From 893e3b030998354ddacf101627cefa8f96490fdd Mon Sep 17 00:00:00 2001 From: Andrew Parnell Date: Mon, 20 Apr 2020 22:37:21 +0100 Subject: [PATCH 1/6] Added record buttons --- slides/class_1_intro.Rmd | 12 +++++++----- slides/class_1_intro.pdf | Bin 208130 -> 210300 bytes slides/class_2_inference.Rmd | 3 ++- slides/class_2_inference.pdf | Bin 227565 -> 227692 bytes slides/class_3_intro_bayes.Rmd | 1 + slides/class_3_intro_bayes.pdf | Bin 377660 -> 377834 bytes slides/class_4_bglms.Rmd | 1 + slides/class_4_bglms.pdf | Bin 494058 -> 493796 bytes slides/class_5_hlms.Rmd | 1 + slides/class_5_hlms.pdf | Bin 403467 -> 403622 bytes slides/class_6_hglms.Rmd | 1 + slides/class_6_hglms.pdf | Bin 369287 -> 369363 bytes slides/class_7_multihms.Rmd | 1 + slides/class_7_multihms.pdf | Bin 509408 -> 509575 bytes slides/class_8_pp_zi_multinom.Rmd | 1 + slides/class_8_pp_zi_multinom.pdf | Bin 823014 -> 823266 bytes slides/class_9_varsel_JAGS.Rmd | 1 + slides/class_9_varsel_JAGS.pdf | Bin 335505 -> 339156 bytes 18 files changed, 16 insertions(+), 6 deletions(-) diff --git a/slides/class_1_intro.Rmd b/slides/class_1_intro.Rmd index 663513b..9c205bf 100644 --- a/slides/class_1_intro.Rmd +++ b/slides/class_1_intro.Rmd @@ -2,8 +2,9 @@ title: 'Class 1: An introduction to Bayesian Hierarchical Modelling' author: Andrew Parnell \newline \texttt{andrew.parnell@mu.ie} \newline \vspace{1cm} \newline \includegraphics[width=3cm]{maynooth_uni_logo.jpg} - \newline \vspace{2cm} - https://andrewcparnell.github.io/bhm_course + \newline \vspace{1cm} + https://andrewcparnell.github.io/bhm_course + \newline PRESS RECORD output: beamer_presentation: includes: @@ -26,6 +27,7 @@ par(mar=c(3,3,2,1), mgp=c(2,.7,0), tck=-.01,las=1) - your previous experience in working with R and regression models, - what you are working on, - what you want to get out of the week + - waht you are most looking forward to when we can all go outside again - Timetable for the week - Pre-requisites @@ -69,7 +71,7 @@ support your individual studies. ## Thinking hierarchically: example 1 -```{r, echo = FALSE} +```{r, echo = FALSE, fig.height = 5} # Feed conversion rate example fcr = read.csv(file = '../data/fcr.csv') plot(fcr$food_wt, fcr$weight_gain, @@ -79,7 +81,7 @@ plot(fcr$food_wt, fcr$weight_gain, ## More information: -```{r, echo = FALSE} +```{r, echo = FALSE, fig.height = 5} sex = fcr$sex plot(fcr$food_wt[sex=='male'], fcr$weight_gain[sex=='male'], @@ -145,7 +147,7 @@ head(swt) - The data directory contains a few more data sets which we will play with throughout the week - The `data_descriptions.txt` file shows what they contain - If you have some spare time it's worth loading them in, exploring relationships, and fitting some simple models - + ## Summary - In hierarchical models we avoid fitting models separately as much as possible diff --git a/slides/class_1_intro.pdf b/slides/class_1_intro.pdf index 805fed1d81ba26c9ea955c2a692bbc80089f5076..6051d5aead085215099cc28a9245e9d1d7e65e38 100644 GIT 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zn|BjG4gzi3fEd~hzH7Kkhx3ko`tgVA{0Mo@^S+-<2oZZ6B*EzRMI@n`&Y)i}Z;bIq z^Jw(X>5!-6!ts|yLgtEn)ZB1rey4zU%q8GSXkh1;(AADz&ORtf4peIA$rsVDOJHaC z`rBJj2#v)``c_2&uhYxxkY)BN{#%+vmNKJwGxmi&SwGQn4V zlGCJ?G~=Z5T>CgG+UQgU4W(!