\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[ngerman,english]{babel}



\usepackage{float}








\begin{document}

\title{Information-Theoretic Scores for Bayesian Model Selection and Similarity
Analysis: Concept and Application to a Groundwater Problem}



\author[1]{Maria Fernanda Morales Oreamuno}%
\author[1]{Sergey Oladyshkin}%
\author[2]{Wolfgang Nowak}%
\affil[1]{University of Stuttgart}%
\affil[2]{Universität Stuttgart}%


\vspace{-1em}



  
  \date{May 08, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Bayesian model selection (BMS) and Bayesian model justifiability
analysis (BMJ) provide a statistically rigorous framework to compare
competing conceptual models through the use of Bayesian model evidence
(BME). However, BME-based analysis has two main limitations: (1) it's
powerless when comparing models with different data set sizes and/or
types of data and (2) doesn't allow to judge a model's performance based
on its posterior predictive capabilities. Thus, traditional BME-based
approaches ignore useful data or models due to issue (1) or disregards
Bayesian updating because of issue (2). To address these limitations, we
advocate to include additional information-theoretic scores into BMS and
BMJ analysis: expected log-predictive density (ELPD), relative entropy
(RE) and information entropy (IE). Exploring the connection between
Bayesian inference and information theory, we explicitly link BME and
ELPD together with RE and IE to indicate the information flow in BMS and
BMJ analysis. We show how to compute and interpret these scores
alongside BME, and apply it in a model selection and similarity analysis
framework. We test the methodology on a controlled 2D groundwater setup
considering five competing conceptual models accompanied with different
data sets. The results show how the information-theoretic scores
complement BME by providing a more complete picture concerning the
Bayesian updating process. Additionally, we present how both RE and IE
can be used to objectively compare models that feature different data
sets. Overall, the introduced Bayesian information-theoretic framework
helps to avoid any potential loss of information and leads to an
informed decision for model selection and similarity.%
\end{abstract}%



\sloppy




\selectlanguage{english}
\FloatBarrier
\end{document}

