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Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data

Evan Archer, Il Park, Jonathan Pillow
2013 Entropy  
First, we discuss three "quasi-Bayesian" estimators that result from linear combinations of Bayesian estimates for conditional and marginal entropies.  ...  Mutual information (MI) quantifies the statistical dependency between a pair of random variables, and plays a central role in the analysis of engineering and biological systems.  ...  Derivations In this appendix we derive the posterior mean of mutual information under a Dirichlet prior. Entropy 2013, 15  ... 
doi:10.3390/e15051738 fatcat:ankgykcajfacnpk6y5a2r7n7hq

A Review of Modern Computational Algorithms for Bayesian Optimal Design

Elizabeth G. Ryan, Christopher C. Drovandi, James M. McGree, Anthony N. Pettitt
2015 International Statistical Review  
The Bayesian framework provides a unified approach for incorporating prior information and/or uncertainties regarding the statistical model with a utility function which describes the experimental aims  ...  In this paper, we provide a general overview on the concepts involved in Bayesian experimental design, and focus on describing some of the more commonly-used Bayesian utility functions and methods for  ...  Ryan (2003) used mutual information to find static designs for efficient parameter estimation.  ... 
doi:10.1111/insr.12107 fatcat:wicpixliwrfephhsr5n7j4wamq

From Single Cell Data to Mechanistic Insights Into Stem Cell Differentiation [article]

Michael Stumpf
2018 Figshare  
◦ identifying molecular interaction networks from data and available prior knowledge ◦ building dynamical systems representations for detailed (in)validation and hypothesis evaluation The presentation  ...  Empirical Bayes Meets Information Theoretical Network Reconstruction from Single Cell Data. bioRxiv, 264853. http://doi.org/10.1101/264853  ...  We can establish empirical Null distributions for MI and PUC and use these to calculate local the FDR to score edges. We can infer networks for different True Discovery Rates.  ... 
doi:10.6084/m9.figshare.5899252 fatcat:ynjjvczpjjb7ngqokokv3tb6yy

Information Regularized Maximum Likelihood for Binary Motion Sensors

Umut Ozertem, Deniz Erdogmus
2007 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07  
We propose a pairwise mutual information based regularization technique for maximum likelihood sensor fusion in dense distributed sensor networks.  ...  The extensions of the information regularization principle to various sensor and data fusion problems such as outlier detection, and sensor failure identification are discussed.  ...  Acknowledgements: This work is partially supported by the NSF grants ECS-0524835, and ECS-0622239.  ... 
doi:10.1109/icassp.2007.366412 dblp:conf/icassp/OzertemE07 fatcat:xtx5wwvjmfgy7csqnynb22frjq

Estimating the Mutual Information between two Discrete, Asymmetric Variables with Limited Samples [article]

Damián G. Hernández, Inés Samengo
2019 arXiv   pre-print
The established measure for quantifying such relations is the mutual information. However, estimating mutual information from limited samples is a challenging task.  ...  Since the mutual information is the difference of two entropies, the existing Bayesian estimators of entropy may be used to estimate information.  ...  Acknowledgments We thank Ilya Nemenman for his fruitful comments and discussions.  ... 
arXiv:1905.02034v1 fatcat:ubu5ozbx4balnmxcu7y6k7jbdq

Estimating the Mutual Information between Two Discrete, Asymmetric Variables with Limited Samples

Damián G. Hernández, Inés Samengo
2019 Entropy  
The established measure for quantifying such relations is the mutual information. However, estimating mutual information from limited samples is a challenging task.  ...  Since the mutual information is the difference of two entropies, the existing Bayesian estimators of entropy may be used to estimate information.  ...  Acknowledgments: We thank Ilya Nemenman for his fruitful comments and discussions. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e21060623 pmid:33267337 fatcat:3qbcby5pyjez5k2dhcaptbihre

Page 5262 of Mathematical Reviews Vol. , Issue 93i [page]

1993 Mathematical Reviews  
Recursion algorithms for recognition and estimation of the state of a dynamic object on the basis of information from measurers and indicators. I. Observation with lag. J. Comput. Systems Sci.  ...  Three key issues are dealt with—reduction of excessive information, approximation of the ideal Bayesian solution and numerical implementation of the resulting estimator.”  ... 

Particle filter-based real-time estimation and prediction of traffic conditions

Jacques Sau, Nour-Eddin El Faouzi, Anis Ben Aissa, Olivier de Mouzon
2007 Recent Advances in Stochastic Modeling and Data Analysis  
Real-time estimation and short-term prediction of traffic conditions is one of major concern of traffic managers and ITS-oriented systems.  ...  Not only shall we show that travel time prediction is successfully realized, but also that we are able to estimate, in real time, the motorway traffic conditions, even on points with no measurement facilities  ...  Acknowledgements The authors wish to thank the APRR motorway company for providing the realworld data used in this research.  ... 
doi:10.1142/9789812709691_0049 fatcat:slm4lw7tbbccbbzekfgy3xmn4e

Quasi-Fluid-Mechanics-Based Quasi-Bayesian CramÉr–Rao Bounds for Deformed Towed-Array Direction Finding

