4. Methods

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\newcommand{\lnLphys}[2][]{l^{{p}}_{#1|#2}} \newcommand{\lnLphysL}[3][]{l^{{p},(#3)}_{#1|#2}} \newcommand{\Elmu}[2][1]{μ_{{#2}}^{(#1)}} \newcommand{\Elmuh}[2][1]{\hat{μ}_{{#2}}^{(#1)}} \newcommand{\Elsig}[2][1]{Σ_{{#2}}^{(#1)}} \newcommand{\Elsigh}[2][1]{\hat{Σ}_{{#2}}^{(#1)}} \newcommand{\pathP}{\mathop{{p}}} % Path-sampling process (generic) \newcommand{\pathPhb}{\mathop{{p}}_{\mathrm{Beta}}} % Path-sampling process (hierarchical beta) \newcommand{\interval}{\mathcal{I}} \newcommand{\Phiset}[1]{\{\Phi\}^{\small (#1)}} \newcommand{\Phipart}[1]{\{\mathcal{I}_Φ\}^{\small (#1)}} \newcommand{\qhset}[1]{\{\qh\}^{\small (#1)}} \newcommand{\Dqpart}[1]{\{Δ\qh_{2^{#1}}\}} \newcommand{\LsAzl}{\mathcal{L}_{\smash{{}^{\,*}_A},z,L}} \newcommand{\LsBzl}{\mathcal{L}_{\smash{{}^{\,*}_B},z,L}} \newcommand{\lsA}{l_{\smash{{}^{\,*}_A}}} \newcommand{\lsB}{l_{\smash{{}^{\,*}_B}}} \newcommand{\lsAz}{l_{\smash{{}^{\,*}_A},z}} \newcommand{\lsAzj}{l_{\smash{{}^{\,*}_A},z_j}} 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\newcommand{\Phil}[2][]{Φ_{#1|#2}} % Φ_{\la} \newcommand{\Philt}[2][]{\widetilde{Φ}_{#1|#2}} % Φ_{\la} \newcommand{\Philhat}[2][]{\hat{Φ}_{#1|#2}} % Φ_{\la} \newcommand{\Philsaz}{Φ_{\smash{{}^{*}_a},z}} % Φ_{\lasz} \newcommand{\Phileaz}{Φ_{\smash{{}^{ε}_a},z}} % Φ_{\laez} \newcommand{\Philseaz}{Φ_{\smash{{}^{*ε}_a},z}} % Φ_{\lasez} \newcommand{\mus}[1][1]{μ^{(#1)}_*} \newcommand{\musA}[1][1]{μ^{(#1)}_{\smash{{}^{\,*}_A}}} \newcommand{\SigsA}[1][1]{Σ^{(#1)}_{\smash{{}^{\,*}_A}}} \newcommand{\musB}[1][1]{μ^{(#1)}_{\smash{{}^{\,*}_B}}} \newcommand{\SigsB}[1][1]{Σ^{(#1)}_{\smash{{}^{\,*}_B}}} \newcommand{\musa}[1][1]{μ^{(#1)}_{\smash{{}^{*}_a}}} \newcommand{\Sigsa}[1][1]{Σ^{(#1)}_{\smash{{}^{*}_a}}} \newcommand{\Msah}{{\color{highlight-red}\mathcal{M}^{*}_a}} \newcommand{\Msazh}{{\color{highlight-red}\mathcal{M}^{*}_{a,z}}} \newcommand{\Meah}{{\color{highlight-blue}\mathcal{M}^{ε}_a}} \newcommand{\Meazh}{{\color{highlight-blue}\mathcal{M}^{ε}_{a,z}}} \newcommand{\lsazh}{{\color{highlight-red}l_{\smash{{}^{*}_a},z}}} \newcommand{\leazh}{{\color{highlight-blue}l_{\smash{{}^{ε}_a},z}}} \newcommand{\lseazh}{{\color{highlight-orange}l_{\smash{{}^{*ε}_a},z}}} \newcommand{\Philsazh}{{\color{highlight-red}Φ_{\smash{{}^{*}_a},z}}} % Φ_{\lasz} \newcommand{\Phileazh}{{\color{highlight-blue}Φ_{\smash{{}^{ε}_a},z}}} % Φ_{\laez} \newcommand{\Philseazh}{{\color{highlight-orange}Φ_{\smash{{}^{*ε}_a},z}}} % Φ_{\lasez} \newcommand{\emdstd}{\tilde{σ}} \DeclareMathOperator{\Mvar}{Mvar} \DeclareMathOperator{\AIC}{AIC} \DeclareMathOperator{\epll}{epll} \DeclareMathOperator{\elpd}{elpd} \DeclareMathOperator{\MDL}{MDL} \DeclareMathOperator{\comp}{COMP} \DeclareMathOperator{\Lognorm}{Lognorm} \DeclareMathOperator{\erf}{erf} \DeclareMathOperator*{\argmax}{arg\,max} \DeclareMathOperator{\Image}{Image} \DeclareMathOperator{\sgn}{sgn} \DeclareMathOperator{\SE}{SE} % standard error \DeclareMathOperator{\Unif}{Unif} \DeclareMathOperator{\Poisson}{Poisson} 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