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Fisher transfer entropy: quantifying the gain in transient sensitivity

Mikhail Prokopenko, Lionel Barnett, Michael Harré, Joseph T. Lizier, Oliver Obst, X. Rosalind Wang
2015 Proceedings of the Royal Society A  
The new measure captures both transient and contextual qualities of transfer entropy and the sensitivity characteristics of Fisher information.  ...  Fisher Transfer Entropy is exemplified for a ferromagnetic 2d lattice Ising model with Glauber dynamics, and is shown to diverge at the critical point.  ...  Fisher information [5] is a measure for the amount of information that an observable random variable X provides about an unknown parameter θ , upon which the likelihood function of θ depends.  ... 
doi:10.1098/rspa.2015.0610 fatcat:csb3uzjxpzdbvesrxblzj2e4ky

Relating Fisher information to order parameters

Mikhail Prokopenko, Joseph T. Lizier, Oliver Obst, X. Rosalind Wang
2011 Physical Review E  
We study phase transitions and relevant order parameters via statistical estimation theory using the Fisher information matrix.  ...  Nevertheless, the resulting representation is sufficiently general and explicitly relates elements of the Fisher information matrix to the rate of change in the corresponding order parameters.  ...  Our tools of choice are Fisher information and the Fisher information matrix, which are well known in statistical estimation theory.  ... 
doi:10.1103/physreve.84.041116 pmid:22181096 fatcat:yqwepcxq6bfkrnhxveeqzk3dzy

Quantum measurement optimization by decomposition of measurements into extremals [article]

Esteban Martínez-Vargas, Carlos Pineda, Pablo Barberis-Blostein
2019 arXiv   pre-print
Using the convex structure of positive operator value measurements and of several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present  ...  We exemplify the method for different cost functions in a qubit and in a harmonic oscillator and find a strong numerical advantage when the desired target error is sufficiently small.  ...  = ψ(θ, η)|ψ(ξ, η) ψ(ξ, η)|ψ(θ, η) , p ξ (2|θ) = 1 − p ξ (1|θ) . (23) The Fisher information for this probability distribution is which is a function of the parameter we want to estimate, i.e. θ.  ... 
arXiv:1901.06179v1 fatcat:7gdkbnqiarem3pefrdu2bmnm6e

Quantum measurement optimization by decomposition of measurements into extremals

Esteban Martínez-Vargas, Carlos Pineda, Pablo Barberis-Blostein
2020 Scientific Reports  
Using the convex structure of positive operator value measurements and several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present  ...  We exemplify the method for different cost functions in a qubit and in a harmonic oscillator and find a strong numerical advantage when the desired target error is sufficiently small.  ...  -HilbertDim 7 and the number of outcomes of the POVM with --Outcomedim 10.  ... 
doi:10.1038/s41598-020-65934-w pmid:32523002 pmcid:PMC7286896 fatcat:hqr6c3cnovbyzndm6srvd7v244

A bivariate marginal likelihood specification of spatial econometric modeling of very large datasets [article]

Giuseppe Arbia
2013 arXiv   pre-print
We establish small sample and asymptotic properties of the estimators and we derive the associated Fisher information matrix needed in confidence interval estimation and hypothesis testing.  ...  of the parameters.  ...  The approach does not require a full specification of a weights matrix and the estimation phase is computationally very simple in that a closed--form solution of the ML estimators can be obtained.  ... 
arXiv:1301.0741v1 fatcat:dgqvgk4afrhudavo2nzwtthq2a

Learning from Complex Systems: On the Roles of Entropy and Fisher Information in Pairwise Isotropic Gaussian Markov Random Fields

Alexandre Levada
2014 Entropy  
Markov Random Field models are powerful tools for the study of complex systems.  ...  We propose analytical expressions to compute local and global versions of these measures using Besag's pseudo-likelihood function, characterizing the system's behavior through its Fisher curve, a parametric  ...  Acknowledgments The author would like to thank CNPQ(Brazilian Council for Research and Development) for the financial support through research grant number 475054/2011-3.  ... 
doi:10.3390/e16021002 fatcat:47gcoe7zqzglhhp7zunatdvfya

Parametric survival densities from phase-type models

Eric V. Slud, Jiraphan Suntornchost
2013 Lifetime Data Analysis  
However, consideration of Fisher Information and likelihood-ratio type tests to discriminate between model families indicates that only the simplest phase-type model topologies can be stably estimated  ...  These models are now supported by computational statistical methods that make numerical calculation of likelihoods and statistical estimation of parameters feasible in theory for quite complicated settings  ...  Philip Rosenberg and William Anderson for an introduction to the breast cancer dataset and research questions of Anderson et al. (2006), and for their encouragement on this project.  ... 
doi:10.1007/s10985-013-9278-0 pmid:23963960 fatcat:cvbdsnhls5duvkmepbzb4yj2ci

