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1. Bayesian Multiagent Inverse Reinforcement Learning for Policy Recommendation

   Martin, C. ; Sandholm, T. ( January 2021 , AAAI-21 Workshop on Reinforcement Learning in Games)

   null (Ed.)

   We study the following problem, which to our knowledge has been addressed only partially in the literature and not in full generality. An agent observes two players play a zero-sum game that is known to the players but not the agent. The agent observes the actions and state transitions of their game play, but not rewards. The players may play either op-timally (according to some Nash equilibrium) or according to any other solution concept, such as a quantal response equilibrium. Following these observations, the agent must recommend a policy for one player, say Player 1. The goal is to recommend a policy that is minimally exploitable un-der the true, but unknown, game. We take a Bayesian ap-proach. We establish a likelihood function based on obser-vations and the specified solution concept. We then propose an approach based on Markov chain Monte Carlo (MCMC), which allows us to approximately sample games from the agent’s posterior belief distribution. Once we have a batch of independent samples from the posterior, we use linear pro-gramming and backward induction to compute a policy for Player 1 that minimizes the sum of exploitabilities over these games. This approximates the policy that minimizes the ex-pected exploitability under the full distribution. Our approach is also capable of handling counterfactuals, where known modifications are applied to the unknown game. We show that our Bayesian MCMC-based technique outperforms two other techniques—one based on the equilibrium policy of the maximum-probability game and the other based on imitation of observed behavior—on all the tested stochastic game envi-ronments. 

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2. Bayesian Poroelastic Aquifer Characterization From InSAR Surface Deformation Data. 2. Quantifying the Uncertainty

   https://doi.org/10.1029/2021WR029775  

   Alghamdi, Amal ; Hesse, Marc A. ; Chen, Jingyi ; Villa, Umberto ; Ghattas, Omar ( November 2021 , Water Resources Research)

   Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the parameters. Here, we develop a Bayesian inversion framework that uses Interferometric Synthetic Aperture Radar (InSAR) surface deformation data to infer the laterally heterogeneous permeability of a transient linear poroelastic model of a confined GW aquifer. The Bayesian solution of this inverse problem takes the form of a posterior probability density of the permeability. Exploring this posterior using classical Markov chain Monte Carlo (MCMC) methods is computationally prohibitive due to the large dimension of the discretized permeability field and the expense of solving the poroelastic forward problem. However, in many partial differential equation (PDE)‐based Bayesian inversion problems, the data are only informative in a few directions in parameter space. For the poroelasticity problem, we prove this property theoretically for a one‐dimensional problem and demonstrate it numerically for a three‐dimensional aquifer model. We design a generalized preconditioned Crank‐Nicolson (gpCN) MCMC method that exploits this intrinsic low dimensionality by using a low‐rank‐based Laplace approximation of the posterior as a proposal, which we build scalably. The feasibility of our approach is demonstrated through a real GW aquifer test in Nevada. The inherently two‐dimensional nature of InSAR surface deformation data informs a sufficient number of modes of the permeability field to allow detection of major structures within the aquifer, significantly reducing the uncertainty in the pressure and the displacement quantities of interest.

    

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3. Efficient Krylov subspace methods for uncertainty quantification in large Bayesian linear inverse problems

   https://doi.org/10.1002/nla.2325  

   Saibaba, Arvind K. ; Chung, Julianne ; Petroske, Katrina ( August 2020 , Numerical Linear Algebra with Applications)

   Uncertainty quantification for linear inverse problems remains a challenging task, especially for problems with a very large number of unknown parameters (e.g., dynamic inverse problems) and for problems where computation of the square root and inverse of the prior covariance matrix are not feasible. This work exploits Krylov subspace methods to develop and analyze new techniques for large‐scale uncertainty quantification in inverse problems. In this work, we assume that generalized Golub‐Kahan‐based methods have been used to compute an estimate of the solution, and we describe efficient methods to explore the posterior distribution. In particular, we use the generalized Golub‐Kahan bidiagonalization to derive an approximation of the posterior covariance matrix, and we provide theoretical results that quantify the accuracy of the approximate posterior covariance matrix and of the resulting posterior distribution. Then, we describe efficient methods that use the approximation to compute measures of uncertainty, including the Kullback‐Liebler divergence. We present two methods that use the preconditioned Lanczos algorithm to efficiently generate samples from the posterior distribution. Numerical examples from dynamic photoacoustic tomography demonstrate the effectiveness of the described approaches.