*^_FF*WqS1jsQ~OF1l%3W{2$NZtCjp?P_U-%*DaS&BKdKODnA^gZ%#h7+M^3 diff --git a/slides/class_2_inference.Rmd b/slides/class_2_inference.Rmd index 20e0497..551819a 100644 --- a/slides/class_2_inference.Rmd +++ b/slides/class_2_inference.Rmd @@ -2,6 +2,7 @@ title: 'Class 2: Likelihood and Inference' author: Andrew Parnell \newline \texttt{andrew.parnell@mu.ie} \newline \vspace{1cm} \newline \includegraphics[width=3cm]{maynooth_uni_logo.jpg} + \newline PRESS RECORD output: beamer_presentation: includes: @@ -14,7 +15,7 @@ classoption: "aspectratio=169" knitr::opts_chunk$set(dev = 'pdf') options(width = 40) par(mar=c(3,3,2,1), mgp=c(2,.7,0), tck=-.01,las=1) -pkgs = c('R2jags','rjags', 'lubridate', 'tidyverse','forecast', 'rstan') +pkgs = c('R2jags', 'rjags', 'lubridate', 'tidyverse', 'rstan') 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z9>_K5r}y5*>o`rm|Jv0OI0pkZ1i6={V30w%mkDF6Tf diff --git a/slides/class_6_hglms.Rmd b/slides/class_6_hglms.Rmd index bf5c6cb..a62f120 100644 --- a/slides/class_6_hglms.Rmd +++ b/slides/class_6_hglms.Rmd @@ -2,6 +2,7 @@ title: 'Class 6: Hierarchical generalised linear models' author: Andrew Parnell \newline \texttt{andrew.parnell@mu.ie} \newline \vspace{1cm} \newline \includegraphics[width=3cm]{maynooth_uni_logo.jpg} + \newline PRESS RECORD output: beamer_presentation: includes: diff --git a/slides/class_6_hglms.pdf b/slides/class_6_hglms.pdf index e6e0606c56e32bd794188be2570412e9947b78cb..add94ccb13b06f89a6738821afc38a04b8b04bf3 100644 GIT binary patch delta 75315 zcmYg%WmFwaux+ql!8N!OT!KSz3j}xf;O^nT;4Z=4-QC@TySux)Ka%_1x9*QQYi9b4 ztnR8^yK2`2^kPo+V*Vxr=U|WDFae_m!S;QLx?j^;tAp9qFFLtfy5<_0&L4ds`WNA&g>~YilapDT zI5``sWq_4+fVdo^bFj;84xY>)SI?^pQ=TdvU7vpZ$s&cnm=AV)rX5@w!gUKhenSBa zt-2TN#s!?2DH_F$7)WVVm9$r4|FpWMvtd-#p?cZe+!a&z&fht3_$1;I$${E^)&dF=j+(tD_H&{)V{r;DGFUl`vW$Z}w 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YH(66FnBd7#IM_ZzK(w^t3KF3I1^C!A3;+NC From 08e8f229d2c786a0b0df4da328d5580520597268 Mon Sep 17 00:00:00 2001 From: Andrew Parnell Date: Tue, 21 Apr 2020 14:56:02 +0100 Subject: [PATCH 2/6] Updated horseshoe formatting and fixed type --- data/horseshoe.csv | 175 ++++++++++++++++++++++++++++++++++++++- slides/class_1_intro.Rmd | 4 +- slides/class_1_intro.pdf | Bin 210300 -> 210299 bytes 3 files changed, 176 insertions(+), 3 deletions(-) diff --git a/data/horseshoe.csv b/data/horseshoe.csv index 6d63d7c..be3fb3d 100644 --- a/data/horseshoe.csv +++ b/data/horseshoe.csv @@ -1 +1,174 @@ -color,spine,width,satell,weight 2,3,28.3,8,3.05 3,3,22.5,0,1.55 1,1,26,9,2.3 3,3,24.8,0,2.1 3,3,26,4,2.6 2,3,23.8,0,2.1 1,1,26.5,0,2.35 3,2,24.7,0,1.9 2,1,23.7,0,1.95 3,3,25.6,0,2.15 3,3,24.3,0,2.15 2,3,25.8,0,2.65 2,3,28.2,11,3.05 4,2,21,0,1.85 2,1,26,14,2.3 1,1,27.1,8,2.95 2,3,25.2,1,2 2,3,29,1,3 4,3,24.7,0,2.2 2,3,27.4,5,2.7 2,2,23.2,4,1.95 1,2,25,3,2.3 2,1,22.5,1,1.6 3,3,26.7,2,2.6 4,3,25.8,3,0.2 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zD=SCJAaAKLjyb4-T9}3h%cR(QNQyx{e-x~#zwxmm)WHf?;(}FBvZlYsN&~EfMreU1 z>+yU{SHl`;h7GXRdh#u%t*{Q(b3M*=G|YljZlXg&KK&&sgbnt2h&PUwQ2 z+>$44v7QgabSrFw?Xbg|{U>YgM@;*m+j{-~CGLa$&4H;Sj$i-u-bnVlDiNl>s;k$DjfytPlM$Jqf4aG+cl)*2kAIJqzdHJY0s0 z*5}rk4#E&z;>!!9`!EVu;Tnv=I9!JtFkyZ96t_&;r9z~e_QY(YTlU;yq}%qNkw|x( zRf>`BI-7qR>7KJ{OQb31dWPd)Po+qSBBdx2HA^L+K8gAy>XRr}Y66;*XijQ&u1v>! ze`*Pz=1K4hWo~41baG{3Z3<;>WN%_>3UhQ}a&&ldWo8O8FgZ3dGYTaoMNdWw{3ve8 From