PATTERN CLUSTERING BY MULTIVARIATE MIXTURE ANALYSIS

John H. Wolfe
1970 Multivariate Behavioral Research  
Table 2 presents the maximum-likelihood estimates of some of the parameters obtained by NORMAP and NORMIX for three types and compares them with the estimates obtained by Fisher when he used a priori  ...  The approximation for I,@ is seen to be where I, is the information matrix of the parameters {OS,} for a single observation from a pure distribution, (Ye.  ...  Two computer programs have been written to implement this procedure : the program for Theorem 3 is called NORMIX and the program for Theorem 4 is called NORMAP.  ... 
doi:10.1207/s15327906mbr0503_6 pmid:26812701 fatcat:v7ab54knpfer3broacp2kiumli

System-Orthogonal Functions for Sound Speed Profile Perturbation

W. Xu, H. Schmidt
2006 IEEE Journal of Oceanic Engineering  
The derived functions make the CRB matrix diagonal, decoupling the errors in the estimation of the expansion coefficients.  ...  the SSP parameters and the system response.  ...  ACKNOWLEDGMENT The authors would thank Dr. G. Potty, Dr. A. Fredricks, and Dr. J. Lynch for helping the shelf break PRIMER simulation.  ... 
doi:10.1109/joe.2006.872221 fatcat:2opsnbd375gphgj5dtjvnikuwu

Displacement Estimation by Maximum-Likelihood Texture Tracking

Olivier Harant, Lionel Bombrun, Gabriel Vasile, Laurent Ferro-Famil, Michel Gay
2011 IEEE Journal on Selected Topics in Signal Processing  
For random variables with Fisher distributions, the ratio distribution is established.  ...  Based on the Spherically Invariant Random Vectors (SIRV) theory, the ML estimator of the texture is computed.  ...  and the Euler Beta function . and are the two shape parameters of the Fisher pdf.  ... 
doi:10.1109/jstsp.2010.2100365 fatcat:jsmr2nerdbc7dbtkzjan7tqngy

Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

P. Tichavsky, C.H. Muravchik, A. Nehorai
1998 IEEE Transactions on Signal Processing  
of mutually independent random variables or vectors); and (in general) nonlinear functions.  ...  Fisher information for slowly varying parameter of an AR(1) process as a function of this parameter for Q = 10 02 ; 10 03; and 10 04 (from the bottom up), respectively. Fig. 2 . 2 Fig. 2.  ... 
doi:10.1109/78.668800 fatcat:bzygd7kmcfgxjcmcfui5jkad7a

Fourier analysis of multitracer cosmological surveys

L. Raul Abramo, Lucas F. Secco, Arthur Loureiro
2015 Monthly notices of the Royal Astronomical Society  
We present optimal quadratic estimators for the Fourier analysis of cosmological surveys that detect several different types of tracers of large-scale structure.  ...  We show that the multi-tracer estimators are unbiased, and that their covariance is given by the inverse of the multi-tracer Fisher matrix (Abramo, MNRAS 2013; Abramo & Leonard, MNRAS 2013).  ...  For two types of tracers, the variables which diagonalize the 2 × 2 Fisher matrix are P = P1 + P2, and P1/P2 (or, equivalently, P and P2/P1).  ... 
doi:10.1093/mnras/stv2588 fatcat:5brkh2ru75cydesruxmcq77stu

Adaptive Stimulus Design for Dynamic Recurrent Neural Network Models

R. Ozgur Doruk, Kechen Zhang
2019 Frontiers in Neural Circuits  
Here we specified the time course of each stimulus by a Fourier series whose amplitudes and phases were determined by maximizing a utility function based on the Fisher information matrix.  ...  design of time-varying stimuli may actually improve parameter estimation for this common type of recurrent network models.  ...  All the computer codes in Matlab for the simulations in this paper are freely available upon request for scientific research and education or any noncommercial use.  ... 
doi:10.3389/fncir.2018.00119 pmid:30723397 pmcid:PMC6349832 fatcat:hpnhks53jjhizppc5pw5d4wqgi

Information geometric analysis of phase transitions in complex patterns: the case of the Gray-Scott reaction–diffusion model

Omri Har-Shemesh, Rick Quax, Alfons G Hoekstra, Peter M A Sloot
2016 Journal of Statistical Mechanics: Theory and Experiment  
We describe the system by a probability density function that represents the size distribution of blobs in the patterns and compute its Fisher information with respect to changing the two rate parameters  ...  We estimate the distribution non-parametrically so that we do not assume any statistical model. The resulting Fisher map can be interpreted as a phase-map of the different patterns.  ...  Acknowledgments OHS would like to thank L J Krieg from the University of Amsterdam for many enlightening discussions and the critical reading of the manuscript.  ... 
doi:10.1088/1742-5468/2016/04/043301 fatcat:z3nnkxtmxzbgvfedda4mhxvkja

Neural network–featured timing systems for radiation detectors: performance evaluation based on bound analysis [article]

Pengcheng Ai, Zhi Deng, Yi Wang, Linmao Li
2021 arXiv   pre-print
Furthermore, we propose an estimation of multivariate Cram\'er Rao lower bound within the model using intrinsic-extrinsic parametrization and prior information.  ...  Two case studies (single photon detection and shashlik-type calorimeter) verify the reliability of the proposed method and show it works as a useful guideline when assessing the abilities of various feature  ...  Acknowledgments This research is supported by the National Key Research and Development Program of China (under project no. 2020YFE0202001).  ... 
arXiv:2105.14687v3 fatcat:vct4rfxygfddhjljw2655xyh7y
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