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@jonathan-taylor
Last active February 2, 2018 07:05
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One and two sided truncation
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import norm as ndist\n",
"%matplotlib inline\n",
"from selection.truncated.gaussian import truncated_gaussian_old as TG\n",
"\n",
"tg = TG([(-np.inf, -3), (3, np.inf)])\n",
"tg1 = TG([(3, np.inf)])"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.25284231, 5.93267262])"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tg.equal_tailed_interval(4, 0.05)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"Z = np.linspace(3.02, 6.02, 51)\n",
"L, U = [], []\n",
"L1, U1 = [], []\n",
"for z in Z:\n",
" l, u = tg.equal_tailed_interval(z, 0.05)\n",
" L.append(l); U.append(u)\n",
" l, u = tg1.equal_tailed_interval(z, 0.05)\n",
" L1.append(l); U1.append(u)\n",
"L = np.array(L); U = np.array(U)\n",
"L1 = np.array(L1); U1 = np.array(U1)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(2.8881931304931641, 3.9945793151855469)\n",
"0.950000071864\n",
"(-0.54578602313995361, 2.3424071073532104)\n"
]
},
{
"data": {
"image/png": 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26+zzwH5gHPAT8C+CM0eHhTOgiIjEMWspC5CY6DpJxO3u35+fgSaTNHdPTlXs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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10cb68e10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10,10))\n",
"plt.plot(Z, L, 'k-', label='Two-sided')\n",
"plt.plot(Z, U, 'k-')\n",
"plt.plot(-Z, -L, 'k-')\n",
"plt.plot(-Z, -U, 'k-')\n",
"plt.plot([-8,8], [0,0], 'k--')\n",
"plt.plot([-3,-3], [-8,8], 'k--')\n",
"plt.plot([3,3], [-8,8], 'k--')\n",
"plt.plot(Z, L1, 'r-', label='One-sided')\n",
"plt.plot(Z, U1, 'r-')\n",
"plt.gca().set_ylim([-8,8])\n",
"plt.gca().set_xlabel('Observation', fontsize=20)\n",
"plt.gca().set_ylabel('Confidence interval', fontsize=20)\n",
"plt.legend(fontsize=20)\n",
"print(U[0] - L[0], U[-1]- L[-1]) # superefficiency\n",
"tg.mu = U[0]; lower_tail = tg.cdf(Z[0])\n",
"tg.mu = L[0]; upper_tail = tg.cdf(Z[0])\n",
"print(float(upper_tail - lower_tail)) # coverage near cutoff\n",
"print(L[0], U[0]) # if you want to double check with R"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(2.1741700172424316, 3.928605318069458)\n",
"0.950000009629\n",
"(-0.75675785541534424, 1.4174121618270874)\n"
]
}
],
"source": [
"tg = TG([(-np.inf, -2), (2, np.inf)])\n",
"tg1 = TG([(2, np.inf)])\n",
"Z = np.linspace(2.02, 6.02, 51)\n",
"L, U = [], []\n",
"L1, U1 = [], []\n",
"for z in Z:\n",
" l, u = tg.equal_tailed_interval(z, 0.05)\n",
" L.append(l); U.append(u)\n",
" l, u = tg1.equal_tailed_interval(z, 0.05)\n",
" L1.append(l); U1.append(u)\n",
"L = np.array(L); U = np.array(U)\n",
"L1 = np.array(L1); U1 = np.array(U1)\n",
"print(U[0] - L[0], U[-1]- L[-1]) # superefficiency\n",
"tg.mu = U[0]; lower_tail = tg.cdf(Z[0])\n",
"tg.mu = L[0]; upper_tail = tg.cdf(Z[0])\n",
"print(float(upper_tail - lower_tail)) # coverage near cutoff\n",
"print(L[0], U[0]) # if you want to double check with R"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Checking equal tailed property of short interval by hand to be sure"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.97500001265601954, 0.025000003026615817)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def tg_cdf(z, mu, ltrunc, utrunc):\n",
" \n",
" if not ((z >= utrunc) + (z <= ltrunc)):\n",
" stop\n",
" den = 1 - (ndist.cdf(utrunc - mu) - ndist.cdf(ltrunc - mu))\n",
" if z >= utrunc:\n",
" num = ndist.cdf(z - mu) - ndist.cdf(utrunc - mu) + ndist.cdf(ltrunc - mu)\n",
" else:\n",
" num = ndist.cdf(z - mu)\n",
"\n",
" return num / den\n",
"tg_cdf(Z[0], L[0], -2, 2), tg_cdf(Z[0], U[0], -2, 2)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1103cac10>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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TmTNnWs0gnheodV/3wQdc+8QTbA8NpUpyMsUrVLAdSQKct89hA3gE+OTUHaJb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\nSUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1101b2490>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10,10))\n",
"plt.plot(Z, L, 'k-', label='Two-sided')\n",
"plt.plot(Z, U, 'k-')\n",
"plt.plot(-Z, -L, 'k-')\n",
"plt.plot(-Z, -U, 'k-')\n",
"plt.plot([-8,8], [0,0], 'k--')\n",
"plt.plot([-2,-2], [-8,8], 'k--')\n",
"plt.plot([2,2], [-8,8], 'k--')\n",
"plt.plot(Z, L1, 'r-', label='One-sided')\n",
"plt.plot(Z, U1, 'r-')\n",
"plt.gca().set_ylim([-8,8])\n",
"plt.gca().set_xlabel('Observation', fontsize=20)\n",
