Sim-Prior

Published

November 5, 2022

Exercise

Gegeben dem folgenden Modell, simulieren Sie Daten aus der Prior-Verteilung (Priori-Prädiktiv-Verteilung).

Likelihood: \(h_i \sim \mathcal{N}(\mu, \sigma)\)

Prior für \(\mu\): \(\mu \sim \mathcal{N}(0, 1)\)

Prior für \(\sigma\): \(\sigma \sim \mathcal{U}(0, 10)\)

Solution

library(tidyverse)

n <- 1e4


sim <- tibble(
  mu = rnorm(n = n),  # Default-Werte sind mean=0, sd = 1
  sigma = runif(n = n, 0, 10)) %>%
  mutate(
    y = rnorm(n = n, mean = mu, sd = sigma))

ggplot(sim, aes(x = y)) +
  geom_density() +
  labs(x = "y", y = "Dichte") +
  theme_minimal()

Categories:

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---
extype: string
exsolution: NA
exname: sim-prior
expoints: 1
date: '2022-11-05'
slug: Sim-Prior
title: Sim-Prior

---




```{r libs, include = FALSE}
library(tidyverse)
library(testthat)
library(glue)
library(printr)
```


```{r global-knitr-options, include=FALSE}
knitr::opts_chunk$set(fig.pos = 'H',
                      fig.asp = 0.618,
                      fig.width = 4,
                      fig.cap = "", 
                      fig.path = "",
                      echo = TRUE,
                      message = FALSE,
                      fig.show = "hold")
```






# Exercise



Gegeben dem folgenden Modell, simulieren Sie Daten aus der Prior-Verteilung (Priori-Prädiktiv-Verteilung).

Likelihood:
$h_i \sim \mathcal{N}(\mu, \sigma)$

Prior für $\mu$:
$\mu \sim \mathcal{N}(0, 1)$

Prior für $\sigma$:
$\sigma \sim \mathcal{U}(0, 10)$



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# Solution

```{r}
library(tidyverse)

n <- 1e4


sim <- tibble(
  mu = rnorm(n = n),  # Default-Werte sind mean=0, sd = 1
  sigma = runif(n = n, 0, 10)) %>%
  mutate(
    y = rnorm(n = n, mean = mu, sd = sigma))

ggplot(sim, aes(x = y)) +
  geom_density() +
  labs(x = "y", y = "Dichte") +
  theme_minimal()
```




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Categories: 

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