From f746455478b1a1b345a8c9ed3769d797d4b17e0c Mon Sep 17 00:00:00 2001 From: "Carl A. B. Pearson" Date: Sat, 9 May 2026 09:55:26 -0400 Subject: [PATCH 1/4] headline rev --- ICI3D_Lab_MCMC-Binomial.R | 9 ++++----- 1 file changed, 4 insertions(+), 5 deletions(-) diff --git a/ICI3D_Lab_MCMC-Binomial.R b/ICI3D_Lab_MCMC-Binomial.R index 692867b..c289249 100644 --- a/ICI3D_Lab_MCMC-Binomial.R +++ b/ICI3D_Lab_MCMC-Binomial.R @@ -1,9 +1,8 @@ -#' Introduction to MCMC 1: Estimating a posterior binomial probability -#' Clinic on the Meaningful Modeling of Epidemiological Data -#' International Clinics on Infectious Disease Dynamics and Data (ICI3D) Program -#' African Institute for Mathematical Sciences, Muizenberg, RSA +#' Introduction to Inference: Understanding MCMC with Binomial Data +#' [MMED](https://www.ici3d.org/MMED) #' Steve Bellan 2012, 2015 -#' Carl Pearson 2025 +#' Carl Pearson 2025, 2026 +#' Claire Perrin Smith 2026 #' #' By the end of this tutorial you should be able to: #' * Write a likelihood function for binomially distributed data From 179dc6a37aa0d74231b6d8fcc309531db8885805 Mon Sep 17 00:00:00 2001 From: "Carl A. B. Pearson" Date: Sat, 9 May 2026 11:18:55 -0400 Subject: [PATCH 2/4] outline done for mcmc lab 1 overhaul --- ICI3D_Lab_MCMC-Binomial.R | 36 ++++++++++++++++++++++++++++++++++++ 1 file changed, 36 insertions(+) diff --git a/ICI3D_Lab_MCMC-Binomial.R b/ICI3D_Lab_MCMC-Binomial.R index c289249..4b3f466 100644 --- a/ICI3D_Lab_MCMC-Binomial.R +++ b/ICI3D_Lab_MCMC-Binomial.R @@ -11,6 +11,10 @@ #' * Assess MCMC convergence with the Gelman-Rubin diagnostic #' and trace plots +#' Revisit the notion of population true value => distribution of plausible samples +#' - have them generate the plot, using a functional form they'll use again later? +#' - have them add a particular observation + library(ggplot2) library(dplyr) library(tidyr) @@ -29,6 +33,38 @@ sample_size <- 100 sample_positive <- rbinom(1, sample_size, true_prevalence) sample_prevalence <- sample_positive / sample_size +#' @carl have them make the dbinom link +#' and then insert into our figure code + +#' @carl have them convert that code into a likelihood function +#' and feed that into a plot we provide + +#' @carl have them write a prior "function" to feed to prior + likelihood = posterior plot +#' + +#' @carl build up MCMC answer: +#' - implement a proposal distribution + acceptance rejection logic +#' - insert that into a loop structure that we provide, FROM A STARTING POINT WE PROVIDE +#' - that loop structure should do a pass, draw a plot, prompt for do 1 step more +#' - also provide a run-until-option +#' - MVP++: also provide a save animation option + +#' prompt with "what if we started at a different (bad) place?" (repeat previous, but from +#' different BAD starting point that we provide) + +#' have them run the chain sampling code that we provide - have them provide +#' that method all of their previous inputs, plus the good and bad starting points, +#' and some points of their choice +#' should be another step-step-etc-continue loop, but plot is chains and posteriors +#' needs to show R hat calculation as well + + +#' have them implement the three different proposals, drop them into the chain sampling code +#' and see the final results + +######## EVERYTHING BELOW IS OLD - POTENTIALLY USEFUL FOR ABOVE, BUT NO LONGER NECESSARILY IN CODE + + #' @question How do the true_ and sample_prevalence compare? What could #' you change to make them more likely to be close for any given draw? 