direction_central_bias.Rmd

---
title: "Direction bias and Central bias"
author: "Simon Kucharsky"
date: "`r Sys.Date()`"
output: 
  rmarkdown::github_document:
    pandoc_args: --webtex
bibliography: "`r here::here('bibliography.bib')`"
csl: "`r here::here('apa.csl')`"
---




```{r}
library(rstan)
source(here::here("R", "expose_helpers_stan.R"))
```



## Fitting a direction bias


```{r}
dir_weigths <- c(0.5, 0.5)
dir_mu      <- c(0, pi)
dir_kappa   <- c(8, 8)

cen_sigma   <- c(100, 100)
mix_weights <- c(0.4, 0.6)

xy <- matrix(NA, nrow = 500, ncol = 2)
for(i in 1:nrow(xy)){
  k <- sample(1:2, 1, TRUE, mix_weights)
  
  if(k == 1){
    x <- ifelse(i == 1, 400, xy[i-1, 1])
    y <- ifelse(i == 1, 300, xy[i-1, 2])
    xy[i,] <- direction_bias_rng(c(0.5, 0.5), c(0, pi), c(8, 8), x, y, 0, 800, 0, 600)
  } else {
    xy[i,1] <- trunc_normal_rng(400, cen_sigma[1], 0, 800)
    xy[i,2] <- trunc_normal_rng(300, cen_sigma[2], 0, 600)
  }
}

plot(xy, pch = 19, xlab = "x", ylab = "y")
lines(xy)
```

```{r}
stan_model <- rstan::stan_model(here::here("stan", "examples", "direction_central_bias_single.stan"), isystem = here::here())

stan_data  <- list(N_obs = nrow(xy), x = xy[,1], y = xy[,2])

stan_fit   <- rstan::sampling(stan_model, stan_data, chains = 4, cores = 4, warmup = 500, iter = 1000, refresh = 250)

print(stan_fit)
```