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Parameter estimation and uncertainty quantification using information geometry [article]

Jesse A Sharp, Alexander P Browning, Kevin Burrage, Matthew J Simpson
2022 arXiv   pre-print
In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic  ...  curves and Riemann scalar curvature, to supplement typical techniques for uncertainty quantification such as Bayesian methods, profile likelihood, asymptotic analysis and bootstrapping.  ...  Acknowledgements We thank Professor Alan Garfinkel (UCLA) for introducing K.B. to information geometry, and for numerous discussions while both were at the University of Oxford. We also thank Dr.  ... 
arXiv:2111.12201v3 fatcat:rqpho3wo3vdarprdlpqx6ahmwi

Why does statistics have two theories? [chapter]

Donald Fraser
2014 Past, Present, and Future of Statistical Science  
As we will see, if continuity that is present in the model is also required for the methods, then the conflicts and contradictions resolve.  ...  The public image of statistics is changing, and recently the changes have been mostly for the better, as we've all seen.  ...  Wang for help in preparing the manuscript.  ... 
doi:10.1201/b16720-27 fatcat:htjwdl5rcrcxxodtc3ansd72ve

Dominant parameter selection in the marginally identifiable case

Ilya Ioslovich, Per-Olof Gutman, Ido Seginer
2004 Mathematics and Computers in Simulation  
In this situation, only some parameter values can be estimated. Based on an analysis of the Fisher information matrix, a method for a reasonable selection of parameters is suggested here.  ...  Often a rather limited set of experimental data is available for the identification of a dynamic model, which contains many parameters. This is, e.g. the usual case for crop growth models.  ...  Acknowledgements This study was supported by the European Community through Project FAIR6-CT98-4362 (Nicolet). Appendix A. Nominal (initial) parameter values  ... 
doi:10.1016/j.matcom.2003.09.012 fatcat:rya7qhgtbza4zfem6kq32mdkzu

Comparison of Accuracy for Methods to Approximate Fisher Information in the Scalar Case [article]

Shenghan Guo
2015 arXiv   pre-print
In such cases, we need to utilize the approximation of FIM. In general, there are two ways to estimate FIM.  ...  The Fisher information matrix (FIM) has long been of interest in statistics and other areas.  ...  comparison of accuracy for the two approximation methods in the scalar case and mainly focused our analysis on the family of symmetric density functions.  ... 
arXiv:1501.00218v3 fatcat:4i7q5xcbkzaclkylwjlxsal2m4

Constraints on Einstein-dilation-Gauss-Bonnet gravity from Black Hole-Neutron Star Gravitational Wave Events [article]

Zhenwei Lyu and Nan Jiang and Kent Yagi
2022 arXiv   pre-print
In order to check the validity of the effect of higher post-Newtonian terms, we derive corrections to the waveform phase up to second post Newtonian order by mapping results in scalar-tensor theories to  ...  km, whose consistency is checked with an independent Fisher analysis.  ...  Fisher analysis We next explain the second method for the data analysis, namely the Fisher information matrix (FIM) method [65, [79] [80] [81] , which is valid when the SNR is large and the noise is stationary  ... 
arXiv:2201.02543v2 fatcat:tzgbqdwhuzejxiu456pcbcngyy

Improved gravitational-wave constraints on higher-order curvature theories of gravity [article]

Scott E. Perkins, Remya Nair, Hector O. Silva, Nicolas Yunes
2021 arXiv   pre-print
Importantly, we also show that our bounds are robust to (i) the choice of general-relativity base waveform model, upon which we add modifications, (ii) unknown higher post-Newtonian order terms in the  ...  modifications to general relativity, (iii) the small-coupling approximation, and (iv) uncertainties on the nature of the constituent compact objects.  ...  To this end, we use the more computationally tractable method of predicting the error covariances through the Fisher Information Matrix, or the Fisher for short [63] [64] [65] .  ... 
arXiv:2104.11189v1 fatcat:xylzqugko5hsvkdwfbnokw7vqu

CMB beam systematics: Impact on lensing parameter estimation

N. J. Miller, M. Shimon, B. G. Keating
2009 Physical Review D  
In this work we use Fisher-matrix-based estimations and apply, for the first time, Monte-Carlo Markov Chain (MCMC) simulations to determine the effect of beam systematics on the inferred cosmological parameters  ...  We determine allowable levels of beam systematics for given tolerances on the induced parameter errors and check for possible biases in the inferred parameters concomitant with potential increases in the  ...  Acknowledgments We acknowledge the use of the publically available code by Lesgourgues, Perotto, Pastor & Piat for the calculation of the noise in lensing reconstruction.  ... 
doi:10.1103/physrevd.79.063008 fatcat:ogtdwrraxjazxbhmkplz57r4um

Can We Determine Electric Fields and Poynting Fluxes from Vector Magnetograms and Doppler Measurements?

