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22 changes: 13 additions & 9 deletions slides/01_how_bayes/index.Rmd
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Original file line number Diff line number Diff line change
@@ -1,5 +1,6 @@
---
title: "Introduction to Bayesian (Linear) Models"
title: "Introduction to Bayesian Linear Models"
subtitle: "Part I"
author: "Stefano Coretta"
institute: "University of Edinburgh"
date: "2023/05/16"
Expand Down Expand Up @@ -62,10 +63,13 @@ mald <- readRDS("./data/mald.rds")

| Time | Topic |
|---------------|------------------------------------------------|
| 11.00 - 11.45 | **Model basics and plotting** |
| 11.45 - 12.00 | Break |
| 12.00 - 12.45 | **Diagnostics, interactions, group-level effects** |
| 12.45 - 13.00 | Q&A |
| 09.00 - 10.30 | **Introduction to Bayesian Linear Models** |
| 10.30 - 11.00 | Break |
| 11.00 - 12.30 | **Diagnostics, interactions, group-level effects** |
| 12.30 - 14.30 | Lunch + Posters |
| 14.30 - 16.00 | **Priors** |
| 16.00 - 16.30 | Break |
| 16.30 - 18.00 | Q&A/Consultations |

<br>

Expand Down Expand Up @@ -259,7 +263,7 @@ brm_1 <- brm(
backend = "cmdstanr",
cores = 4,
threads = threading(2),
file = "data/rds/brm_1"
file = "data/cache/brm_1"
)
```

Expand Down Expand Up @@ -294,7 +298,7 @@ brm_2 <- brm(
# Use cmdstanr
backend = "cmdstanr",
# Save model output to file
file = "./data/rds/brm_2.rds"
file = "./data/cache/brm_2.rds"
)
```

Expand Down Expand Up @@ -338,7 +342,7 @@ brm_2 <- brm(
# Use cmdstanr
backend = "cmdstanr"
# Save model output to file
file = "./data/rds/brm_2.rds",
file = "./data/cache/brm_2.rds",
# Number of chains
chains = 4,
# Number of iterations per chain
Expand Down Expand Up @@ -560,7 +564,7 @@ brm_1_bis <- brm(
backend = "cmdstanr",
cores = 4,
threads = threading(2),
file = "data/rds/brm_1_bis"
file = "data/cache/brm_1_bis"
)
```

Expand Down
154 changes: 72 additions & 82 deletions slides/01_how_bayes/index.html
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Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<title>Introduction to Bayesian (Linear) Models</title>
<title>Introduction to Bayesian Linear Models</title>
<meta charset="utf-8" />
<meta name="author" content="Stefano Coretta" />
<script src="libs/header-attrs/header-attrs.js"></script>
Expand All @@ -20,7 +20,10 @@
class: center, middle, inverse, title-slide

.title[
# Introduction to Bayesian (Linear) Models
# Introduction to Bayesian Linear Models
]
.subtitle[
## Part I
]
.author[
### Stefano Coretta
Expand All @@ -47,10 +50,13 @@

| Time | Topic |
|---------------|------------------------------------------------|
| 11.00 - 11.45 | **Model basics and plotting** |
| 11.45 - 12.00 | Break |
| 12.00 - 12.45 | **Diagnostics, interactions, group-level effects** |
| 12.45 - 13.00 | Q&amp;A |
| 09.00 - 10.30 | **Introduction to Bayesian Linear Models** |
| 10.30 - 11.00 | Break |
| 11.00 - 12.30 | **Diagnostics, interactions, group-level effects** |
| 12.30 - 14.30 | Lunch + Posters |
| 14.30 - 16.00 | **Priors** |
| 16.00 - 16.30 | Break |
| 16.30 - 18.00 | Q&amp;A/Consultations |

&lt;br&gt;

Expand Down Expand Up @@ -231,8 +237,7 @@