e90ec901256e7d2b2bb5e8457618729ca4b78f20 Mon Sep 17 00:00:00 2001 From: Andrew Parnell Date: Thu, 23 Apr 2020 09:28:11 +0100 Subject: [PATCH 3/6] Minor updates --- practicals/tutor_2_R_jags_stan.R | 2 +- slides/class_4_bglms.Rmd | 2 +- slides/class_4_bglms.pdf | Bin 493796 -> 494123 bytes 3 files changed, 2 insertions(+), 2 deletions(-) diff --git a/practicals/tutor_2_R_jags_stan.R b/practicals/tutor_2_R_jags_stan.R index c306bcb..a6f832b 100644 --- a/practicals/tutor_2_R_jags_stan.R +++ b/practicals/tutor_2_R_jags_stan.R @@ -26,7 +26,7 @@ model { } ' model_parameters = c("intercept", "slope", "residual_sd") -model_run = jags(data = list(N=nrow(dat), +model_run = jags(data = list(N = nrow(dat), y = log(dat$earn), x = dat$height_cm), parameters.to.save = model_parameters, diff --git a/slides/class_4_bglms.Rmd b/slides/class_4_bglms.Rmd index ccae7d2..b0cc767 100644 --- a/slides/class_4_bglms.Rmd +++ b/slides/class_4_bglms.Rmd @@ -1,5 +1,5 @@ --- -title: 'Class 4: Bayesian Linear and generalised linear models (GLMs)' +title: 'Class 4: Bayesian linear and generalised linear models (GLMs)' author: Andrew Parnell \newline \texttt{andrew.parnell@mu.ie} \newline \vspace{1cm} \newline \includegraphics[width=3cm]{maynooth_uni_logo.jpg} \newline PRESS RECORD diff --git a/slides/class_4_bglms.pdf b/slides/class_4_bglms.pdf index 3ad7a3df389c71e960f3fbf15bdc3ecd47a944a6..1fd80843ea80970147fd904518140fa2562d1093 100644 GIT binary patch delta 122881 zcmc$_XIN8B8#VgaKtKT%2?_)e=`|pofP#oLsnQ7@M4I%TtsMu798!CzV9oDD8>0j*k%jza>} 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05d4acb30915db51f3867b85cc19b5ab65ca201e Mon Sep 17 00:00:00 2001 From: Andrew Parnell Date: Fri, 24 Apr 2020 07:55:59 +0100 Subject: [PATCH 4/6] Updated some minor mistakes --- practicals/tutor_3_fit_hm.R | 16 ++++++++++------ slides/class_5_hlms.Rmd | 20 ++++++-------------- slides/class_5_hlms.pdf | Bin 403622 -> 403750 bytes slides/class_6_hglms.Rmd | 6 +++++- 4 files changed, 21 insertions(+), 21 deletions(-) diff --git a/practicals/tutor_3_fit_hm.R b/practicals/tutor_3_fit_hm.R index 639ad93..70341ba 100644 --- a/practicals/tutor_3_fit_hm.R +++ b/practicals/tutor_3_fit_hm.R @@ -8,7 +8,7 @@ x = sort(runif(N, 150, 190)) ## ---- fig.height = 4----------------------------------------------------- -dat = read.csv('../data/earnings.csv') +dat = read.csv('data/earnings.csv') alpha = rnorm(1, mean = 10, sd = 2) beta = rnorm(1, mean = 0, sd = 0.1) sigma = runif(1, 0, 5) @@ -117,7 +117,7 @@ eth_names = c('Blacks','Hispanics','Whites','Others') for(i in 1:4) { curr_dat = subset(dat, dat$eth == i) plot(curr_dat$height_cm, log(curr_dat$earn), main = eth_names[i], ylab = 'log(earnings)', xlab = 'Height (cm)') - lines(dat$height_cm, pars$alpha[i] + pars$beta[i]*(dat$height_cm - mean (dat$height_cm)), col = i) + lines(dat$height_cm, pars$alpha[i] + pars$beta[i]*(dat$height_cm - mean(dat$height_cm)), col = i) } par(mfrow=c(1,1)) @@ -213,7 +213,7 @@ model{ # Class 6 ----------------------------------------------------------------- ## ------------------------------------------------------------------------ -swt = read.csv('../data/swt.csv') +swt = read.csv('data/swt.csv') head(swt) @@ -286,7 +286,11 @@ library(boot) par(mfrow=c(1,3)) pars = jags_run$BUGSoutput$mean for(i in c(2,3,1)) { - plot(swt$forest, y/N, main = paste('Altitude type:',levels(swt$alt)[i]), xlab = '% forest cover', ylab = 'Estimated proporton') + curr_rows = which(swt$alt == levels(swt$alt)[i]) + plot(swt$forest[curr_rows], y[curr_rows]/N[curr_rows], + main = paste('Altitude type:',levels(swt$alt)[i]), + xlab = '% forest cover', + ylab = 'Estimated proporton') points(swt$forest, inv.logit(pars$alpha[i] + pars$beta[i] * swt$forest), col = i+1) } par(mfrow=c(1,1)) @@ -350,9 +354,8 @@ model{ for(i in 1:N) { y[i] ~ dt(alpha + beta * (x[i] - mean(x)), sigma, df[i] + 1) - df[i] ~ dbin(p, 10) + df[i] ~ dcat(p) } - p ~ dunif(0, 1) alpha ~ dnorm(0, 1^-2) beta ~ dnorm(0, 1^-2) sigma ~ dt(0,1,1)T(0,) @@ -363,6 +366,7 @@ model{ ## ---- echo = FALSE, message=FALSE, results = 'hide'---------------------- jags_run = jags(data = list(N = N, y = y, + p = rep(1, 10)/10, x = x), parameters.to.save = c('alpha', 'beta', diff --git a/slides/class_5_hlms.Rmd b/slides/class_5_hlms.Rmd index ea19b80..e345c4f 100644 --- a/slides/class_5_hlms.Rmd +++ b/slides/class_5_hlms.Rmd @@ -139,15 +139,7 @@ $$y_i \sim N(\alpha_{\mbox{ethnicity}_i} + \beta (x_i - \bar{x}), \sigma^2) $$ ## Writing a varying intercepts/slopes model in JAGS/Stan \small -- One way to write the varying intercepts model is to simply include it an extra effect: -``` -log_earn[i] ~ dnorm(alpha1 * ethnicity_1 - + alpha2 * ethnicity_2 + ... - + beta * height[i], - sigma^-2) -``` - -- A neater way is to use the double indexing: +- The neat way to write this model is to use the double indexing: ``` log_earn[i] ~ dnorm(alpha[ethnicity[i]] + beta * height[i], sigma^-2) @@ -257,7 +249,7 @@ par(mfrow=c(1,1)) ## Setting up hierarchical prior distributions -- In general a hierarchical model is created whenever we put prior distributions on prior distributions +- In general a hierarchical model is created whenever we put prior distributions on parameters that depend on other parameters - The lower level parameters in the model are often called _hyper-parameters_ @@ -280,19 +272,19 @@ par(mfrow=c(1,1)) \small ```{r} jags_code = ' -model{ +model { # Likelihood for(i in 1:N) { y[i] ~ dnorm(alpha[eth[i]] + beta[eth[i]]*(x[i] - mean(x)), sigma^-2) } - # Priors + # Independent priors for(j in 1:N_eth) { alpha[j] ~ dnorm(11, 10^-2) beta[j] ~ dnorm(0, 0.1^-2) } - sigma ~ dt(0, 2, 1)T(0,) + sigma ~ dt(0, 2, 1)T(0,) # Note new t prior } ' ``` @@ -367,7 +359,7 @@ where $p$ is the number of parameters and $n$ is the number of observations - The first, called the _Deviance Information Criteria_ (DIC) is calculated via: $$\mbox{DIC}: - 2 \log L_{\mbox{max}} + 2p_D$$ where $p_D$ is the _effective number of parameters_ -- The second called the Widely Applicable Information Criterion (WAIC) which is calculated as: +- The second is called the Widely Applicable Information Criterion (WAIC) which is calculated as: $$\mbox{WAIC}: - 2 \log L_{\mbox{max}} + p_{\mbox{WAIC}}$$ - Here $p_{\mbox{WAIC}}$ is a measure of the variability of the likelihood scores diff --git a/slides/class_5_hlms.pdf b/slides/class_5_hlms.pdf index dfe6fba08ec0c6fdaeef6551244f96c1644d3725..f8505c19ca89994ceb15ad0b8c5cf3fd201afda6 100644 GIT binary patch delta 175076 zcmY(pbzD^K^FA(J(kU$|jUpu}ASt0pcT1=A?x8!RQ#z%)yQI6jyJLZ6;fK%jeBQ6` 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