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updating typos

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This commit is contained in:
Morten Hjorth-Jensen
2023-09-19 14:46:00 +02:00
parent c38c1c3bbb
commit 33123d4bf2
13 changed files with 549 additions and 1408 deletions
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doc/LectureNotes/exercisesweek38.ipynb
+15 -15
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@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
"id": "d8f7704f",
"id": "ce05d309",
"metadata": {
"editable": true
},
@@ -14,7 +14,7 @@
},
{
"cell_type": "markdown",
"id": "9e388b87",
"id": "5b7c1442",
"metadata": {
"editable": true
},
@@ -27,7 +27,7 @@
},
{
"cell_type": "markdown",
"id": "80d7df2a",
"id": "02e09b06",
"metadata": {
"editable": true
},
@@ -45,7 +45,7 @@
},
{
"cell_type": "markdown",
"id": "80e18e80",
"id": "babb7346",
"metadata": {
"editable": true
},
@@ -57,7 +57,7 @@
},
{
"cell_type": "markdown",
"id": "3a74059f",
"id": "a5ee908c",
"metadata": {
"editable": true
},
@@ -76,7 +76,7 @@
},
{
"cell_type": "markdown",
"id": "1f92f219",
"id": "afa3df2c",
"metadata": {
"editable": true
},
@@ -88,7 +88,7 @@
},
{
"cell_type": "markdown",
"id": "416cd63a",
"id": "9665df80",
"metadata": {
"editable": true
},
@@ -102,19 +102,19 @@
},
{
"cell_type": "markdown",
"id": "d65d4905",
"id": "25391aba",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathrm{Bias}[y]+\\mathrm{var}[\\tilde{y}]+\\sigma^2,\n",
"\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathrm{Bias}[\\tilde{y}]+\\mathrm{var}[\\tilde{y}]+\\sigma^2,\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "d102dec2",
"id": "b6e8652c",
"metadata": {
"editable": true
},
@@ -124,19 +124,19 @@
},
{
"cell_type": "markdown",
"id": "869dc9d9",
"id": "77755270",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\mathrm{Bias}[y]=\\mathbb{E}\\left[\\left(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]\\right)^2\\right],\n",
"\\mathrm{Bias}[\\tilde{y}]=\\mathbb{E}\\left[\\left(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]\\right)^2\\right],\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "fee09cce",
"id": "fa94db90",
"metadata": {
"editable": true
},
@@ -146,7 +146,7 @@
},
{
"cell_type": "markdown",
"id": "b6fb6522",
"id": "4ecda624",
"metadata": {
"editable": true
},
@@ -158,7 +158,7 @@
},
{
"cell_type": "markdown",
"id": "6fa010b9",
"id": "2dcb3e9a",
"metadata": {
"editable": true
},
doc/Projects/2023/Project1/html/._Project1-bs000.html
+2 -2
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@@ -489,12 +489,12 @@ term which measures the deviation from the true data and the mean value of the m
That is, show that
</p>
$$
\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathrm{Bias}[y]+\mathrm{var}[\tilde{y}]+\sigma^2,
\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathrm{Bias}[\tilde{y}]+\mathrm{var}[\tilde{y}]+\sigma^2,
$$
<p>with </p>
$$
\mathrm{Bias}[y]=\mathbb{E}\left[\left(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right],
\mathrm{Bias}[\tilde{y}]=\mathbb{E}\left[\left(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right],
$$
<p>and </p>
doc/Projects/2023/Project1/html/Project1-bs.html
+2 -2
View File
@@ -489,12 +489,12 @@ term which measures the deviation from the true data and the mean value of the m
That is, show that
</p>
$$
\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathrm{Bias}[y]+\mathrm{var}[\tilde{y}]+\sigma^2,
\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathrm{Bias}[\tilde{y}]+\mathrm{var}[\tilde{y}]+\sigma^2,
$$
<p>with </p>
$$
\mathrm{Bias}[y]=\mathbb{E}\left[\left(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right],
\mathrm{Bias}[\tilde{y}]=\mathbb{E}\left[\left(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right],
$$
<p>and </p>
doc/Projects/2023/Project1/html/Project1.html
+2 -2
View File
@@ -525,12 +525,12 @@ term which measures the deviation from the true data and the mean value of the m