```
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0396074 (tol = 0.002, component 1)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.0396074 (tol = 0.002, component 1)
```

.center[
Expand Down Expand Up @@ -282,31 +287,24 @@
##
## Group-Level Effects:
## ~Subject (Number of levels: 30)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 98.96 32.80 44.73 173.67 1.00 973
## sd(PhonLev) 7.86 4.95 0.39 18.64 1.00 330
## sd(IsWordFALSE) 97.82 19.02 63.89 139.05 1.00 1780
## cor(Intercept,PhonLev) -0.42 0.44 -0.94 0.68 1.00 1120
## cor(Intercept,IsWordFALSE) 0.56 0.26 -0.01 0.97 1.01 291
## cor(PhonLev,IsWordFALSE) -0.40 0.42 -0.95 0.59 1.01 421
## Tail_ESS
## sd(Intercept) 1196
## sd(PhonLev) 521
## sd(IsWordFALSE) 2415
## cor(Intercept,PhonLev) 1376
## cor(Intercept,IsWordFALSE) 192
## cor(PhonLev,IsWordFALSE) 847
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 100.12 34.37 45.19 179.30 1.00 987 601
## sd(PhonLev) 7.62 5.31 0.37 20.46 1.01 376 519
## sd(IsWordFALSE) 96.76 19.35 64.53 138.81 1.00 2040 1972
## cor(Intercept,PhonLev) -0.42 0.45 -0.94 0.68 1.00 1397 871
## cor(Intercept,IsWordFALSE) 0.55 0.25 -0.01 0.93 1.00 741 1777
## cor(PhonLev,IsWordFALSE) -0.38 0.42 -0.94 0.62 1.01 496 953
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 755.16 49.02 654.38 849.31 1.00 1784 2855
## PhonLev 32.00 6.50 19.60 45.19 1.00 1845 2895
## IsWordFALSE 207.41 69.21 74.07 343.68 1.00 1897 1574
## PhonLev:IsWordFALSE -10.89 9.17 -28.88 6.99 1.00 1985 1422
## Intercept 755.46 49.79 655.84 854.33 1.00 2541 2260
## PhonLev 31.97 6.57 19.04 45.25 1.00 3007 2410
## IsWordFALSE 207.98 68.79 71.00 341.61 1.00 2608 2280
## PhonLev:IsWordFALSE -11.10 9.34 -29.43 7.14 1.00 2655 2356
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 320.23 4.25 312.32 329.08 1.00 4599 1386
## sigma 320.22 4.19 312.28 328.32 1.00 5312 2889
##
## Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
Expand Down Expand Up @@ -336,7 +334,7 @@
# Use cmdstanr
backend = "cmdstanr",
# Save model output to file
file = "./data/rds/brm_2.rds"
file = "./data/cache/brm_2.rds"
)
```

Expand Down Expand Up @@ -381,7 +379,7 @@
# Use cmdstanr
backend = "cmdstanr"
# Save model output to file
file = "./data/rds/brm_2.rds",
file = "./data/cache/brm_2.rds",
# Number of chains
chains = 4,
# Number of iterations per chain
Expand Down Expand Up @@ -426,12 +424,12 @@
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 981.16 8.91 963.23 998.37 1.00 3759 2908
## IsWordFALSE 132.93 12.71 107.86 158.04 1.00 3882 3123
## Intercept 981.05 8.71 964.84 998.62 1.00 4383 2892
## IsWordFALSE 133.48 12.76 108.63 158.37 1.00 4071 2663
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 341.07 4.39 332.74 349.93 1.00 4058 2910
## sigma 341.11 4.44 332.64 349.84 1.00 4149 2987
##
## Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
Expand All @@ -445,8 +443,8 @@
```
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 981.16 8.91 963.23 998.37 1.00 3759 2908
## IsWordFALSE 132.93 12.71 107.86 158.04 1.00 3882 3123
## Intercept 981.05 8.71 964.84 998.62 1.00 4383 2892
## IsWordFALSE 133.48 12.76 108.63 158.37 1.00 4071 2663
```

* `Intercept`: There is a **95% probability** that (based on model and data) the mean RT when the word is real is **between 964 and 999 ms**.
Expand Down Expand Up @@ -497,16 +495,16 @@
```
## # A draws_df: 1000 iterations, 4 chains, and 5 variables
## b_Intercept b_IsWordFALSE sigma lprior lp__
## 1 985 121 343 -13 -21761
## 2 978 148 333 -13 -21763
## 3 987 116 339 -13 -21761
## 4 992 116 344 -13 -21762
## 5 989 122 344 -13 -21761
## 6 977 140 339 -13 -21760
## 7 983 122 346 -13 -21762
## 8 969 147 338 -13 -21762
## 9 986 129 339 -13 -21760
## 10 981 136 341 -13 -21760
## 1 979 132 343 -13 -21760
## 2 991 133 341 -13 -21761
## 3 982 143 346 -13 -21762
## 4 982 110 339 -13 -21764
## 5 979 113 333 -13 -21765
## 6 973 124 331 -13 -21765
## 7 966 150 341 -13 -21762
## 8 984 131 334 -13 -21762
## 9 980 132 348 -13 -21762
## 10 976 137 339 -13 -21761
## # ... with 3990 more draws
## # ... hidden reserved variables {'.chain', '.iteration', '.draw'}
```
Expand All @@ -523,8 +521,7 @@
```

```
## [1] "b_Intercept" "b_IsWordFALSE" "sigma" "lprior"
## [5] "lp__"
## [1] "b_Intercept" "b_IsWordFALSE" "sigma" "lprior" "lp__"
```

---
Expand Down Expand Up @@ -632,12 +629,12 @@
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 981.16 8.91 963.23 998.37 1.00 3759 2908
## IsWordFALSE 132.93 12.71 107.86 158.04 1.00 3882 3123
## Intercept 981.05 8.71 964.84 998.62 1.00 4383 2892
## IsWordFALSE 133.48 12.76 108.63 158.37 1.00 4071 2663
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 341.07 4.39 332.74 349.93 1.00 4058 2910
## sigma 341.11 4.44 332.64 349.84 1.00 4149 2987
##
## Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
Expand Down Expand Up @@ -688,7 +685,7 @@
backend = "cmdstanr",
cores = 4,
threads = threading(2),
file = "data/rds/brm_1_bis"
file = "data/cache/brm_1_bis"
)
```

