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@dcalacci
Created October 5, 2016 18:25
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{
"cells": [
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"import seaborn as sns"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 1\n",
"### Likelihoods"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def likelihood_h1(data):\n",
" \"\"\"likelihood that the coin is fair\n",
" \"\"\"\n",
" return 1 / (2 ** (len(data)))\n",
"\n",
"def likelihood_h2_single_theta(theta, data):\n",
" \"\"\"likelihood that the coin is weighted\n",
" \"\"\"\n",
" # n is number of heads, m is number of tails\n",
" N = sum(data)\n",
" M = len(data) - sum(data)\n",
" P_d_theta = (theta ** N) * ((1 - theta) ** M)\n",
" return P_d_theta\n",
" \n",
"def likelihood_h2(data):\n",
" \"\"\"\n",
" \"\"\"\n",
" thetas = np.linspace(0,1,100,endpoint=True)\n",
" likelihoods = [likelihood_h2_single_theta(theta, data) / 100 for theta in thetas]\n",
" return sum(likelihoods)\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sanity check:"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 106,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"likelihood_h1(coinflips[1]) == likelihood_h2_single_theta(0.5, coinflips[1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, from `likelihood_h1`, we have:\n",
"$$ P(D|H_1) = \\frac{1}{2^{H+T}}$$\n",
"\n",
"and from `likelihood_h2`, we have:\n",
"\n",
"$$ P(D|H_2) = \\sum_{n=1}^{100}{P(D|\\theta_n)P(\\theta_n|H_2)}$$\n",
"\n",
"where:\n",
"$$ P(D|\\theta_n) = \\theta_n^N(1-\\theta_n)^M $$ and $N$ is the number of heads in the series, and $M$ is the number of tails.\n",
"\n",
"and where $P(\\theta_n | H_2)$ is uniformly distributed in the range $[0,1]$, and we are testing 100 hypotheses, it is independent of $n$: \n",
"$$P(\\theta_n | H_2) = \\frac{1}{100}$$\n",
"\n",
"So then we can compute an approximated likelihood for $H_2$ by:\n",
"\n",
"$$ P(D|H_2) \\approx \\sum_{n=1}^{100}{\\frac{\\theta_n^N(1-\\theta_n)^M}{100}}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Log Posterior Odds Ratio"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can compute the log posterior odds ratio by :\n",
"\n",
"$$ \\log{\\frac{P(H_1|D)}{P(H_2|D)}} = \\log{\\frac{P(D|H_1)}{P(D|H_2)}} + \\log{\\frac{P(H_1)}{P(H_2)}}$$"
]
},
{
"cell_type": "code",
"execution_count": 264,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"prior_h1 = 1\n",
"prior_h2 = 1\n",
"def log_posterior_odds(data, prior_h1=1, prior_h2=1):\n",
" \"\"\"compute log posterior odds ratio from the likelihood and\n",
" priors for two different hypotheses\n",
" \"\"\"\n",
" return np.log(likelihood_h1(data) / likelihood_h2(data)) + np.log(prior_h1 / prior_h2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To scale to our \"human scale\":\n",
"\n",
"$$ f(x) = \\frac{1}{1 +\\exp(-ax + b)}$$"
]
},
{
"cell_type": "code",
"execution_count": 176,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def logistic_scale(a, b, val):\n",
" return 1 / (1 + np.exp((-a * val) + b))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Model the real data"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import pandas as pd"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A colleague (Abdullah Almaatouq) and I merged our datasets. Here, I'm combining our control conditions together, and keeping our interventions separate. \n",
"\n",
"Abdullah's intervention was crafted with the intent of weighting peoples' priors towards beleiving that the coins were fair. Mine tried to nudge participants into believing the coins were unfair. Mine and Abdullah's interventions are labeled here as `intervention-d` and `intervention-a`, respectively."