G. H. Fisher, B. T. Welsch, W. P. Abbett
2011 Solar Physics  
Here, we show how additional information in the form of line-of-sight Doppler flow measurements, and motions transverse to the line-of-sight determined with ad-hoc methods such as local correlation tracking  ...  of a scalar potential.  ...  This new era of measurement demands new approaches for the analysis and use of this data.  ... 
doi:10.1007/s11207-011-9816-4 fatcat:ptlk4rfglngo7cbfbwpnxdijue

Planck priors for dark energy surveys

Pia Mukherjee, Martin Kunz, David Parkinson, Yun Wang
2008 Physical Review D  
We also demonstrate that the method can be used for scalar field dark energy independently of the parametrisation of the equation of state, and discuss how this method should be used for other kinds of  ...  In this paper we consider the compression of the projected Planck CMB data into four parameters, R (scaled distance to last scattering surface), l_a (angular scale of sound horizon at last scattering),  ...  In our case we find that the procedure works quite well for the case where the Planck data is combined with the SN Ia and BAO data, since there the information loss is negligible. 3 Indeed, we find about  ... 
doi:10.1103/physrevd.78.083529 fatcat:x4vppc2qpvawbfzztedjem5bou

Constraints on perfect fluid and scalar field dark energy models from future redshift surveys

L. Amendola, C. Quercellini, E. Giallongo
2005 Monthly notices of the Royal Astronomical Society  
In the scalar field case we show that the slope n of the inverse power-law potential for dark energy can be constrained to Δ n=0.26 (spectroscopic redshifts) or Δ n=0.40 (photometric redshifts), i.e. better  ...  We model the dark energy either with a perfect fluid or a scalar field and take into account the information contained in the linear growth function.  ...  FISHER MATRIX METHOD The method proposed in SE is based on the Fisher matrix, an approximation to the likelihood function that provides under some conditions the minimal errors that a given experiment  ... 
doi:10.1111/j.1365-2966.2004.08558.x fatcat:km6sjbzqkndvhfb2riuekyweny

Data Fusion for Electromagnetic and Electrical Resistive Tomography Based on Maximum Likelihood

Sven Nordebo, Mats Gustafsson, Therese Sjöden, Francesco Soldovieri
2011 International Journal of Geophysics  
In this paper, a proper scalar product is defined for the measurements and a truncated Singular Value Decomposition (SVD) based algorithm is devised which combines the measurement data of the two imaging  ...  The Fisher information is particularly useful for inverse problems which can be linearized similar to the Born approximation.  ...  Acknowledgment The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement no. 225663.  ... 
doi:10.1155/2011/617089 fatcat:i4wakknonjabxlikieognadz5e

On Evolution of Statistical Inference

D A S Fraser
2018 Journal of Statistical Theory and Applications (JSTA)  
The foundations of statistics have evolved over many centuries, perhaps millennia, with major paradigm shifts of the form described in Kuhn (1962) .  ...  But there is a progressive clarification in the processes of statistical inference so that current theory can now coherently and definitively handle a wide range of inference problems.  ...  Acknowledgements This research has been supported by the Natural Sciences and Engineering Research Counsel of Canada and the Senior Scholars Funding of York University. References  ... 
doi:10.2991/jsta.2018.17.2.1 fatcat:jqtza5swxjgfnafzviltbkbm54

Harrison-Zel'dovich primordial spectrum is consistent with observations

Stefania Pandolfi, Asantha Cooray, Elena Giusarma, Edward W. Kolb, Alessandro Melchiorri, Olga Mena, Paolo Serra
2010 Physical Review D  
The first important step for inflationary cosmology is to check the consistency of the HZ primordial spectrum with current observations.  ...  Inflation predicts primordial scalar perturbations with a nearly scale-invariant spectrum and a spectral index approximately unity (the Harrison--Zel'dovich (HZ) spectrum).  ...  We adopt two methods for parametrizing the reionization history. The first method, developed in Ref.  ... 
doi:10.1103/physrevd.81.123509 fatcat:3rkmx36g4vd2vewanatsfavo74

Microwave Background Constraints on Cosmological Parameters

Matias Zaldarriaga, David N. Spergel, Uroš Seljak
1997 Astrophysical Journal  
resolved with the temperature data alone.  ...  the ionization history of the universe.  ...  In §5, we explore the accuracy of the Fisher method by performing a more general type of analysis and investigate the effects of prior information in the accuracy of the reconstruction.  ... 
doi:10.1086/304692 fatcat:bt63oyyutjevbjxoqwastbmprm

Spatially sensitive statistical shape analysis for pedestrian recognition from LIDAR data

Michalis A. Savelonas, Ioannis Pratikakis, Theoharis Theoharis, Georgios Thanellas, Frédéric Abad, Rémy Bendahan
2018 Computer Vision and Image Understanding  
This work introduces encoding methods for pedestrian recognition, based on statistical shape analysis of 3D LIDAR data.  ...  The proposed approach has two variants, based on the encoding of local shape descriptors either in a spatially agnostic or spatially sensitive fashion.  ...  This work introduces encoding methods for pedestrian recognition, based on statistical shape analysis of 3D LIDAR data.  ... 
doi:10.1016/j.cviu.2018.06.001 fatcat:xj5aa44r4fddvaaiaem5n43ztm
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