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The Bayesian Reconstruction (BR) Method

Alexander Rothkopf


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    "description": "<p>//*********************************************************************************<br>\n//<br>\n//&nbsp;&nbsp; &nbsp;Bayesian Spectral Reconstruction and Extended MEM<br>\n//<br>\n// &nbsp; &nbsp;Code:&nbsp;Dr. Alexander Karl Rothkopf&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; DATE: July 14th 2021<br>\n//<br>\n// &nbsp; &nbsp;Method: Dr. Yannis Burnier, Dr. Alexander Karl Rothkopf DATE: 2013<br>\n//&nbsp;&nbsp; &nbsp;========================================================================<br>\n//<br>\n//&nbsp;&nbsp; &nbsp;THIS PROGRAM IS AN IMPLEMENTATION OF TWO BAYESIAN APPROACHES<br>\n//&nbsp;&nbsp; &nbsp;FOR THE NUMERICAL INVERSION OF THE TYPICALLY ILL DEFINED TASK<br>\n//<br>\n//&nbsp;&nbsp; &nbsp;DATA[t] = Int_-WMIN^WMAX [ K[w,t] * SPEC[w] ]dw<br>\n//<br>\n//&nbsp;&nbsp; &nbsp;WHERE THE GOAL IS TO EXTRACT THE SPECTRAL FUNCTION SPEC[w] FROM<br>\n//&nbsp;&nbsp; &nbsp;THE PROVIDED LATTICE DATA DATA[t] USING A PREVIOUSLY SPECIFIED<br>\n//&nbsp;&nbsp; &nbsp;KERNEL FUNCTION K[w,t].<br>\n//<br>\n//&nbsp;&nbsp; &nbsp;References:<br>\n//<br>\n//&nbsp;&nbsp; &nbsp;Y.&nbsp;Burnier and A.&nbsp;Rothkopf,<br>\n//&nbsp;&nbsp; &nbsp;&quot;Bayesian Approach to Spectral Function Reconstruction for<br>\n//&nbsp;&nbsp; &nbsp; Euclidean Quantum Field Theories&quot;<br>\n//&nbsp;&nbsp; &nbsp;arXiv:1307.6106 [hep-lat]<br>\n//&nbsp;&nbsp; &nbsp;Phys. Rev. Lett. 111, 182003 (2013)<br>\n//<br>\n//&nbsp;&nbsp; &nbsp;A.&nbsp;Rothkopf<br>\n//&nbsp;&nbsp; &nbsp;&quot;Improved Maximum Entropy Analysis with an Extended Search Space&quot;<br>\n//&nbsp;&nbsp; &nbsp;arXiv:1110.6285 [physics.comp-ph]<br>\n//&nbsp;&nbsp; &nbsp;J.Comput.Phys. 238 (2013) 106-114<br>\n//<br>\n//*********************************************************************************</p>\n\n<p>//*********************************************************************************<br>\n//&nbsp;&nbsp; &nbsp;This program uses adapted code from two libraries:<br>\n//<br>\n//&nbsp;&nbsp; &nbsp;1. The GNU Scientific Library:<br>\n//<br>\n//&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;SINGULAR VALUE DECOMPOSITION<br>\n//&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;EIGENSYSTEMS OF SYMMETRIC MATRICES<br>\n//&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;MATRIX INVERSION BASED ON QR DECOMPOSITION<br>\n//&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;SOLVER FOR Ax=b BASED ON QR DECOMPOSITION<br>\n//<br>\n//&nbsp;&nbsp; &nbsp;2. The ALGLIB Library (MPFR part 2.6.):<br>\n//<br>\n//&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;LBFGS MINIMIZER<br>\n//&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;LEVENBERG MARQUARD + LBFGS PRECONDITIONER MINIMIZER<br>\n//&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;EIGENVALUES FOR NON_SYMMETRIC MATRICES<br>\n//<br>\n//*********************************************************************************</p>\n\n<p>&nbsp;</p>", 
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    "title": "The Bayesian Reconstruction (BR) Method", 
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    "references": [
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    "keywords": [
      "Bayesian inference, spectral reconstruction, spectral function, inverse problem, BR Method, Maximum Entropy Method,"
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    "publication_date": "2021-07-14", 
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        "orcid": "0000-0002-5526-0809", 
        "affiliation": "University of Stavanger", 
        "name": "Alexander Rothkopf"
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