.

   This article is categorized under:

   Applications of Computational Statistics > Signal and Image Processing and Coding

   Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)

   Statistical Models > Time Series Models

    

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4. Bayesian Decision Making in Uncertain MDPs with Large or Infinite-Dimensional Spaces

   Imani, Mandi ; Ghoreishi, Seyede ; Braga-Neto, Ulisses ( December 2018 , Advances in Neural Information Processing Systems 31 (NeurIPS’2018))

   We propose a Bayesian decision making framework for control of Markov Decision Processes (MDPs) with unknown dynamics and large, possibly continuous, state, action, and parameter spaces in data-poor environments. Most of the existing adaptive controllers for MDPs with unknown dynamics are based on the reinforcement learning framework and rely on large data sets acquired by sustained direct interaction with the system or via a simulator. This is not feasible in many applications, due to ethical, economic, and physical constraints. The proposed framework addresses the data poverty issue by decomposing the problem into an offline planning stage that does not rely on sustained direct interaction with the system or simulator and an online execution stage. In the offline process, parallel Gaussian process temporal difference (GPTD) learning techniques are employed for near-optimal Bayesian approximation of the expected discounted reward over a sample drawn from the prior distribution of unknown parameters. In the online stage, the action with the maximum expected return with respect to the posterior distribution of the parameters is selected. This is achieved by an approximation of the posterior distribution using a Markov Chain Monte Carlo (MCMC) algorithm, followed by constructing multiple Gaussian processes over the parameter space for efficient prediction of the means of the expected return at the MCMC sample. The effectiveness of the proposed framework is demonstrated using a simple dynamical system model with continuous state and action spaces, as well as a more complex model for a metastatic melanoma gene regulatory network observed through noisy synthetic gene expression data. 

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5. MFBO-SSM: Multi-Fidelity Bayesian Optimization for Fast Inference in State-Space Models

   Imani, M ; Ghoreishi, S.F. ; Allaire, D. ; Braga-Neto, U ( July 2019 , Proceedings of the ... AAAI Conference on Artificial Intelligence)

   Nonlinear state-space models are ubiquitous in modeling real-world dynamical systems. Sequential Monte Carlo (SMC) techniques, also known as particle methods, are a well-known class of parameter estimation methods for this general class of state-space models. Existing SMC-based techniques rely on excessive sampling of the parameter space, which makes their computation intractable for large systems or tall data sets. Bayesian optimization techniques have been used for fast inference in state-space models with intractable likelihoods. These techniques aim to find the maximum of the likelihood function by sequential sampling of the parameter space through a single SMC approximator. Various SMC approximators with different fidelities and computational costs are often available for sample- based likelihood approximation. In this paper, we propose a multi-fidelity Bayesian optimization algorithm for the inference of general nonlinear state-space models (MFBO-SSM), which enables simultaneous sequential selection of parameters and approximators. The accuracy and speed of the algorithm are demonstrated by numerical experiments using synthetic gene expression data from a gene regulatory network model and real data from the VIX stock price index. 

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