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Doing Bayesian Data Analysis: A Tutorial with R, Stan, brms, and the tidyverse
Doing Bayesian Data Analysis: A Tutorial with R, Stan, brms, and the tidyverse - Kindle edition by Kruschke, John, Kurz, Solomon. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Doing Bayesian Data Analysis: A Tutorial with R, Stan, brms, and the tidyverse.
![df = data.frame(x = -1:10, y = c(-3,2,1,2,5,3,6,7,3,6,10,11))
smooth_spline_x = \(formula, data) {
X = model.matrix(formula[-2], data)
# this is dumb but good enough for a hack
X %*% rep(1, ncol(X))
}
smooth_spline = \(formula, data, ..., weights = NULL) {
x = smooth_spline_x(formula, data)
y = eval(formula[[2]], data, environment(formula))
structure(
splinefun(x, y, ...),
class = c("smooth_spline", "function"),
formula = formula
)
}
predict.smooth_spline = \(object, newdata, ..., weights = NULL, se.fit = FALSE) {
fit = object(smooth_spline_x(attr(object, "formula"), newdata))
if (se.fit) {
list(fit = data.frame(fit = fit, lwr = 0, upr = 0), se.fit = NA_real_)
} else {
fit
}
}
df |>
ggplot(aes(x, y)) +
stat_smooth(formula = y ~ x, method = smooth_spline) +
geom_point()](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:6fs5x6cofzyz4si2xhqiqj37/bafkreiacuzr4k36gdw3hfpomiayv5a6f3tegppea5czle5yxqaap5aqelm)
![These days of the year now match the actual distribution of birthdays in the United States. If we simulated thousands of birthdays, we'd get more in September, fewer on the 13th of each money, and far fewer around Thanksgiving and Christmas.
We can now update our simulation to use this more realistic distribution of birthdays:
```{r}
#| label: fun-simulate-prob-real
simulate_prob_real <- function(n, num_simulations = 1000) {
results <- map_lgl(1:num_simulations, ~{
birthdays <- sample(
prob_per_day$day_of_year,
size = n,
replace = TRUE,
prob = prob_per_day$prob
)
birthdays_doubled <- sort(c(birthdays, birthdays + 366))
any(map_lgl(1:n, ~ birthdays_doubled[.x + n - 1] - birthdays_doubled[.x] <= (366 / 2)))
})
mean(results)
}
```](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:2zcfjzyocp6kapg6jc4eacok/bafkreigktbnkjagj3yuo73slsqq2sf4d4g6sd65nq7hz63cpib4b3jshcm)
![StatRightEnd <- ggproto(
"RightEnd",
Stat,
compute_group = function(data, scales) {
data[which.max(data$x), ]
}
)
ggplot(grid2) +
aes(mean_log_prob, plogis(preds)) +
geom_line(aes(group = item), linewidth = .5) +
geom_text(
aes(label = tocs_prompt, group = tocs_prompt),
stat = StatRightEnd
)](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:tpgnsvgqsu5b752uud3wmtja/bafkreie5ato6i2t4wjcdm5tztztlclk7zquqn2qmwavcmhwso55g2c2o4u)