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= + \frac{\textcolor{likelihood}{P\left(y \middle| \theta\right)}\textcolor{prior}{P\left(\theta\right)}}{\textcolor{denom}{P\left(y\right)}} + } + \] + +\end{document} + diff --git a/mcmc_lecture/colors.aux b/mcmc_lecture/colors.aux new file mode 100644 index 0000000..e54b19f --- /dev/null +++ b/mcmc_lecture/colors.aux @@ -0,0 +1,21 @@ +\relax +\@setckpt{colors}{ +\setcounter{page}{1} +\setcounter{equation}{0} +\setcounter{enumi}{0} +\setcounter{enumii}{0} +\setcounter{enumiii}{0} +\setcounter{enumiv}{0} +\setcounter{footnote}{0} +\setcounter{mpfootnote}{0} +\setcounter{sapage}{0} +\setcounter{part}{0} +\setcounter{section}{0} +\setcounter{subsection}{0} +\setcounter{subsubsection}{0} +\setcounter{paragraph}{0} +\setcounter{subparagraph}{0} +\setcounter{figure}{0} +\setcounter{table}{0} +\setcounter{parentequation}{0} +} diff --git a/mcmc_lecture/colors.tex b/mcmc_lecture/colors.tex new file mode 100644 index 0000000..9b10eb8 --- /dev/null +++ b/mcmc_lecture/colors.tex @@ -0,0 +1,8 @@ +\usepackage{xcolor} + +% Define your colors +\definecolor{posterior}{HTML}{00b300} % green +\definecolor{likelihood}{HTML}{cc00ff} % purple +\definecolor{prior}{HTML}{ff9933} % orange +\definecolor{denom}{HTML}{0099ff} % Med blue +\definecolor{default}{HTML}{000000} % Black \ No newline at end of file diff --git a/mcmc_lecture/wrapper.log b/mcmc_lecture/wrapper.log new file mode 100644 index 0000000..cb6e415 --- /dev/null +++ b/mcmc_lecture/wrapper.log @@ -0,0 +1,379 @@ +This is pdfTeX, Version 3.141592653-2.6-1.40.29 (MiKTeX 26.5) (preloaded format=pdflatex 2026.5.28) 30 MAY 2026 13:57 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**./wrapper.tex +(wrapper.tex +LaTeX2e <2025-11-01> +L3 programming layer <2026-04-28> + +(C:\Users\cpsmit\AppData\Local\Programs\MiKTeX\tex/latex/standalone\standalone. +cls +Document Class: standalone 2025/02/22 v1.5a Class to compile TeX sub-files stan +dalone 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Missing $ inserted. + + $ +l.1 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing } inserted. + + } +l.1 + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Display math should end with $$. + + \tex_par:D +l.1 + +The `$' that I just saw supposedly matches a previous `$$'. +So I shall assume that you typed `$$' both times. + +! Missing $ inserted. + + $ +l.2 ...posterior}{P\left(\theta \middle| y\right)} + = +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +\@textcolor ...otect \leavevmode {\color #1{#2}#3} + +l.2 ...posterior}{P\left(\theta \middle| y\right)} + = +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +) +! Extra }, or forgotten $. +\@textcolor ...otect \leavevmode {\color #1{#2}#3} + +l.13 } + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.14 \] + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.14 \] + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. 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\theta\right)}\textcolor{prior}{P\left(\theta\right)} + } + \] + +\end{document} + diff --git a/mcmc_lecture/bayes_rule_prop_text.pdf b/mcmc_lecture/bayes_rule_prop_text.pdf new file mode 100644 index 0000000000000000000000000000000000000000..588285d362b00b3211f1c71d8d0867d2a15dec5a GIT binary patch literal 22383 zcma&M1CV9S(y-gMZCkr-+wN)GwykN~w%ya_wC$d@ZJT%AbG~!W7xzZ|@vn$ok(HIG zovU)kjVV4K-|XA#Z=VP*xtkxhMynC*~Q7!&=$sHEkmA)&7Gc;Vl(#mtW!89X z>Z!E3Fn{GsKsU*VP?FX#DQ9YO`ln>MP(Ocy|BPh}+u#8fO~2&fq)s03rkzjXr4txs zwmAIPT}1drHUt{OOkbK}ePEe|rhlip@j~3k1tM(j;$ROOwK8j}X#yRcqiVju0@ZIo zprP)9(_N)UrN#)lb*(QeqIdfmZbDA+;BWPVN@|DsuHSo5#khXF%C#SfH3|gQwtCwz zrgkR(v;Du)KVO~sf0aPh)4`MoplE1r3Ihqw4MsfPO ze^U_g^8T$a3o{YxKZgH^oJ4H@694)D6rJpiRZLxowEyl(RGbK)YU<%ar2Ef3_@8hb z{}WD|gM)+NuO}lT(f?Qa_x%4nGBN&j{Kxsf0shYp|2M1u3i_|%e_Q`o`=5OO)%-8x z|0>y;m>8Id{yqLz`(IPt|I~u>Keb?EV`E?