Expand All @@ -706,31 +703,24 @@
##
## Group-Level Effects:
## ~Subject (Number of levels: 30)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 98.67 31.21 48.28 167.59 1.00 1124
## sd(PhonLev) 7.38 4.72 0.34 17.65 1.00 489
## sd(IsWordFALSE) 97.62 19.84 63.89 141.96 1.01 1369
## cor(Intercept,PhonLev) -0.42 0.44 -0.94 0.69 1.00 1642
## cor(Intercept,IsWordFALSE) 0.54 0.26 -0.05 0.93 1.00 673
## cor(PhonLev,IsWordFALSE) -0.39 0.42 -0.94 0.64 1.00 521
## Tail_ESS
## sd(Intercept) 1989
## sd(PhonLev) 979
## sd(IsWordFALSE) 1697
## cor(Intercept,PhonLev) 1912
## cor(Intercept,IsWordFALSE) 1309
## cor(PhonLev,IsWordFALSE) 841
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 95.32 31.73 45.61 170.35 1.01 1224 2012
## sd(PhonLev) 6.46 4.81 0.24 17.49 1.02 373 1553
## sd(IsWordFALSE) 96.22 19.16 62.98 137.45 1.00 2049 2612
## cor(Intercept,PhonLev) -0.36 0.48 -0.94 0.76 1.00 1431 2270
## cor(Intercept,IsWordFALSE) 0.52 0.26 -0.06 0.94 1.00 573 1181
## cor(PhonLev,IsWordFALSE) -0.32 0.47 -0.95 0.76 1.01 390 793
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 756.49 49.71 658.85 855.72 1.00 2244 1367
## PhonLev 31.72 6.50 18.85 44.56 1.00 2429 1248
## IsWordFALSE 204.02 66.69 71.69 334.30 1.00 2666 2529
## PhonLev:IsWordFALSE -10.61 8.91 -27.88 7.00 1.00 2703 2779
## Intercept 754.05 48.22 662.19 848.00 1.00 2534 2795
## PhonLev 32.10 6.34 19.86 44.40 1.00 2805 2897
## IsWordFALSE 208.79 65.13 78.73 333.10 1.00 2436 2804
## PhonLev:IsWordFALSE -11.29 8.75 -27.87 6.44 1.00 2543 2525
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 320.22 4.18 312.39 328.50 1.00 5085 2618
## sigma 320.28 4.24 312.11 328.50 1.00 7014 3116
##
## Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
Expand Down Expand Up @@ -758,12 +748,12 @@


```
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 756.49 49.71 658.85 855.72 1.00 2244 1367
## PhonLev 31.72 6.50 18.85 44.56 1.00 2429 1248
## IsWordFALSE 204.02 66.69 71.69 334.30 1.00 2666 2529
## PhonLev:IsWordFALSE -10.61 8.91 -27.88 7.00 1.00 2703 2779
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 320.28 4.24 312.11 328.50 1.00 7014 3116
##
## Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
```

* `Intercept`: At 95% confidence, the mean RT when the word is real and the mean phone-level distance is 0 is between 661 and 849 ms.
Expand Down Expand Up @@ -804,13 +794,13 @@
```
## Group-Level Effects:
## ~Subject (Number of levels: 30)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 98.67 31.21 48.28 167.59 1.00 1124
## sd(PhonLev) 7.38 4.72 0.34 17.65 1.00 489
## sd(IsWordFALSE) 97.62 19.84 63.89 141.96 1.01 1369
## cor(Intercept,PhonLev) -0.42 0.44 -0.94 0.69 1.00 1642
## cor(Intercept,IsWordFALSE) 0.54 0.26 -0.05 0.93 1.00 673
## cor(PhonLev,IsWordFALSE) -0.39 0.42 -0.94 0.64 1.00 521
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 95.32 31.73 45.61 170.35 1.01 1224 2012
## sd(PhonLev) 6.46 4.81 0.24 17.49 1.02 373 1553
## sd(IsWordFALSE) 96.22 19.16 62.98 137.45 1.00 2049 2612
## cor(Intercept,PhonLev) -0.36 0.48 -0.94 0.76 1.00 1431 2270
## cor(Intercept,IsWordFALSE) 0.52 0.26 -0.06 0.94 1.00 573 1181
## cor(PhonLev,IsWordFALSE) -0.32 0.47 -0.95 0.76 1.01 390 793
```

--
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