CINXE.COM
Just a moment...
<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="390"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "statmodeling.stat.columbia.edu",cType: 'managed',cRay: '8e9e00c50ebc4b50',cH: 'Ixz30Yrt3KdJBnDj7dLQisDwO5nHJZnTSvafTNY2AUE-1732835129-1.2.1.1-pq_RvPSexoi5VD2VuxLhxUE7oOHBQXrGK2U3qJBzORNtXSUd.sPGCBcH0MQ2JUGj',cUPMDTk: "\/2020\/01\/29\/rao-blackwellization-and-discrete-parameters-in-stan\/?__cf_chl_tk=775gNlmFXsj8gF6tleH97A60OWo5fhBstPR9YIGwA64-1732835129-1.0.1.1-TZqtvSRzLDkfebb9QpckEsaIq4gZVg.I_mojrQBhMpg",cFPWv: 'b',cITimeS: '1732835129',cTTimeMs: '1000',cMTimeMs: '390000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/2020\/01\/29\/rao-blackwellization-and-discrete-parameters-in-stan\/?__cf_chl_f_tk=775gNlmFXsj8gF6tleH97A60OWo5fhBstPR9YIGwA64-1732835129-1.0.1.1-TZqtvSRzLDkfebb9QpckEsaIq4gZVg.I_mojrQBhMpg",md: "FqFJOMitjMWhiCdRS2eE7RF.x.nNhH4RfePZDlmZswM-1732835129-1.2.1.1-1neOkRIZq0B18GrQzT82_Tx4aAkAvTA8cH1oRi2nO_avg0.mTRAZoXrJRNcUfVAQW.zdppna3CO90SL6.USHVF0.3fy__ajJgJyywcEmu0Q9MJM6Dh1FE2lvjsPgmhaEh4CqaNCF_33h1dFeIOXMl3mKr9Dr4kHPvRFksuZYpdoC2ZmqYm7IjGisiav9N0hAe6ne5BovbeVtpoTsyGSFXIiCWDvFLXrMYVp0velUxUpHADoalBIvIjD.xcjn9bedrxoHyTqXOjFH9qvQ0pX99y4uJduhnrqprMp5.CaHHlYxVDBp12wt5O55NGNZUlJGHXFAVJyPuoVpCZpFL4PrYrcyZtdq3z6TeR5S0mmZVJqXjq4X_EvYW920pcyicTrHFbNYJpWrSmUyeN7LG7z41zhTslr2N7pivnQERiFZ0vUA.Kia0NLh7WAHjHx14dWP8ceoCan77pOwtHrEgFVYgqNdz2YKFp32KaGruG3Z6Bi8JhBH7O8uFH.7W5SeJS2NhoJ262AQB5tpQgBtZmspeRhyIK7JgmzIccOhsMYc0EfrgRva6cOD.gC7sRk7Gj.Ms8M9kAsfxtVFzQvbq6o4qKz2i.siyR44.aCf_SmlyRXliLBAerEZWM.9qkJYfr2JZZnbe08FZ_JZijq59qu7M0N2rn0htuBaxqPTLNjDMZPnst7aCQbkHI7J7dbFQirRWS7gIcgUv0BrviLUSk58CgJYI9JN6D_oZY9wU1BJM5SsyAR0r06GgSEx58pfMCWSbyQOfkaScU1l87iNDWqzCvVppeu.eBHcV5zYCuZfa5o8uqSAHbxnlJI9tAADZS7yjUlWPytCEdfmCL8fte08OSQ4_04TPjtGLfRBA1vX3mWH5ECnIYwghL3z6JQlI85009LaqUWHsK7UqqpzR8.4SEAO.W8K7DVAipBeK5ZIuESBs32qWxH_fvSM3EvSrUSXoreOKa4Q0aqavWFD.RgxybeklKbuQt1Ug6v3Tk2.l6r0xDZ4BSIk7bzX4ZFOmfHHw2zDNJMhpRBA_gBK9smXiHcMw7hxnV7FN1cpzON7Q2T8t8y4nKI0TrkILehQdtzg0.cjK5Y3apJlKVtE_v5GtcFoYNKdmDFVUP.uVhKIGz2Tsvu.BstaJWNBxvaejSfVQ0jNLNlJ4xqKNE36OOG4E4uPKESg47PIu0ZcP6DCVYNsou76obkTtSH33TKJWmHyaSKxZQu0q8T5Sd9TDQxuO1