% acronyms


\newcommand{\stddmuccprior}{1.03} 
\newcommand{\stdmubiasccprior}{0.15}
\newcommand{\Dzbias}{\overline{\Dz}}
\newcommand{\URLSNANA}{\url{https://github.com/RickKessler/SNANA}}
\newcommand{\URLLSST}{\url{www.lsst.org}}
\newcommand{\URLDESC}{\url{https://lsstdesc.org}}
\newcommand{\URLOPSIM}{\url{http://opsim.lsst.org/runs/minion_1016/data/minion_1016_sqlite.db.gz}}
\newcommand{\HOSTLIB}{{\tt HOSTLIB}}
\newcommand{\SALTII}{{\sc SALT-II}}
\newcommand{\DESSN}{DES-SN}
\newcommand{\lowz}{low-$z$~}
\newcommand{\mosfit}{{\tt MOSFiT}\xspace}
\newcommand{\bands}{$ugrizY$}
\newcommand{\PLASTICC}{Photometric LSST Astronomical Time Series Classification Challenge}
\newcommand{\acro}{{\tt ELAsTiCC}}
\newcommand{\SNANA}{{\tt SNANA}}
\newcommand{\pippin}{{\tt Pippin}}
\newcommand{\LSST}{Large Synoptic Survey Telescope}
\newcommand{\DES}{Dark Energy Survey}
\newcommand{\OPSIM}{\verb|OpSim|}
\newcommand{\Spec}{Spectroscopic}
\newcommand{\spec}{spectroscopic}
\newcommand{\specy}{spectroscopically}
\newcommand{\ZPHOT}{{\bf\tt ZPHOT}}
\newcommand{\zSpec}{z_{\rm spec}}
\newcommand{\LCDM}{\Lambda{\rm CDM}}
\newcommand{\OL}{\Omega_{\Lambda}}
\newcommand{\OM}{\Omega_{\rm M}}
\newcommand{\zcmb}{z_{\rm cmb,true}}
\newcommand{\RateUnit}{{\rm yr}^{-1}{\rm Mpc}^{-3}}
\newcommand{\Ftrue}{F_{\rm true}}
\newcommand{\sigF}{\sigma_{F}}
\newcommand{\sigFi}{\sigma_{F,i}}
\newcommand{\sigFtrue}{\sigma_{\rm Ftrue}}
\newcommand{\zSN}{z_{\rm SN}}
\newcommand{\zHOST}{z_{\rm HOST}}
\newcommand{\Ngen}{$N_{\rm gen}$} % 


\newcommand{\FiData}{F_i^{\rm data}}
\newcommand{\FiModel}{F_i^{\rm model}}
\newcommand{\xvecSALT}{\vec{x}_5}
\newcommand{\be}{\begin{equation}}
\newcommand{\ee}{\end{equation}}
\newcommand{\bea}{\begin{eqnarray}}
\newcommand{\eea}{\end{eqnarray}}
\newcommand{\iu}{{i\mkern1mu}} 
\newcommand{\sigFiTilde}{\Tilde{\sigma}_{F,i}}
\newcommand{\logsigmodel}{2\ln({\sigFi/\sigFiTilde})}
\newcommand{\sigzhost}{\sigma_{z,{\rm host}}}
\newcommand{\alphaTrue}{\alpha^{\rm true}}
\newcommand{\betaIntTrue}{\beta_{\rm int}^{\rm true}}
\newcommand{\DESVYR}{DES-SN5YR}
\newcommand{\PPLUS}{Pantheon+}
\newcommand{\chisqflux}{\chi^2_{F_i}}
\newcommand{\chisqhost}{\chi^{2}_{\rm host}}
\newcommand{\chisqsyst}{\chi^{2}_{\rm syst}}
\newcommand{\probzhost}{\mathcal{P}_{host}(\zphot)}
\newcommand{\rcc}{R_{CC}}
\newcommand{\NSAMPLE}{25} % RK 
\newcommand{\NBIASCORTOT}{$1 \times 10^8$}
\newcommand{\NBIASCORHIZ}{$9 \times 10^7$}
\newcommand{\NBIASCORLOZ}{$4 \times 10^6$}
\newcommand{\NSYST}{7}
\newcommand{\dz}{\delta z}
\newcommand{\fout}{f_{\rm out}}
\newcommand{\sigIQR}{\sigma_{\rm IQR}}
\newcommand{\ztrue}{z_{\rm true}}
\newcommand{\zphot}{z_{\rm phot}}
\newcommand{\zspec}{z_{\rm spec}}
\newcommand{\zcheat}{z_{\rm cheat}}
\newcommand{\zhost}{z_{\rm host}}
\newcommand{\Dz}{\Delta z_{(1+z)}}
\newcommand{\Pfit}{P_{\rm fit}}
\newcommand{\ayan}[1]{\textcolor{red}{#1}} 
\newcommand{\rk}[1]{\textcolor{brown}{#1}}
\newcommand{\rkout}[1]{\textcolor{red}{\sout{\protect#1}}}
\newcommand{\rkred}[1]{\textcolor{red}{#1}}
\newcommand{\IR}[1]{\textcolor{cyan}{#1}}
\newcommand{\G}{G_{\rm host}}
\newcommand{\mubias}{\Delta\mu_{\rm bias}}
\newcommand{\mutrue}{\mu_{\rm true}}
\newcommand{\pkref}{p_k^{\rm ref}}
\newcommand{\pk}{p_k}
\newcommand{\ddlr}{d_{DLR}}
\newcommand{\sigkref}{\sigma_k^{\rm ref}}
\newcommand{\Pia}{P_{\text{Ia}}}
\newcommand{\dzsyst}{\Delta z_{\rm syst-z}}
\newcommand{\dmusyst}{\Delta\mu_{\rm syst-z}}
\newcommand{\meanlamb}{\langle\lambda_{\rm cen}\rangle}
\newcommand{\alphaTrueSym}{\alpha_{\rm true}}
\newcommand{\betaTrueSym}{\beta_{\rm true}}
\newcommand{\alphaTrueVal}{0.15}
\newcommand{\betaTrueVal}{3.1}
\newcommand{\nrebinx}{$4$}
\newcommand{\nrebinc}{$8$}
\newcommand{\HDSIZEREBIN}{448} %4 X 8 X 14
\newcommand{\hdsizerebin}{300} %Average from 25 HD file sizes in rebinned folder. 
\newcommand{\sigmu}{\sigma_{\mu}}
\newcommand{\sigmubar}{\overline{\sigma_{\mu}}}
\newcommand{\URLDIFFSKY}{\url{https://diffsky.readthedocs.io/en/latest}}
\newcommand{\sigz}{\sigma_{z}}
\newcommand{\sigR}{\sigma_{R}}
\newcommand{\sigint}{\sigma_{\rm int}}