]
},
{
"cell_type": "code",
"execution_count": 241,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>condition</th>\n",
" <th>coin1</th>\n",
" <th>coin2</th>\n",
" <th>coin3</th>\n",
" <th>coin4</th>\n",
" <th>coin5</th>\n",
" <th>coin6</th>\n",
" <th>coin7</th>\n",
" <th>coin8</th>\n",
" <th>coin9</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>control-a</td>\n",
" <td>2</td>\n",
" <td>3</td>\n",
" <td>5</td>\n",
" <td>4</td>\n",
" <td>4</td>\n",
" <td>6</td>\n",
" <td>4</td>\n",
" <td>6</td>\n",
" <td>7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>control-a</td>\n",
" <td>3</td>\n",
" <td>5</td>\n",
" <td>7</td>\n",
" <td>2</td>\n",
" <td>6</td>\n",
" <td>7</td>\n",
" <td>2</td>\n",
" <td>6</td>\n",
" <td>7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>control-a</td>\n",
" <td>2</td>\n",
" <td>4</td>\n",
" <td>5</td>\n",
" <td>1</td>\n",
" <td>6</td>\n",
" <td>7</td>\n",
" <td>1</td>\n",
" <td>7</td>\n",
" <td>7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>intervention-d</td>\n",
" <td>1</td>\n",
" <td>2</td>\n",
" <td>5</td>\n",
" <td>2</td>\n",
" <td>5</td>\n",
" <td>6</td>\n",
" <td>2</td>\n",
" <td>6</td>\n",
" <td>7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>intervention-d</td>\n",
" <td>3</td>\n",
" <td>4</td>\n",
" <td>5</td>\n",
" <td>3</td>\n",
" <td>5</td>\n",
" <td>6</td>\n",
" <td>3</td>\n",
" <td>5</td>\n",
" <td>6</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>intervention-d</td>\n",
" <td>2</td>\n",
" <td>5</td>\n",
" <td>7</td>\n",
" <td>1</td>\n",
" <td>7</td>\n",
" <td>7</td>\n",
" <td>2</td>\n",
" <td>5</td>\n",
" <td>7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>intervention-d</td>\n",
" <td>3</td>\n",
" <td>4</td>\n",
" <td>5</td>\n",
" <td>4</td>\n",
" <td>5</td>\n",
" <td>6</td>\n",
" <td>5</td>\n",
" <td>6</td>\n",
" <td>7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>control-d</td>\n",
" <td>4</td>\n",
" <td>5</td>\n",
" <td>6</td>\n",
" <td>4</td>\n",
" <td>6</td>\n",
" <td>6</td>\n",
" <td>3</td>\n",
" <td>6</td>\n",
" <td>4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>control-d</td>\n",
" <td>2</td>\n",
" <td>3</td>\n",
" <td>4</td>\n",
" <td>2</td>\n",
" <td>2</td>\n",
" <td>6</td>\n",
" <td>2</td>\n",
" <td>3</td>\n",
" <td>7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>intervention-a</td>\n",
" <td>1</td>\n",
" <td>3</td>\n",
" <td>4</td>\n",
" <td>3</td>\n",
" <td>3</td>\n",
" <td>4</td>\n",
" <td>2</td>\n",
" <td>5</td>\n",
" <td>7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>intervention-a</td>\n",
" <td>1</td>\n",
" <td>4</td>\n",
" <td>5</td>\n",
" <td>1</td>\n",
" <td>5</td>\n",
" <td>6</td>\n",
" <td>2</td>\n",
" <td>6</td>\n",
" <td>7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>intervention-a</td>\n",
" <td>1</td>\n",
" <td>5</td>\n",
" <td>6</td>\n",
" <td>1</td>\n",
" <td>4</td>\n",
" <td>5</td>\n",
" <td>1</td>\n",
" <td>1</td>\n",
" <td>7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>intervention-a</td>\n",
" <td>2</td>\n",
" <td>2</td>\n",
" <td>4</td>\n",
" <td>1</td>\n",
" <td>5</td>\n",
" <td>7</td>\n",
" <td>2</td>\n",
" <td>6</td>\n",
" <td>7</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" condition coin1 coin2 coin3 coin4 coin5 coin6 coin7 coin8 \\\n",
"0 control-a 2 3 5 4 4 6 4 6 \n",
"1 control-a 3 5 7 2 6 7 2 6 \n",
"2 control-a 2 4 5 1 6 7 1 7 \n",
"3 intervention-d 1 2 5 2 5 6 2 6 \n",
"4 intervention-d 3 4 5 3 5 6 3 5 \n",
"5 intervention-d 2 5 7 1 7 7 2 5 \n",
"6 intervention-d 3 4 5 4 5 6 5 6 \n",
"7 control-d 4 5 6 4 6 6 3 6 \n",
"8 control-d 2 3 4 2 2 6 2 3 \n",
"9 intervention-a 1 3 4 3 3 4 2 5 \n",
"10 intervention-a 1 4 5 1 5 6 2 6 \n",
"11 intervention-a 1 5 6 1 4 5 1 1 \n",
"12 intervention-a 2 2 4 1 5 7 2 6 \n",
"\n",
" coin9 \n",
"0 7 \n",
"1 7 \n",
"2 7 \n",
"3 7 \n",
"4 6 \n",
"5 7 \n",
"6 7 \n",
"7 4 \n",
"8 7 \n",
"9 7 \n",
"10 7 \n",
"11 7 \n",
"12 7 "
]
},
"execution_count": 241,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = pd.read_csv('../flip_control.csv', index_col=0)\n",
"df = df.reset_index()\n",
"df = df.rename(columns={'index': 'condition'})\n",
"df"
]
},
{
"cell_type": "code",
"execution_count": 266,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"df.condition = df.condition.apply(lambda s: 'control' if 'control' in s else s)\n",
"#df['control'] = np.mean(df['control-a', 'control-d'])\n",
"#df = df.T\n",
"std_df = df.groupby('condition').agg(np.std)\n",