rEoUxIrNtLKE9sud1KbghQimWNQaYcUt46Tldfyt7orIeZYgPhAD0DQuQstgIMJPrgEAef606gzzEDTjxQ1fPWSagskIx3kaIbOvJfUOD3lxYcBQBr2OjcsPGaA8XlnzFGIL8oOJpndFhz3Wv0eststtDk0HpRAewsa78v3HW.rYFlb9NuoloT.lCryhhjRBkUs8D_zw2eHl6papMBIJ6Di0ayS8bigc3RFI5XTuQeR0l404wCreVnkblFES1RaG5vwvpWM7xl1K0JkX4gx2q4fzoiJw2hzFADiUshGFmlaWlKiz5vzque09FAU0KHbvLXZtPqQYyzsIuvQDc7sK6.PFqK0mFy7M4ZRWsit2rNM.fCyOUNRDqQp18FFo2I3SayZFdi1smwKiLYZgw14gDfRj3xOHGQ3pGSqrcw6ps4zmeZWtSbRafxlfFItXnJkQ9Eo5p1dYJGznys5fLcPGFmcp627MOJuItAt3Kc8Y6WV7yzAuMEqjvKByh7uVrtAXAIjTAODg3khQSZ14nvAp4MgMwi7yfZedd1h2SA4CB6cOFHBxvGbR422mbeDFdFVOwZsmcBIvynPCU..9WHcS__ySVARaggUsmaE8fYMCN5W.R5As7CJBynkeSVp1B2vWsPoJ9jkMJj.MigLyJ6ppaI63AIbmM8eTfB7S0y47rZe6hysvGc73zx7vSlO46n8T87tO_CcEfPDUvlo8I16a6wRs2AkC.vKcKy3sG7Tw6EqQsGEMY9TVTvayKTKpQ1Lt3Owa6_stKRVTLtxDiO_xUybCm3nuS08vYqhDOfpbMGnHTkoGA9IwYh1fXkQWeXg.9oUR0M8BnGeeh8MQucUR2exfau0MQqTlU.KtBTJx79fwKcE53iZFipBJDHYDqIfLxy6tcHuvKjlCFKCzcyobESp_BSnAqCfnzJUSiaL_D4HpJ6Gf80dUUCbeigy1I4VXI32fl4XTt_VuzzVbg5mpDcL_Ml8.BGPcYvcC0l9OOvg.Vtsp1qqWQFQ89V.r6dSEbb0PWd0W7NEKmn3t6i1EUXfXRCIB0n6qPBJH99R7k.sPR7e40J33F7OCGPC2MMUCkaOnvXFIZTuZBAY7G0EDIMyegcbtUNPdvE0TJ2eSflfYsBPPXnbGO914HjWcgbXhJOEccFWIR9FoJIdM0ur4ZXnWXZ1byYQT4gXfuEGSWzALN3RCQQfb4UnQ4nal_jt7yOqiXmhu1PXs_UuU6KLabZ.uiu_NFqfVAoue5l9t3WCxMA_eBuRzAlvzXzepan31LWQnhVME6osHRU_6HIGL84n_AEAaY3Y8oBpREz45BuoIvhl1hUXk4VaM7JSsuUNrcg9EKQ78xHtXfv5oGnQ103mFXzYliElwCQzxjVNChsvpNmOQW_M0mfNgoj9xTLcYDZsA5q88BJ7IVzMeobii_vSwM9R0WiAr1flztlcV59Z7qRr.vPBk3tGPejCLOTG1xdnuA8fNHe28JJH9eb3QV83S5QwUn5vZo.VslMNUFMuxuumGJjqo8vZ05yccynk_YMN26rdLjujVZiNNjHDqIFHkctiYvV1LV5pQGRdi_Qg38CpVLVMG1NLCn5kN3tqvH_jxrum_yJf6x0qUYHMAEqG4r2vbVmaKR1QqETWish5MfILupDz5WUVXei6qHCnDUNLVDCsvPtGnFQhOnRw9PgGIjzTjTgvCtbrJuRbzpvikYrC.OJEG7gATgig3NuNa2YYb0saihzrIVS.poxZT.Ab24U5_wxS6ghQ2G8uocXQY6OIKkJRfes2RygB_h1kTGzBKu3mHSVh_zePHHjYjRHHLz1d4lD8JH0lLU_b2b_uSAnuAkvQeI5tsspA4m2mQ",mdrd: "Rh4qAHxPu_0OLp2EA_qnhvHeWyXdNJWKlBYmtpV7iHs-1732835129-1.2.1.1-rNV5Ll1vkumpxUwl.hXFtGEuVapHlqFhouZyT89fAxiG.CJs9F3uqR3QRn31F1Vqvqd86Twi8wP6MTUbfcLZQLSRi4dBrMT0cPvfHjI3lIItnzp3NfjDFVDhlF5PPzUwtvHLjfKK1wJLRwVL3aLS.wBwjjuxyGVA8qA1rW9hQ3E2aBi16HQVM7X5FQQb5eHH0X.X1bYZkGKU7Vp6MSiRa307aZRBMdevb7XoDElgObMgEadzy2Qk7_XhEtvxysAOK116YUSSlJFZaSsIs.KU4IfVpp4DljboLvbcwtoptHCDCcuC0dWnC76u479ZiAzvLscNqV5TCjEk5sRLNvtWEy4mQ_.5UvidnCksspTqEwn1pTC.oWHk2nYPAzJ19GIRokY7bjHU1.vewwcDw_XvA0pVZWjk._ctDLchFyA9a.9obeD3o2IO4m5RqRtH8IHdBiF1uibmZfP.v3kiZsRpIXFzOad.bgiYlHnKSO7m86aVNQWDc2DuC3DIi4XlDJ8kGKNgEG9smMzz57IH6KV3jmawI2WY.qgtGKw3Rd8qaH.cTQe7WINxY3pph3atPtu9.bFl7fnSZFVWhk8fG8VtpzRiUO0em4joW3xvcYhGl7JIkXTZPsWqmQckJDWfx4HD4T9a5MRxQVDbbSRZopk544dLnpW4Vkh4cHQFjSO.uh65TW62RHzGxUmK5IE1Suqpw3BtO8yNDYvWTB2vKPMNZ8FkZA.T3SWsq1U0tv7ELyYb4i79X3VCFRWQzKys9cwH9QfjsvG4vJO7.06mC7enJgIN3MbE99Dv5OCk84MQEmhESnKzTjD4qu0RYurlFQCQkjv_PsDdVsIzh3nQC96PBT_DUrRSrcxtQnIpISbildRKNl8z6A8GqELnIsxAz8AKCABYln2qxnZm1XILfVuu9_ABKJ41mgo.aOT2RthW0GkUQJjzKHFCLC2pc1YXZRM1i32SrFPQUqV22tJh6eSP5iDyAPb4ePd4MAMnV9K1mbBOUWlCjJK5zCVWN2t8g4.c5WvgPvTuskvQfZPl2EyCoATng1DAE7vNAuF_X7Y66xclE23HZkxxtm3oIDTwS6OTYEnr4nuesnx0JV7f6ljyQE1KJI0hemeuA_YqZyR3rUDL6SeERb9pxhCtloepl.yTM3clT7OPt4qeJviONYID2xBMyHI8X5mfqxGpIYTZJvvHf5xThnlnmhGnhmC8Ju5er6yolfYh043hfAWJEae.kipCtvF9EEfhtnhcj1FJYiyEVI2ayUfpuUo.u23K7k2sjIGYkKN8AuIT6ueEvhimWZzAgcSGYxu89f2EgqAjbcS_B1KSgo5gNLg3y3LqqW8VrkUOlgmdiYfPqYsrsi5FZEFMpYR42MD13En4qggYyO9UZLNdyuXvRo8l4mVMM52vZW5liJ0bui0cvLdThFg2qUjc6EhPref40yzmur09PXzRZq1NUjettitiriWJlzE10shMg5XS4fF_n0cNlF5P9HsNziOyRgz8rtJDlQXyYgJExaJnUvscqYlfGXTngMlkMiTSgZJFpDG8P2YtUiI.e39L1nPnJUuY7QbY43.IT7wydQ2RKHzivBv9SvpLtXgiY6bR2d788T06g_1CUIcAZS0L6F8sKROJt5JPpNFEp4iPXCnyUzIN5VPFpYxHGshPumIu8MhpmmSJQWhiX3TA9AolSSD_K8ldMSyhzdquGhMfoFlTyVn3O.zWGsYQj__tfufqvSy41n2G.p69FrBnOjLV5skVPozBmjZ0hmp9iiDxJDjJvGjXCkEjtzt_4EQK5n3ukwMxQcZaWrXQ02294Yq.h0hNVu.anNnjHVo5tVDjfu5SCE3QABxFmGdMAVxPUDW10BBqLudwLcmXMuNGyIviByQCKaRkCgv7iZYexLqkfWpP_s8Xmt6xvpT8K12aB5xd8CQOt0dinsb7SjYhkphYcKeZzmMpc1M6p.WMManmdikC83_pcB6czdoj.SK1YvRghSmdkmKhr2U_8I0HmA"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/b/orchestrate/chl_page/v1?ray=8e9e00c50ebc4b50';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/2020\/01\/29\/rao-blackwellization-and-discrete-parameters-in-stan\/?__cf_chl_rt_tk=775gNlmFXsj8gF6tleH97A60OWo5fhBstPR9YIGwA64-1732835129-1.0.1.1-TZqtvSRzLDkfebb9QpckEsaIq4gZVg.I_mojrQBhMpg" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>