\newcommand{\COVsyst}{{\rm COV}_{\rm syst}}
\newcommand{\COVsysti}{{\rm COV}_{{\rm syst},i}}
\newcommand{\COVstat}{{\rm COV}_{\rm stat}}

\newcommand{\wCDM}{$w$CDM}
\newcommand{\wwCDM}{$w_0w_a$CDM}
\newcommand{\ww}{$w_0$-$w_a$}
\newcommand{\URLDDF}{\url{https://www.lsst.org/scientists/survey-design/ddf}}
\newcommand{\URLELASTICC}{\url{https://portal.nersc.gov/cfs/lsst/DESC_TD_PUBLIC/ELASTICC}}
\newcommand{\NZBIN}{\textcolor{red}{14}}

\newcommand{\AVGwbias}{\langle w$-bias$\rangle}
\newcommand{\AVGwsigbiaszspecsyst}{$0.025$}
\newcommand{\AVGwsigbiaszphotsyst}{$0.025$}
\newcommand{\AVGwsig}{\langle\sigma_w\rangle}
\newcommand{\STDw}{{\rm STD}_w}

\newcommand{\AVGwwbias}{\langle {w_0}$-bias$\rangle}
\newcommand{\AVGwwsig}{\langle\sigma_{w_0}\rangle}
\newcommand{\STDww}{{\rm STD}_{w_0}}

\newcommand{\desfv}{DES-SN5YR}
\newcommand{\AVGwabias}{\langle {w_a}$-bias$\rangle}
\newcommand{\AVGwasig}{\langle\sigma_{w_a}\rangle}
\newcommand{\STDwa}{{\rm STD}_{w_a}}

\newcommand{\AVGFoM}{{\langle}{\rm FoM}{\rangle}}

\newcommand{\RatioFoM}{{\cal R}_{{\rm FoM},i}}
\newcommand{\FoM}{{\rm FoM}}
\newcommand{\FoMStat}{{\rm FoM}_{\rm stat}}
\newcommand{\FoMSysti}{{\rm FoM}_{{\rm syst},i}}

\newcommand{\AVGFOMzspecstat}{$114$}
\newcommand{\AVGFOMzspecsyst}{$92$}
\newcommand{\AVGFOMzspecstatU}{$115$}
\newcommand{\AVGFOMzspecsystU}{$106$}
\newcommand{\URLDIA}{\url{https://github.com/LSSTDESC/dia_pipe}}
\newcommand{\URLMINION}{\url{http://ls.st/Collection-4604}}


\newcommand{\AVGFOMzphotstat}{$193$}
\newcommand{\AVGFOMzphotsyst}{$131$}
\newcommand{\AVGFOMzphotstatU}{$182$}
\newcommand{\AVGFOMzphotsystU}{$156$}
\newcommand{\AVGFOMzphotsystR}{$159$}

\newcommand{\AVGwbiaszphotsyst}{$0.0091$}
\newcommand{\AVGwabiaszphotsyst}{$0.0363$}
\newcommand{\AVGwbiaszspecsyst}{$0.0140$}
\newcommand{\AVGwabiaszspecsyst}{$0.0662$}

%\newcommand{\zcmbObs}{z_{\rm cmb,obs}}
%\newcommand{\zhel}{z_{\rm hel,true}}
%\newcommand{\zhelObs}{z_{\rm hel,obs}}
%\newcommand{\mutrue}{\mu_{\rm true}}
% \newcommand{\muLCDM}{\mu_{\LCDM}}
%\newcommand{\muwCDM}{\mu_{\rm wCDM}}
%\newcommand{\sigz}{\sigma_{z}}
%\newcommand{\mtrue}{m_{\rm true}}
%\newcommand{\ZPHOTERR}{{\bf\tt ZPHOTERR}}
%\newcommand{\PEAKMJD}{{\bf\tt PEAKMJD}}