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Correct answers about sigma in ch4 lin reg #220

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Correct answers about sigma in ch4 lin reg #220

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17 changes: 10 additions & 7 deletions Rethinking_2/End_of_chapter_problems/Chapter_4.ipynb
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Expand Up @@ -157,7 +157,10 @@
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"### 4M2.\n",
"Translate the model just above into a quap formula.\n",
Expand Down Expand Up @@ -188,7 +191,7 @@
"\n",
"$\\beta$ ~ $logN(0,1)$ #It seems perfectly sensible that the amount an average student's height changes per year should only be positive. Additionally, I have no idea what the growth rate is so this enocodes ignorance about the rate of change of height per year\n",
"\n",
"$\\sigma$ ~ $Unif(0,50)$"
"$\\sigma$ ~ $Unif(0,0.5)$ #This is the standard deviation of height, at a given age and expected height. This cannot conceivably be more than 1 metre. Half is a more sensible upper bound."
]
},
{
Expand All @@ -215,7 +218,9 @@
"more than 64cm. How does this lead you to revise your priors?\n",
"\n",
"#### Answer \n",
"This would cause me to use an even larger range of plausable values in my prior for $\\sigma$. Given my assumption for the students ages, increasing the range seems to be not sensible for the data at hand.\n",
"A maximum variance ($\\sigma^2$) can be enforced through an upper bound on the prior for $\\sigma$, set to $\\sqrt(64) = 8$ cm, or 0.08 m. Therefore the prior becomes\n",
"\n",
"$\\sigma$ ~ $Unif(0,0.08)$\n",
"\n",
"### 4M7.\n",
"\n",
Expand Down Expand Up @@ -1621,9 +1626,7 @@
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Expand Down Expand Up @@ -1714,7 +1717,7 @@
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