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This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable.
Sur les fonctions convexes et les inégalités entre les valeurs moyennes,
JOHAN LUDWIG WILLIAM VALDEMAR JENSEN, · 1906
Earlier work this paper cites.
Maximum likelihood from incomplete data via the em algorithm,
ARTHUR P. DEMPSTER, NAN M. LAIRD, and DONALD B. RUBIN, · 1977
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Nonequilibrium equality for free energy differences,
C. JARZYNSKI, · 1997
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Refining Jensen’s inequality,
SHOSHANA ABRAMOVICH, GRAHAM JAMESON, AND GORD SINNAMON, · 2004
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The Cauchy-Schwarz Master Class: an Introduction to the Art of Mathematical Inequalities
J. MICHAEL STEELE, · 2004
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Jensen’s inequality for nonconvex functions,
SANJO ZLOBEC, · 2004
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Graphical models, exponential families, and variational inference,
MARTIN J. WAINWRIGHT, MICHAEL I. JORDAN, et al, · 2008
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Jensen’s inequality and new entropy bounds,
SLAVKO SIMIC, · 2009
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On an upper bound for Jensen’s inequality,
SLAVKO SIMIC, · 2009
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Moments of sums of independent and identically distributed random variables,
DANIEL M. PACKWOOD, · 2011
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Elements of information theory
THOMAS M. COVER and JOY A. THOMAS, · 2012
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On a lower bound for the Jensen inequality,
STEPHEN G. WALKER, · 2014
Cited alongside, same era.
Jensen–ostrowski type inequalities and applications for f-divergence measures,
PIETRO CERONE, SEVER S. DRAGOMIR, and EDER KIKIANTY, · 2015
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How sharp is the Jensen inequality?,
DANILO COSTARELLI and RENATO SPIGLER, · 2015
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Some new estimates of the ’Jensen gap’,
SHOSHANA ABRAMOVICH and LARS-ERIK PERSSON, · 2016
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Jensen and ostrowski type inequalities for general lebesgue integral with applications,
SEVER DRAGOMIR, · 2016
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Ostrowski and Jensen type inequalities for higher derivatives with applications,
SILVESTRU DRAGOMIR, P. CERONE, and EDER KIKIANTY, · 2016
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Jensen–ostrowski inequalities and integration schemes via the darboux expansion,
P. CERONE, S. S. DRAGOMIR, and E. KIKIANTY, · 2017
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Sharpening Jensen’s inequality,
J. G. LIAO and ARTHUR BERG, · 2017
Closest in time.
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On inequalities of Jensen-Ostrowski type,
PIETRO CERONE, SEVER S. DRAGOMIR, and EDER KIKIANTY, · 2015
Cited alongside, same era.