P. Tichavsky, K.T. Wong
2004 IEEE Transactions on Signal Processing  
New quasi-Bayesian (hybrid) Cramér-Rao bound (CRB) expressions are herein derived for far-field deep-sea direction-of-arrival (DOA) estimation with a nominally linear towed-array that 1) is deformed by  ...  to produce a shape-deformation statistical model physically more realistic than those previously used for DOA performance analysis and b) rigorously derive a mathematical analysis to characterize quantitatively  ...  The Paidoussis equation is discretized both in time and in space and consequently used to derive physically meaningful covariance matrices of the sensor location uncertainties, , , and for use in the quasi-Bayesian  ... 
doi:10.1109/tsp.2003.820072 fatcat:vgxdo3kbdfazvoneoedifxwfm4

Privug: Using Probabilistic Programming for Quantifying Leakage in Privacy Risk Analysis [article]

Raúl Pardo, Willard Rafnsson, Christian Probst, Andrzej Wąsowski
2021 arXiv   pre-print
In Privug, we reinterpret a program probabilistically, using off-the-shelf tools for Bayesian inference to perform information-theoretic analysis of the information flow.  ...  Privug is a tool-supported method to explore information leakage properties of data analytics and anonymization programs.  ...  In Privug, we use the mutual information estimator [25] provided by SKlearn [33] for continuous variables and LeakiEst [11] for discrete variables.  ... 
arXiv:2011.08742v5 fatcat:mechsiah25fxjdc6hsmbkf25au

Everything you always wanted to know about training: guidelines derived using the affine precoding framework and the CRB

A. Vosoughi, A. Scaglione
2006 IEEE Transactions on Signal Processing  
Index Terms-Affine precoding, Bayes estimator, block transmission, Cramer-Rao bound (CRB), Fisher information matrix (FIM), multi-input multi-output (MIMO) systems, mutual information, random parameter  ...  To highlight the tradeoffs between training and data symbols, the Fisher information matrix (FIM) is derived under two circumstances: the random parameter vector to be estimated contains 1) only fading  ...  IMPACT OF THE CHANNEL ESTIMATION ERROR ON THE MUTUAL INFORMATION In this section, we focus on the decoupled channel and symbol estimation scenario and we provide a lower bound on the mutual information  ... 
doi:10.1109/tsp.2005.863031 fatcat:y65lnk7lcbf4hjsoebqr7rqz24

Bayesian Network Modeling Applied to Feline Calicivirus Infection Among Cats in Switzerland

Gilles Kratzer, Fraser I. Lewis, Barbara Willi, Marina L. Meli, Felicitas S. Boretti, Regina Hofmann-Lehmann, Paul Torgerson, Reinhard Furrer, Sonja Hartnack
2020 Frontiers in Veterinary Science  
Finally, we discuss advanced methods, such as Bayesian model averaging, a common way of accounting for model uncertainty in a Bayesian network context.  ...  Bayesian network (BN) modeling is a rich and flexible analytical framework capable of elucidating complex veterinary epidemiological data.  ...  Firth's correction aims at producing reliable estimates in (quasi-)separated datasets.  ... 
doi:10.3389/fvets.2020.00073 pmid:32175337 pmcid:PMC7055399 fatcat:67bd5r7jyfh4hd2e4mz4hyavke

A scalable quasi-Bayesian framework for Gaussian graphical models [article]

Yves Atchade
2015 arXiv   pre-print
We develop a quasi-Bayesian implementation of the neighborhood selection method of Meinshausen and Buhlmann (2006) for the estimation of Gaussian graphical models.  ...  This paper deals with the Bayesian estimation of high dimensional Gaussian graphical models.  ...  Acknowledgements The author would like to thank Shuheng Zhou for very helpful conversations. This work is partially supported by the NSF, grants DMS 1228164 and DMS 1513040.  ... 
arXiv:1512.07934v1 fatcat:bfdndm24nvemdpnft4nlaa3etu

epidemiological application of a Bayesian nonparametric smoother based on a GLMM with an autoregressive error component

Luisa Zuccolo, Milena Maule, Dario Gregori
2005 Metodološki zvezki. Advances in methodology and statistics  
The aim of this preliminary study was to suggest the novel employment of a Bayesian nonparametric model (based on a GLMM), a validated statistical approach, to the context of the estimation of childhood  ...  These data are typically characterised by overdispersion and correlated errors, nevertheless the standard method of analysis in this field has so far been the Poisson regression.  ...  The authors would like to thank Franco Merletti, Neil Pearce, Corrado Magnani and Guido Pastore for useful discussions and suggestions.  ... 
doi:10.51936/uwos9546 fatcat:47eonzuj3ffjpmfcn2thp2qknm

Variational Bayesian inversion (VBI) of quasi-localized seismic attributes for the spatial distribution of geological facies

Muhammad Atif Nawaz, Andrew Curtis
2018 Geophysical Journal International  
We introduce a new Bayesian inversion method that estimates the spatial distribution of geological facies from attributes of seismic data, by showing how the usual probabilistic inverse problem can be  ...  Exact Bayesian inference is impractical because it requires normalization of the posterior distribution which is intractable for large models and must be approximated.  ...  Klaus Mosegaard and an anonymous reviewer for their comments and constructive criticism on an earlier version of this manuscript.  ... 
doi:10.1093/gji/ggy163 fatcat:k3n3tsqq6nalfjfkoxbhe5f5n4
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