{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Distributions, Turing, StatsPlots, Random, RDatasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assignment 2: hierarchical models\n",
    "\n",
    "Students|\n",
    "-------|\n",
    "\n",
    "Name        |       Id\n",
    "------------|----------\n",
    "Ploni Almoni|123489589\n",
    "John Smith  |923352302\n",
    "\n",
    "## Summary\n",
    "\n",
    "In this assignment we explore hierarchical models for analysis of data consisting of multiple related groups. The assignment is based on the [class material](https://bgu-abda.bitbucket.io/#lectures): \n",
    "\n",
    "5. Hierarchical models\n",
    "6. Hierarchical models, cont.\n",
    "\n",
    "The assignment consists of two problems. Solve the problems in either Jupyter or Pluto notebook.\n",
    "In addition to computations, solutions must include **graphical visualization** and **numerical characterization** of the posterior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 1: warp breaks\n",
    "\n",
    "Julia provides to [R datasets](https://www.rdocumentation.org/packages/datasets/versions/3.6.2) via package RDatasets. We will use the [warpbreaks](https://www.rdocumentation.org/packages/datasets/versions/3.6.2/topics/warpbreaks) dataset for this problem. You can load the dataset into data frame `df` as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = RDatasets.dataset(\"datasets\", \"warpbreaks\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Infer the probability distribution of warp breaks for each of two wool types. Compare the results under separate and hierarchical models. Conduct two studies:\n",
    "\n",
    "1. Ignore warp tension and compare wool types based on all experiments. \n",
    "2. Account for warp tension in both the hierarchical model and the separate model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 2. City of Norfolk employee salaries\n",
    "\n",
    "City of Norfolk provides access to [employee salary data](https://data.norfolk.gov/Government/Employee-Salaries/4fsk-z8s8). Analyze the salary distributions \n",
    "\n",
    "1. by department;\n",
    "2. by department and employee status.\n",
    "\n",
    "Compare the analysis under separate and hierarchical models. A small number of groups are very different from the rest, how do you propose to handle the difference in the hierarchical model?"
   ]
  }
 ],
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