    

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4. Hyainailourine and teratodontine cranial material from the late Eocene of Egypt and the application of parsimony and Bayesian methods to the phylogeny and biogeography of Hyaenodonta (Placentalia, Mammalia)

   https://doi.org/10.7717/peerj.2639  

   Borths, Matthew R. ; Holroyd, Patricia A. ; Seiffert, Erik R. ( November 2016 , PeerJ)

   Hyaenodonta is a diverse, extinct group of carnivorous mammals that included weasel- to rhinoceros-sized species. The oldest-known hyaenodont fossils are from the middle Paleocene of North Africa and the antiquity of the group in Afro-Arabia led to the hypothesis that it originated there and dispersed to Asia, Europe, and North America. Here we describe two new hyaenodont species based on the oldest hyaenodont cranial specimens known from Afro-Arabia. The material was collected from the latest Eocene Locality 41 (L-41, ∼34 Ma) in the Fayum Depression, Egypt.Akhnatenavus nefertiticyonsp. nov. has specialized, hypercarnivorous molars and an elongate cranial vault. InA. nefertiticyonthe tallest, piercing cusp on M¹–M²is the paracone.Brychotherium ephalmosgen. et sp. nov. has more generalized molars that retain the metacone and complex talonids. InB. ephalmosthe tallest, piercing cusp on M¹–M²is the metacone. We incorporate this new material into a series of phylogenetic analyses using a character-taxon matrix that includes novel dental, cranial, and postcranial characters, and samples extensively from the global record of the group. The phylogenetic analysis includes the first application of Bayesian methods to hyaenodont relationships.B. ephalmosis consistently placed within Teratodontinae, an Afro-Arabian clade with several generalist and hypercarnivorous forms, andAkhnatenavusis consistently recovered in Hyainailourinae as part of an Afro-Arabian radiation. The phylogenetic results suggest that hypercarnivory evolved independently three times within Hyaenodonta: in Teratodontinae, in Hyainailourinae, and in Hyaenodontinae. Teratodontines are consistently placed in a close relationship with Hyainailouridae (Hyainailourinae + Apterodontinae) to the exclusion of “proviverrines,” hyaenodontines, and several North American clades, and we propose that the superfamily Hyainailouroidea be used to describe this relationship. Using the topologies recovered from each phylogenetic method, we reconstructed the biogeographic history of Hyaenodonta using parsimony optimization (PO), likelihood optimization (LO), and Bayesian Binary Markov chain Monte Carlo (MCMC) to examine support for the Afro-Arabian origin of Hyaenodonta. Across all analyses, we found that Hyaenodonta most likely originated in Europe, rather than Afro-Arabia. The clade is estimated by tip-dating analysis to have undergone a rapid radiation in the Late Cretaceous and Paleocene; a radiation currently not documented by fossil evidence. During the Paleocene, lineages are reconstructed as dispersing to Asia, Afro-Arabia, and North America. The place of origin of Hyainailouroidea is likely Afro-Arabia according to the Bayesian topologies but it is ambiguous using parsimony. All topologies support the constituent clades–Hyainailourinae, Apterodontinae, and Teratodontinae–as Afro-Arabian and tip-dating estimates that each clade is established in Afro-Arabia by the middle Eocene.

    

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5. Bayesian parameter estimation of duration-based variables used in post-earthquake building recovery modeling

   https://doi.org/10.1177/87552930211073717  

   Omoya, Morolake ; Burton, Henry ; Baroud, Hiba ( May 2022 , Earthquake Spectra)

   A Bayesian parameter estimation methodology for updating the distributions of the duration-based variables used in post-earthquake building recovery modeling is presented. The distributions of the recovery-related parameters specified in the resilience-based earthquake design initiative (REDi) and HAZUS are used as the basis of the priors. A data set of observed building damage and recovery following the 2014 South Napa earthquake is assembled and used to illustrate the proposed methodology. The recovery data set includes the permit acquisition and repair time for over 800 buildings affected by the earthquake. With this data, the conjugate prior (CP) and Markov Chain Monte Carlo (MCMC) methods are implemented to update the probability distribution parameters for the duration-based recovery variables. While the CP approach is easier to implement because it offers an analytical solution, the MCMC provides more flexibility in terms of the types of prior and sampling distributions that can be accommodated. Moreover, the results from a comparative implementation on the Napa data set shows that the MCMC method provides a reasonable approximation of the posterior marginal distribution of the duration-based recovery variables relative to the CP analytical solution.

    

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