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| <div style="font-size:12pt; font-family:garamond"> | | <div style="font-size:12pt; font-family:garamond"> |
− | <!-- some LaTeX macros we want to use: -->
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− | $
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− | <!-- Methods macros -->
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− | \def\ieta{m}
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− | \def\Meta{M}
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− | \def\imh{\ell}
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− | \def\ceta{\tilde{\eta}}
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− | \def\cpsi{\tilde{\psi}}
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− | \def\transpose{t}
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− | \newcommand{\Dt}[1]{\partial_\theta #1}
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− | \newcommand{\DDt}[1]{\partial^2_{\theta} #1}
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− | \newcommand{\cov}[1]{\mbox{Cov}\left(#1\right)}
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− | \def\jparam{j}
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− | \newcommand{\Dphi}[1]{\partial_\phi #1}
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− | \newcommand{\Dpsi}[1]{\partial_\psi #1}
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− | \def\llike{\cal LL}
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− | \def\tqpsii{\tilde{p}_{\psi_i}}
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− | \def\tppsii{\tilde{\pmacro}}
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− | \def\petai{\pmacro}
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− | \def\pcetaiyi{\pmacro}
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− | \def\pyietai{\pmacro}
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− | \def\pcyietai{\pmacro}
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− | \def\pphii{\pmacro}
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− | \def\pyiphii{\pmacro}
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− | \def\pcyiphii{\pmacro}
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− | \def\pcphiiyi{\pmacro}
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− | \def\bphi{\boldsymbol{\phi}}
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− | \def\qphii{p_{_{\phi_i}}}
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− | \def\tqpsii{\tilde{p}_{\psi_i}}
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− | \def\tppsii{\tilde{\pmacro}}
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− | \def\tqphii{\tilde{p}_{\phi_i}}
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− | \def\tpphii{\tilde{\pmacro}}
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− | \def\qcphiiyi{p_{_{\phi_i|y_i}}}
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− | <!-- .......... -->
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− |
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− | \newcommand{\argmin}[1]{ \mathop{\rm arg} \mathop{\rm min}\limits_{#1} }
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− | \newcommand{\argmax}[1]{ \mathop{\rm arg} \mathop{\rm max}\limits_{#1} }
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− | \newcommand{\nominal}[1]{#1^{\star}}
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− | \newcommand{\psis}{\psi{^\star}}
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− | \newcommand{\phis}{\phi{^\star}}
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− | \newcommand{\hpsi}{\hat{\psi}}
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− | \newcommand{\hphi}{\hat{\phi}}
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− | \newcommand{\teps}{\varepsilon}
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− | \newcommand{\limite}[2]{\mathop{\longrightarrow}\limits_{\mathrm{#1}}^{\mathrm{#2}}}
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− | \newcommand{\DDt}[1]{\partial^2_\theta #1}
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− |
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− | \def\cpop{c_{\rm pop}}
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− | \def\Vpop{V_{\rm pop}}
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− | \def\iparam{l}
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− | \newcommand{\trcov}[1]{#1}
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− |
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− | \def\bu{\boldsymbol{u}}
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− | \def\bt{\boldsymbol{t}}
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− | \def\bT{\boldsymbol{T}}
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− | \def\by{\boldsymbol{y}}
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− | \def\bx{\boldsymbol{x}}
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− | \def\bc{\boldsymbol{c}}
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− | \def\bw{\boldsymbol{w}}
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− | \def\bz{\boldsymbol{z}}
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− | \def\bpsi{\boldsymbol{\psi}}
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− | \def\bbeta{\beta}
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− |
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− |
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− | \def\aref{a^\star}
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− | \def\kref{k^\star}
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− | \def\model{M}
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− | \def\hmodel{m}
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− | \def\mmodel{\mu}
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− | \def\imodel{H}
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− | \def\thmle{\hat{\theta}}
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− | \def\ofim{I^{\rm obs}}
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− | \def\efim{I^{\star}}
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− |
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− | \def\Imax{\rm Imax}
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− | \def\probit{\rm probit}
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− | \def\vt{t}
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− | \def\id{\rm Id}
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− | \def\teta{\tilde{\eta}}
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− | \newcommand{\eqdef}{\mathop{=}\limits^{\mathrm{def}}}
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− |
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− | \newcommand{\deriv}[1]{\frac{d}{dt}#1(t)}
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− |
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− | \newcommand{\pred}[1]{\tilde{#1}}
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− | \def\phis{\phi{^\star}}
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− | \def\hphi{\tilde{\phi}}
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− | \def\hw{\tilde{w}}
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− | \def\hpsi{\tilde{\psi}}
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− | \def\hatpsi{\hat{\psi}}
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− | \def\hatphi{\hat{\phi}}