^Vr6AzU?pN<{73#*s()#j|5c~|(K7#2 zvwv$iSy&iYi2m*QUu(91S+H<1F>nyEaQ!PDCnp2f|C^HQe^UOpf0+KB04CP|bQ3cX z7dt2We`bGA(tkuECPsEHj(_#p|3#a%f~zK< 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b/mcmc_lecture/binom_mcmc_ex.tex new file mode 100644 index 0000000..0d97846 --- /dev/null +++ b/mcmc_lecture/binom_mcmc_ex.tex @@ -0,0 +1,20 @@ + +\documentclass[varwidth,border=1pt]{standalone} + +\input{colors.tex} + +\usepackage{mathtools} +\usepackage{amsfonts} + +\begin{document} + + \[ + \textcolor{default}{ + \textcolor{posterior}{P\left(\theta\middle|x=28,\ n=100\right)}\ \propto\ + \textcolor{likelihood}{P\left(x=28,\ n=100\middle|\theta\right)} + \textcolor{prior}{P\left(\theta\right)} + } + \] + +\end{document} + diff --git a/mcmc_lecture/binom_mcmc_full_ex.pdf b/mcmc_lecture/binom_mcmc_full_ex.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6893f05b90417646d4d3a4fdb7704debcd688ee9 GIT binary patch literal 37871 zcma&O1yEhf)-H+$4-z!k!rd3{?(Po3-Q8V+1`Y1+9^5^+yF+kyxv=-y_w4)LyY+sm zXnGFo(PMPYTGaRTB9Rjkp<$q9h9#Mp>05wh0?-3&zL~>valz6_8Cjb+ngW;@=>dQL zz|x7BSvnfo1L#C7^&O3bj0|iHjbM3rU>zLojr6TxU6)RjxMh3z;8(AxxO9SX8Y+Jw 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-0,0 +1,18 @@ + +\documentclass[varwidth,border=1pt]{standalone} + +\input{colors.tex} + +\usepackage{mathtools} +\usepackage{amsfonts} + +\begin{document} + + \[ + \textcolor{default}{ + f\left(x\middle|p\right)={n\choose x} \left(p\right)^x \left(1-p\right)^{n-x} + } + \] + +\end{document} + diff --git a/mcmc_lecture/binom_posterior_ex.pdf b/mcmc_lecture/binom_posterior_ex.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e8e6d79fbe2ae81f9af213d9204d29cff3fc0e3d GIT binary patch literal 29297 zcma&NWl&trx;Biv1q(q3cV}R55AF`Z-QC>@?(QBW1b26LcMrkc;Umx9`#rn9^XE*} ztm$?8eRZ#{n(1rE1V(9N8&fAU05gyi@UIsF z<5zPlCu0Wy<5w$vCu0#~Lt7(b1U^0lM<)kkeQN}_l_+^$L_a0ZKoaG#tYJd84b4adQaLJE>ID;BYv2TlLLAm+YoS4F#r zZ%gy;yYPHtd=z=lplhp`jPlR4?$`Z4<3CCh(xtL$!P z3}BSkH#J6J6t=Z-GPZGY1pI|V5rI+B*wNP6!O++d!2Bi)0qe|i7+^`EH!FFEsHWd63R#m3Ibzy@Fi zvVPP6Zm`>A9Zqo{#FiRW&XIb zv2uRk0Q{&I2mrBhen{9sOdk?X4yF%F5EJX)IREO2jRnBL`B%pQ{Kt-&^&d3Z{vrbU z+x5SY_2=y=7fdwBQ6{3KM`4&KBBO( 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0000000..0f03585 --- /dev/null +++ b/mcmc_lecture/binom_posterior_ex_integrate.tex @@ -0,0 +1,18 @@ + +\documentclass[varwidth,border=1pt]{standalone} + +\input{colors.tex} + +\usepackage{mathtools} +\usepackage{amsfonts} + +\begin{document} + + \[ + \textcolor{default}{ + \int\textcolor{posterior}{P\left(\theta\middle|x=28,\ n=100\right)}\ d\theta=1 + } + \] + +\end{document} + diff --git a/mcmc_lecture/pdf_integrate_to_1.pdf b/mcmc_lecture/pdf_integrate_to_1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4719efb47e37672ccc19b2e3ce177ddeb57b772a GIT binary patch literal 36176 zcma&NV{~Rq+o&7ccG9tJ+v%ud+qP{x>DXq+HaoWMj_sYS^{(-*ea?5r`7%ak>bYHa z)id+ssv?mS7NudJWq~4@nj2VxVj`d?u+cY%;^u~;lQyz8aWo}hV5cYe`v;0n)XdV+ z$ew^s)KbsUNZ820#?T0gmlw*x(cVbU3d(gQDvl4nmjGeFg?Avz(HGA}aBNFoKb;-3 z&(O)ja_8uvDP@H(R|XjtxV^n?lM5ghI8c3SvO}jDF1W7{Erj4YoZ9samjfcE5NK|L zi(nx*-#RyL@ekg29tm_)Plg*~%u=@jXv4B@jI&Sy%!P$CK=Wu$t!4EfEBLX@(Jrg4+Iw2ctMlZF1X_%AzxzpM$En3!mp{xkm4 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-0,0 +1,18 @@ + +\documentclass[varwidth,border=1pt]{standalone} + +\input{colors.tex} + +\usepackage{mathtools} +\usepackage{amsfonts} + +\begin{document} + + \[ + \textcolor{default}{ + \int\textcolor{posterior}{P\left(\theta \middle| y\right)}\ d\theta=1 + } + \] + +\end{document} +