"plt.gca().set_ylabel('Confidence interval', fontsize=20)\n",
"plt.legend(fontsize=20)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"tg = TG([(-np.inf, -3), (3, np.inf)])\n",
"tg1 = TG([(3, np.inf)])\n",
"Z = np.linspace(3.02, 6.02, 51)\n",
"L, U = [], []\n",
"L1, U1 = [], []\n",
"for z in Z:\n",
" l, u = tg.equal_tailed_interval(z, 0.1)\n",
" L.append(l); U.append(u)\n",
" l, u = tg1.equal_tailed_interval(z, 0.1)\n",
" L1.append(l); U1.append(u)\n",
"L = np.array(L); U = np.array(U)\n",
"L1 = np.array(L1); U1 = np.array(U1)\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(1.3602316379547119, 3.3360075950622559)\n",
"0.899999971537\n",
"(-0.43640077114105225, 0.92383086681365967)\n"
]
},
{
"data": {
"text/plain": [
"(0.94999996448265434, 0.049999992945507686)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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RnDlzAOjZs6fjJCLeKar7egUFHPH5JdGcgwc55913WV25MsmjRrmOIz4TTMO2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\niIiEOBVsIiIiIiHu/wNFzNZt9zfv1wAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1103d76d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10,10))\n",
"plt.plot(Z, L, 'k-', label='Two-sided')\n",
"plt.plot(Z, U, 'k-')\n",
"plt.plot(-Z, -L, 'k-')\n",
"plt.plot(-Z, -U, 'k-')\n",
"plt.plot([-8,8], [0,0], 'k--')\n",
"plt.plot([-3,-3], [-8,8], 'k--')\n",
"plt.plot([3,3], [-8,8], 'k--')\n",
"plt.plot(Z, L1, 'r-', label='One-sided')\n",
"plt.plot(Z, U1, 'r-')\n",
"plt.gca().set_ylim([-8,8])\n",
"plt.gca().set_xlabel('Observation', fontsize=20)\n",
"plt.gca().set_ylabel('Confidence interval', fontsize=20)\n",
"plt.legend(fontsize=20)\n",
"print(U[0] - L[0], U[-1]- L[-1]) # superefficiency\n",
"tg.mu = U[0]; lower_tail = tg.cdf(Z[0])\n",
"tg.mu = L[0]; upper_tail = tg.cdf(Z[0])\n",
"print(float(upper_tail - lower_tail)) # coverage near cutoff\n",
"print(L[0], U[0]) # if you want to double check with R\n",
"tg_cdf(Z[0], L[0], -3, 3), tg_cdf(Z[0], U[0], -3, 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Translation invariant w.r.t. truncation (complement of) interval?\n",
"\n",
"Not really -- it is now super-efficient around -1, the center of [-4, 2]. BUT, near $H_0$, the law will be concentrated\n",
"on the RHS and the power will still be like the one-sided truncation at 2. Agreement with the test (i.e. where intervals on the RHS cross 0) seems even better now."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"tg = TG([(-np.inf, -4), (2, np.inf)])\n",
"tg1 = TG([(2, np.inf)])\n",
"Z = np.linspace(2.02, 5.02, 51)\n",
"Z0 = np.linspace(-7.02, -4.02, 51)\n",
"L, U = [], []\n",
"L0, U0 = [], []\n",
"L1, U1 = [], []\n",
"for z in Z:\n",
" l, u = tg.equal_tailed_interval(z, 0.05)\n",
" L.append(l); U.append(u)\n",
" l, u = tg1.equal_tailed_interval(z, 0.05)\n",
" L1.append(l); U1.append(u)\n",
"for z in Z0:\n",
" l, u = tg.equal_tailed_interval(z, 0.05)\n",
" L0.append(l); U0.append(u)\n",
"L = np.array(L); U = np.array(U)\n",
"L1 = np.array(L1); U1 = np.array(U1)\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(2.8881931304931641, 3.9945793151855469)\n",
"0.949999932952\n",
"(-1.5457850694656372, 1.3424080610275269)\n"
]
},
{
"data": {
"text/plain": [
"(0.9749999274768909, 0.024999994525094292)"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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MwZeby10AFSq4jhMxfLm5HL7zTnKMoVFKimaFStgF07BtN8Z8aK39TdjSFMAY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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11043aa50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10,10))\n",
"plt.plot(Z, L, 'k-', label='Two-sided')\n",
"plt.plot(Z, U, 'k-')\n",
"plt.plot(Z0, L0, 'k-')\n",
"plt.plot(Z0, U0, 'k-')\n",
"plt.plot([-8,8], [0,0], 'k--')\n",
"plt.plot([-8,8], [-1,-1], 'b--')\n",
"plt.plot([-4,-4], [-8,8], 'k--')\n",
"plt.plot([2,2], [-8,8], 'k--')\n",
"plt.plot(Z, L1, 'r-', label='One-sided')\n",
"plt.plot(Z, U1, 'r-')\n",
"plt.gca().set_ylim([-8,8])\n",
"plt.gca().set_xlabel('Observation', fontsize=20)\n",
"plt.gca().set_ylabel('Confidence interval', fontsize=20)\n",
"plt.legend(fontsize=20)\n",
"print(U[0] - L[0], U[-1]- L[-1]) # superefficiency\n",
"tg.mu = U[0]; lower_tail = tg.cdf(Z[0])\n",
"tg.mu = L[0]; upper_tail = tg.cdf(Z[0])\n",
"print(float(upper_tail - lower_tail)) # coverage near cutoff\n",
"print(L[0], U[0]) # if you want to double check with R\n",
"tg_cdf(Z[0], L[0], -4, 2), tg_cdf(Z[0], U[0], -4, 2)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.13"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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