mooresm

---
title: "BayesComp 2023 abstract booklet"
format: pdf
editor: visual
params:
  echo: FALSE
---

```{r, echo=FALSE, eval=TRUE, results='hide'}
library(stringr)

mooresm

library(serrsBayes)

### read the data ----
library(hyperSpec)
etoh <- read.spc("EtOH.spc")
plot(etoh)

wv <- wl(etoh)
i1 <- which.min(wv < 300)
i2 <- which.min(wv < 1800)

mooresm

# Data downloaded from CovidBaseAU and Our World in Data,
# https://github.com/owid/covid-19-data/
vax_aus <- read.csv("Australia.txt")
vax_aus$Date <- as.Date(vax_aus$date)
ix1 <- which.max(vax_aus$Date > "2021-05-02") - 1
idx <- which.max(vax_aus$Date > "2021-07-02") - 1
ix2 <- which.max(vax_aus$Date > "2021-09-02") - 1
ix3 <- which.max(vax_aus$Date > "2021-11-02") - 1
ix4 <- which.max(vax_aus$Date > "2021-10-02") - 1
vax_aus$Date[idx]

mooresm

# Piecewise basis functions: splines
# ch. 5 of ESL: Hastie, Tibshirani & Friedman (2009)

# one dimension (p=1)
x <- seq(-0.5,1,by=0.05)[-11]
y <- 2 - 5*exp(-8 * x^2) + rnorm(length(x), sd=0.5)
plot(x,y, ylim=range(-3,2,y))
curve(2 - 5*exp(-8 * x^2), from=-0.5, to=1, n=length(x), col=4, add=T)

# kNN regression: piecewise constant

mooresm

functions {
  vector ft(vector t, real r, real y0, real tC, real L) {
    vector[num_elements(t)] mu;
    vector[num_elements(t)] exprt;
    exprt = exp(r*(t-tC));
    mu = y0*L*exprt ./ (L + y0*(exprt - 1));
    return mu;
  }
  
  vector dfdt(vector t, real r, real tC, real L) {

mooresm

set.seed(13)
y <- rnorm(n=5, mean=1, sd=2/3)
n <- length(y)
s_sq <- sum((y-1)^2)/n
# weakly informative priors:
nu0 <- 1
s0 <- 1
post_nu <- nu0 + n
post_ssd <- (nu0 * s0^2 + n*s_sq)/2
post_tau <- rgamma(10000, post_nu/2, post_ssd)

mooresm

set.seed(1234)

# Exercise 3.1: simple symmetric random walk on {0,1,2}
upd <- function(x, U) {
  x + ifelse(x < 2 && U > 0.5, 1, 0) - ifelse(x > 0 && U <= 0.5, 1, 0)
}

x <- 1
upd(x,0.25)
upd(x,0.75)