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− | \def\psis{\psi{^\star}}
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− | \def\transy{u}
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− | \def\psipop{\psi_{\rm pop}}
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− | \newcommand{\psigr}[1]{\hat{\bpsi}_{#1}}
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− | \newcommand{\Vgr}[1]{\hat{V}_{#1}}
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− |
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− | \def\pmacro{\text{p}}
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− | \def\py{\pmacro}
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− | \def\pt{\pmacro}
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− | \def\pc{\pmacro}
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− | \def\pu{\pmacro}
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− | \def\pyi{\pmacro}
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− | \def\pyj{\pmacro}
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− | \def\ppsi{\pmacro}
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− | \def\ppsii{\pmacro}
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− | \def\pcpsith{\pmacro}
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− | \def\pcpsiiyi{\pmacro}
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− | \def\pth{\pmacro}
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− | \def\pypsi{\pmacro}
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− | \def\pcypsi{\pmacro}
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− | \def\ppsic{\pmacro}
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− | \def\pcpsic{\pmacro}
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− | \def\pypsic{\pmacro}
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− | \def\pypsit{\pmacro}
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− | \def\pcypsit{\pmacro}
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− | \def\pypsiu{\pmacro}
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− | \def\pcypsiu{\pmacro}
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− | \def\pypsith{\pmacro}
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− | \def\pypsithcut{\pmacro}
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− | \def\pypsithc{\pmacro}
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− | \def\pcypsiut{\pmacro}
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− | \def\pcpsithc{\pmacro}
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− | \def\pcthy{\pmacro}
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− | \def\pyth{\pmacro}
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− | \def\pcpsiy{\pmacro}
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− | \def\pz{\pmacro}
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− | \def\pw{\pmacro}
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− | \def\pcwz{\pmacro}
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− | \def\pw{\pmacro}
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− | \def\pcyipsii{\pmacro}
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− | \def\pyipsii{\pmacro}
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− | \def\pcetaiyi{\pmacro}
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− | \def\pypsiij{\pmacro}
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− | \def\pyipsiONE{\pmacro}
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− | \def\ptypsiij{\pmacro}
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− | \def\pcyzipsii{\pmacro}
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− | \def\pczipsii{\pmacro}
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− | \def\pcyizpsii{\pmacro}
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− | \def\pcyijzpsii{\pmacro}
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− | \def\pcyiONEzpsii{\pmacro}
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− | \def\pcypsiz{\pmacro}
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− | \def\pccypsiz{\pmacro}
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− | \def\pypsiz{\pmacro}
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− | \def\pcpsiz{\pmacro}
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− | \def\peps{\pmacro}
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− | \def\petai{\pmacro}
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− |
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− | \def\psig{\psi}
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− | \def\psigprime{\psig^{\prime}}
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− | \def\psigiprime{\psig_i^{\prime}}
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− | \def\psigk{\psig^{(k)}}
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− | \def\psigki{\psig_i^{(k)}}
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− | \def\psigkun{\psig^{(k+1)}}
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− | \def\psigkuni{\psig_i^{(k+1)}}
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− | \def\psigi{\psig_i}
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− | \def\psigil{\psig_{i,\ell}}
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− | \def\phig{\phi}
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− | \def\phigi{\phig_i}
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− | \def\phigil{\phig_{i,\ell}}
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− |
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− |
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− | \def\etagi{\eta_i}
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− | \def\IIV{\Omega}
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− | \def\thetag{\theta}
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− | \def\thetagk{\theta_k}
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− | \def\thetagkun{\theta_{k+1}}
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− | \def\thetagkunm{\theta_{k-1}}
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− | \def\sgk{s_{k}}
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− | \def\sgkun{s_{k+1}}
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− | \def\yg{y}
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− | \def\xg{x}
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− |
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− | \def\qx{p_x}
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− | \def\qy{p_y}
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− | \def\qt{p_t}
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− | \def\qc{p_c}
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− | \def\qu{p_u}
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− | \def\qyi{p_{y_i}}
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− | \def\qyj{p_{y_j}}
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− | \def\qpsi{p_{\psi}}
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− | \def\qpsii{p_{\psi_i}}
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− | \def\qcpsith{p_{\psi|\theta}}
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− | \def\qth{p_{\theta}}
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− | \def\qypsi{p_{y,\psi}}
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− | \def\qcypsi{p_{y|\psi}}