"mean_human_df = df.groupby('condition').agg(np.mean)"
]
},
{
"cell_type": "code",
"execution_count": 243,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>coin1</th>\n",
" <th>coin2</th>\n",
" <th>coin3</th>\n",
" <th>coin4</th>\n",
" <th>coin5</th>\n",
" <th>coin6</th>\n",
" <th>coin7</th>\n",
" <th>coin8</th>\n",
" <th>coin9</th>\n",
" </tr>\n",
" <tr>\n",
" <th>condition</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>control</th>\n",
" <td>2.60</td>\n",
" <td>4.00</td>\n",
" <td>5.40</td>\n",
" <td>2.6</td>\n",
" <td>4.80</td>\n",
" <td>6.40</td>\n",
" <td>2.40</td>\n",
" <td>5.6</td>\n",
" <td>6.40</td>\n",
" </tr>\n",
" <tr>\n",
" <th>intervention-a</th>\n",
" <td>1.25</td>\n",
" <td>3.50</td>\n",
" <td>4.75</td>\n",
" <td>1.5</td>\n",
" <td>4.25</td>\n",
" <td>5.50</td>\n",
" <td>1.75</td>\n",
" <td>4.5</td>\n",
" <td>7.00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>intervention-d</th>\n",
" <td>2.25</td>\n",
" <td>3.75</td>\n",
" <td>5.50</td>\n",
" <td>2.5</td>\n",
" <td>5.50</td>\n",
" <td>6.25</td>\n",
" <td>3.00</td>\n",
" <td>5.5</td>\n",
" <td>6.75</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" coin1 coin2 coin3 coin4 coin5 coin6 coin7 coin8 coin9\n",
"condition \n",
"control 2.60 4.00 5.40 2.6 4.80 6.40 2.40 5.6 6.40\n",
"intervention-a 1.25 3.50 4.75 1.5 4.25 5.50 1.75 4.5 7.00\n",
"intervention-d 2.25 3.75 5.50 2.5 5.50 6.25 3.00 5.5 6.75"
]
},
"execution_count": 243,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mean_df"
]
},
{
"cell_type": "code",
"execution_count": 267,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1129c0c50>"
]
},
"execution_count": 267,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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cnZaRzz77xIVFV7///X/y0EP38NhjaykrKz1/1mXjJCdfT0rKzgvJ+XzLyDff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pdDbqL31HZBff8PJCm6/X9os7YjOWw6jHqXHphHJCm9Tu9YM3yk7whMGh6lckWkBao2527RjeNl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\ncyYiItIYNmciIiKNYXMmIiLSmP8HzZpM9z9X0DEAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x113545e10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mean_human_df.T.plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Huh, It looks like Abdullah's intervention is pretty far below the control (and my intervention). That's good, but my intervention is right up there with our control data, instead of above it. Oh well."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Add model predictions"
]
},
{
"cell_type": "code",
"execution_count": 245,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"coinflips = [\n",
" [1, 1, 0, 1, 0],\n",
" [0, 1, 0, 0, 0],\n",
" [1, 1, 1, 1, 1],\n",
" [0, 1, 0, 0, 1, 0, 1, 0, 1, 0],\n",
" [1, 1, 0, 1, 1, 1, 1, 1, 0, 1],\n",
" [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
" [0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0],\n",
" [1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1],\n",
" [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"]"
]
},
{
"cell_type": "code",
"execution_count": 268,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[0.63865900568607925,\n",
" -0.054233092353287313,\n",
" -1.694026598952747,\n",
" 0.823581333711494,\n",
" -0.71686336375730986,\n",
" -4.5784789710436069,\n",
" 0.76948958914506638,\n",
" -3.6218683656392949,\n",
" -14.849006318428241]"
]
},
"execution_count": 268,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model_values = [log_posterior_odds(D) for D in coinflips]\n",
"model_values"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It looks as though using $a=1$ and $b=0$ in the logistic transformation, then multiplying by 7, works well. "
]
},
{
"cell_type": "code",
"execution_count": 269,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[2.4188481510597493,\n",
" 3.5948846563051364,\n",
" 5.9132707420126955,\n",
" 2.1350277999277902,\n",
" 4.7034115435545791,\n",
" 6.9288373334907547,\n",
" 2.2161267010571146,\n",
" 6.8177434237057026,\n",
" 6.9999975096729861]"
]
},
"execution_count": 269,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm_model_values = [(1 - scale_to_likert(1, 0, v)) * 7 for v in model_values]\n",
"norm_model_values"
]
},
{
"cell_type": "code",
"execution_count": 270,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# add the normed values to our data\n",
"mean_df = mean_human_df.T\n",
"mean_df['model'] = norm_model_values\n",
"mean_df = mean_df.T"
]
},
{
"cell_type": "code",
"execution_count": 272,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>coin1</th>\n",
" <th>coin2</th>\n",
" <th>coin3</th>\n",
" <th>coin4</th>\n",
" <th>coin5</th>\n",
" <th>coin6</th>\n",
" <th>coin7</th>\n",
" <th>coin8</th>\n",
" <th>coin9</th>\n",
" </tr>\n",
" <tr>\n",
" <th>condition</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>control</th>\n",
" <td>2.600000</td>\n",
" <td>4.000000</td>\n",
" <td>5.400000</td>\n",
" <td>2.600000</td>\n",
" <td>4.800000</td>\n",
" <td>6.400000</td>\n",
" <td>2.400000</td>\n",
" <td>5.600000</td>\n",
" <td>6.400000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>intervention-a</th>\n",
" <td>1.250000</td>\n",
" <td>3.500000</td>\n",
" <td>4.750000</td>\n",
" <td>1.500000</td>\n",
" <td>4.250000</td>\n",
" <td>5.500000</td>\n",
" <td>1.750000</td>\n",
" <td>4.500000</td>\n",
" <td>7.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>intervention-d</th>\n",
" <td>2.250000</td>\n",
" <td>3.750000</td>\n",
" <td>5.500000</td>\n",
" <td>2.500000</td>\n",
" <td>5.500000</td>\n",
" <td>6.250000</td>\n",
" <td>3.000000</td>\n",
" <td>5.500000</td>\n",
" <td>6.750000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>model</th>\n",
" <td>2.418848</td>\n",
" <td>3.594885</td>\n",
" <td>5.913271</td>\n",
" <td>2.135028</td>\n",
" <td>4.703412</td>\n",
" <td>6.928837</td>\n",
" <td>2.216127</td>\n",
" <td>6.817743</td>\n",
" <td>6.999998</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" coin1 coin2 coin3 coin4 coin5 coin6 \\\n",
"condition \n",
"control 2.600000 4.000000 5.400000 2.600000 4.800000 6.400000 \n",
"intervention-a 1.250000 3.500000 4.750000 1.500000 4.250000 5.500000 \n",
"intervention-d 2.250000 3.750000 5.500000 2.500000 5.500000 6.250000 \n",
"model 2.418848 3.594885 5.913271 2.135028 4.703412 6.928837 \n",
"\n",
" coin7 coin8 coin9 \n",
"condition \n",
"control 2.400000 5.600000 6.400000 \n",
"intervention-a 1.750000 4.500000 7.000000 \n",
"intervention-d 3.000000 5.500000 6.750000 \n",
"model 2.216127 6.817743 6.999998 "
]
},
"execution_count": 272,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mean_df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 1b"
]
},
{
"cell_type": "code",
"execution_count": 273,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x113534390>"
]
},
"execution_count": 273,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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Sn30OSaPBJ/v4sHIzEhJPFD6CJElUt3Tzwb4qKpq6UUkSS6al88iCHGIidLc8/rsTn2F1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\nQgjRyvw/0CEMIAC3NhEAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11356fc18>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mean_df.T.plot(yerr=std_df.T)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The model looks to fit the data pretty well. One of the control conditions appears to be quite an outlier, with values well below both a separate control and the intervention condition human data.\n",
"\n",
"The model appears to overestimate how unfair a coin is by comparison, though.\n",
"\n",
"Fit was estimated by eyeballing the data, but we can do a quick analytical measure of fit, too:"
]
},
{
"cell_type": "code",
"execution_count": 259,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.46572779521975211"
]
},
"execution_count": 259,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.mean(abs(mean_df.ix['model'] - mean_df.ix['control']))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So we get on average about $\\frac{1}{2}$ of a \"scale point\" off from the control data. But the standard deviation of our measurements is over 1:"
]
},
{
"cell_type": "code",
"execution_count": 263,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"1.1901346269459163"
]
},
"execution_count": 263,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"std_df.ix['control'].mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So I'd say it's fitting reasonably well."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### iii\n",
"\n",
"The model seems to systematically overestimate how unfair coins are. It does not model Abdullah's intervention well. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1c"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's first plot a $P(H_1)$ that I think may fit the control data better, $P(H_1) = 0.75$"
]
},
{
"cell_type": "code",