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− | \def\qpsic{p_{\psi,c}}
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− | \def\qcpsic{p_{\psi|c}}
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− | \def\qypsic{p_{y,\psi,c}}
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− | \def\qypsit{p_{y,\psi,t}}
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− | \def\qcypsit{p_{y|\psi,t}}
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− | \def\qypsiu{p_{y,\psi,u}}
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− | \def\qcypsiu{p_{y|\psi,u}}
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− | \def\qypsith{p_{y,\psi,\theta}}
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− | \def\qypsithcut{p_{y,\psi,\theta,c,u,t}}
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− | \def\qypsithc{p_{y,\psi,\theta,c}}
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− | \def\qcypsiut{p_{y|\psi,u,t}}
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− | \def\qcpsithc{p_{\psi|\theta,c}}
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− | \def\qcthy{p_{\theta | y}}
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− | \def\qyth{p_{y,\theta}}
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− | \def\qcpsiy{p_{\psi|y}}
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− | \def\qcpsiiyi{p_{\psi_i|y_i}}
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− | \def\qcetaiyi{p_{\eta_i|y_i}}
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− | \def\qz{p_z}
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− | \def\qw{p_w}
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− | \def\qcwz{p_{w|z}}
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− | \def\qw{p_w}
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− | \def\qcyipsii{p_{y_i|\psi_i}}
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− | \def\qyipsii{p_{y_i,\psi_i}}
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− | \def\qypsiij{p_{y_{ij}|\psi_{i}}}
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− | \def\qyipsi1{p_{y_{i1}|\psi_{i}}}
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− | \def\qtypsiij{p_{\transy(y_{ij})|\psi_{i}}}
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− | \def\qcyzipsii{p_{z_i,y_i|\psi_i}}
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− | \def\qczipsii{p_{z_i|\psi_i}}
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− | \def\qcyizpsii{p_{y_i|z_i,\psi_i}}
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− | \def\qcyijzpsii{p_{y_{ij}|z_{ij},\psi_i}}
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− | \def\qcyi1zpsii{p_{y_{i1}|z_{i1},\psi_i}}
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− | \def\qcypsiz{p_{y,\psi|z}}
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− | \def\qccypsiz{p_{y|\psi,z}}
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− | \def\qypsiz{p_{y,\psi,z}}
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− | \def\qcpsiz{p_{\psi|z}}
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− | \def\qeps{p_{\teps}}
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− | \def\qetai{p_{\eta_i}}
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− |
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− | \def\neta{n_\eta}
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− | \def\ncov{M}
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− | \def\npsi{n_\psig}
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− |
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− |
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− | \def\beeta{\eta}
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− |
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− | \def\logit{\rm logit}
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− | \def\transy{u}
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− | \def\so{O}
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− |
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− | \newcommand{\prob}[1]{ \mathbb{P}\left(#1\right)}
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− | \newcommand{\probs}[2]{ \mathbb{P}_{#1}\left(#2\right)}
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− | \newcommand{\esp}[1]{\mathbb{E}\left(#1\right)}
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− | \newcommand{\esps}[2]{\mathbb{E}_{#1}\left(#2\right)}
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− | \newcommand{\var}[1]{\mbox{Var}\left(#1\right)}
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− | \newcommand{\vars}[2]{\mbox{Var}_{#1}\left(#2\right)}
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− | \newcommand{\std}[1]{\mbox{sd}\left(#1\right)}
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− | \newcommand{\stds}[2]{\mbox{sd}_{#1}\left(#2\right)}
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− | \newcommand{\corr}[1]{\mbox{Corr}\left(#1\right)}
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− | \newcommand{\Rset}{\mbox{$\mathbb{R}$}}
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− | \newcommand{\Yr}{\mbox{$\mathcal{Y}$}}
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− | \newcommand{\teps}{\varepsilon}
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− | \newcommand{\like}{\cal L}
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− | \newcommand{\logit}{\rm logit}
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− | \newcommand{\transy}{u}
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− | \newcommand{\repy}{y^{(r)}}
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− | \newcommand{\brepy}{\boldsymbol{y}^{(r)}}
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− | \newcommand{\vari}[3]{#1_{#2}^{{#3}}}
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− | \newcommand{\dA}[2]{\dot{#1}_{#2}(t)}
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− | \newcommand{\nitc}{N}
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− | \newcommand{\itc}{I}
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− | \newcommand{\vl}{V}
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− | \newcommand{tstart}{t_{start}}
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− | \newcommand{tstop}{t_{stop}}
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− | \newcommand{\one}{\mathbb{1}}
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− | \newcommand{\hazard}{h}
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− | \newcommand{\cumhaz}{H}
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− | \newcommand{\std}[1]{\mbox{sd}\left(#1\right)}
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− | \newcommand{\eqdef}{\mathop{=}\limits^{\mathrm{def}}}
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− |
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− | \def\mlxtran{\text{MLXtran}}
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− | \def\monolix{\text{Monolix}}
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− | $
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| | | |
| The observed log-likelihood ${\llike}(\theta;\by)=\log({\like}(\theta;\by))$ can be estimated without any approximation of the model using a Monte-Carlo approach. | | The observed log-likelihood ${\llike}(\theta;\by)=\log({\like}(\theta;\by))$ can be estimated without any approximation of the model using a Monte-Carlo approach. |