"execution_count": 278,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def plot_ph1(p_h1):\n",
" mv = [log_posterior_odds(D, p_h1, 1 - p_h1) for D in coinflips]\n",
" norm_model_values = [(1 - scale_to_likert(1, 0, v)) * 7 for v in mv]\n",
" # add the normed values to our data\n",
" mean_df = mean_human_df.T\n",
" mean_df['model'] = norm_model_values\n",
" mean_df = mean_df.T\n",
" mean_df.T.plot(yerr=std_df.T)"
]
},
{
"cell_type": "code",
"execution_count": 296,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Bg4fw4ov/5ejRZP7xj7+cq0/9AcOHj+Teex8gLe0o3333HQBnz+axY8c23n13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\nD97SFB/ns91jAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x113b9b470>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_ph1(0.75)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Well, it kind of looks worse. Let's optimize for the error over $P(H_1)$:"
]
},
{
"cell_type": "code",
"execution_count": 304,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def get_best_ph1(condition):\n",
" errs = []\n",
" for p_h1 in np.linspace(0,1,100):\n",
" mv = [log_posterior_odds(D, p_h1, 1 - p_h1) for D in coinflips]\n",
" norm_model_values = [(1 - scale_to_likert(1, 0, v)) * 7 for v in mv]\n",
" # add the normed values to our data\n",
" mean_df = mean_human_df.T\n",
" mean_df['model'] = norm_model_values\n",
" mean_df = mean_df.T\n",
" avg_err = np.mean(abs(mean_df.ix['model'] - mean_df.ix[condition]))\n",
" errs.append((p_h1, avg_err))\n",
" best_ph1 = sorted(errs, key=lambda t: t[1])[0]\n",
" print(\"best P(H_1): {0}. Error: {1}\".format(best_ph1[0], best_ph1[1]))\n",
" plot_ph1(best_ph1[0])"
]
},
{
"cell_type": "code",
"execution_count": 302,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"best P(H_1): 0.4747474747474748. Error: 0.40194308050581273\n"
]
},
{
"data": {
"image/png": 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ueD3Gzj4mTku+7SxsRWO96e/jMqMJi9BRVdrBghXjb9lpSBjdHG1tGLZuxnzq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\nfZ44Nvbh2SMdCUxWJ//+ThkdQXHkWBv4f76+HoVchtvl4R9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CKwBi2Dd6kp6mUyex19Vh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\nEDZGBmchhBDCxsjgLIQQQtiY/wdjpwTO4M40oQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x112d971d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"get_best_ph1('control')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, modeling the control condition brings us pretty close to $P(H_1) = 0.5$. Amazing! What about Abdullah's control condition where the guesses seemed to be lower?"
]
},
{
"cell_type": "code",
"execution_count": 306,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"best P(H_1): 0.5858585858585859. Error: 0.6557557165163634\n"
]
},
{
"data": {
"image/png": 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rqdg9OfLJXHx6FwRZltn/czYAw5IDKP1kOdW7d4LdTrmrP2d6jebOx+bj7ubY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xttFL4zIsnZ7lD5j20XOHKhjqykcH781RmEBbtIzNVVVP7ql6g93Zif/W+EPTDnns//YeknNFta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\nlmMDz//wcHtYW9M0j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"text/plain": [
"<matplotlib.figure.Figure at 0x1121c91d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"get_best_ph1('intervention-a')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It looks like something closer to $P(H_1) = 0.6$ is better here, which makes sense. Abdullah's condition was created to increase the likelihood of thinking that the coins were fair."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 1d\n",
"\n",
"I think this hypothesis space is limited for two reasons. One, it doesn't capture the idea that humans likely think that a coin is either weighted fully (heads 100% of the time), or not at all (50%). Another is that a coin could potentially have a \"sequence\" baked into it that it repeats (although this is difficult to imagine). \n",
"\n",
"##### ii\n",
"Examples:\n",
"\n",
"HHTHHTHHTHHTHHTHHTHHT\n",
"\n",
"TTHTTTHTTHTTTHTTTHTTTHT\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"-----\n",
"### Problem 2"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.2"
},
"nav_menu": {},
"toc": {
"navigate_menu": true,
"number_sections": true,
"sideBar": true,
"threshold": 6,
"toc_cell": false,
"toc_section_display": "block",
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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