That is, show that
</p>
$$
\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathrm{Bias}[y]+\mathrm{var}[\tilde{y}]+\sigma^2,
\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathrm{Bias}[\tilde{y}]+\mathrm{var}[\tilde{y}]+\sigma^2,
$$
<p>with </p>
$$
\mathrm{Bias}[y]=\mathbb{E}\left[\left(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right],
\mathrm{Bias}[\tilde{y}]=\mathbb{E}\left[\left(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right],
$$
<p>and </p>
doc/Projects/2023/Project1/ipynb/Project1.ipynb
+52 -52
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@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
"id": "ee871b85",
"id": "f8900c95",
"metadata": {
"editable": true
},
@@ -14,7 +14,7 @@
},
{
"cell_type": "markdown",
"id": "de647a13",
"id": "e1595afd",
"metadata": {
"editable": true
},
@@ -27,7 +27,7 @@
},
{
"cell_type": "markdown",
"id": "f0094ea8",
"id": "8d3e72b9",
"metadata": {
"editable": true
},
@@ -63,7 +63,7 @@
},
{
"cell_type": "markdown",
"id": "9d47e07f",
"id": "8293cb06",
"metadata": {
"editable": true
},
@@ -85,7 +85,7 @@
},
{
"cell_type": "markdown",
"id": "13b3c63c",
"id": "e49db9ae",
"metadata": {
"editable": true
},
@@ -100,7 +100,7 @@
},
{
"cell_type": "markdown",
"id": "588eb391",
"id": "7108aee4",
"metadata": {
"editable": true
},
@@ -133,7 +133,7 @@
{
"cell_type": "code",
"execution_count": 1,
"id": "2b565e88",
"id": "2f54fcda",
"metadata": {
"collapsed": false,
"editable": true
@@ -185,7 +185,7 @@
},
{
"cell_type": "markdown",
"id": "5a80d8fa",
"id": "91ce0ca4",
"metadata": {
"editable": true
},
@@ -207,7 +207,7 @@
},
{
"cell_type": "markdown",
"id": "2b8a75d3",
"id": "3bf84fef",
"metadata": {
"editable": true
},
@@ -220,7 +220,7 @@
},
{
"cell_type": "markdown",
"id": "de8e68ca",
"id": "568afb54",
"metadata": {
"editable": true
},
@@ -232,7 +232,7 @@
},
{
"cell_type": "markdown",
"id": "70a2795e",
"id": "a44eb2fc",
"metadata": {
"editable": true
},
@@ -244,7 +244,7 @@
},
{
"cell_type": "markdown",
"id": "07d74c94",
"id": "5603e809",
"metadata": {
"editable": true
},
@@ -254,7 +254,7 @@
},
{
"cell_type": "markdown",
"id": "cb7a1688",
"id": "7d6f55ea",
"metadata": {
"editable": true
},
@@ -266,7 +266,7 @@
},
{
"cell_type": "markdown",
"id": "0c273378",
"id": "5407a481",
"metadata": {
"editable": true
},
@@ -295,7 +295,7 @@
},
{
"cell_type": "markdown",
"id": "b6aa07e9",
"id": "aa8fbc15",
"metadata": {
"editable": true
},
@@ -313,7 +313,7 @@
},
{
"cell_type": "markdown",
"id": "4c297a7f",
"id": "5d805d8c",
"metadata": {
"editable": true
},
@@ -330,7 +330,7 @@
},
{
"cell_type": "markdown",
"id": "9b65abbd",
"id": "2dde585d",
"metadata": {
"editable": true
},
@@ -346,7 +346,7 @@
},
{
"cell_type": "markdown",
"id": "9f2c97bc",
"id": "ed0dd5d4",
"metadata": {
"editable": true
},
@@ -358,7 +358,7 @@
},
{
"cell_type": "markdown",
"id": "1390caea",
"id": "e0429f21",
"metadata": {
"editable": true
},
@@ -369,7 +369,7 @@
},
{
"cell_type": "markdown",
"id": "757a87d4",
"id": "3daec21b",
"metadata": {
"editable": true
},
@@ -381,7 +381,7 @@
},
{
"cell_type": "markdown",
"id": "cf182a2a",
"id": "2d2524c6",
"metadata": {
"editable": true
},
@@ -393,7 +393,7 @@
},
{
"cell_type": "markdown",
"id": "c7f15f3d",
"id": "ff089285",
"metadata": {
"editable": true
},
@@ -405,7 +405,7 @@
},
{
"cell_type": "markdown",
"id": "70c8c4e9",
"id": "3d168dd6",
"metadata": {
"editable": true
},
@@ -416,7 +416,7 @@
},
{
"cell_type": "markdown",
"id": "3879a5b4",
"id": "f8be4ad2",
"metadata": {
"editable": true
},
@@ -428,7 +428,7 @@
},
{
"cell_type": "markdown",
"id": "17191387",
"id": "ec6b847d",
"metadata": {
"editable": true
},
@@ -441,7 +441,7 @@
},
{
"cell_type": "markdown",
"id": "a7e3a698",
"id": "1a9533ed",
"metadata": {
"editable": true
},
@@ -453,7 +453,7 @@
},
{
"cell_type": "markdown",
"id": "93fc4a12",
"id": "b9da1087",
"metadata": {
"editable": true
},
@@ -463,7 +463,7 @@
},
{
"cell_type": "markdown",
"id": "85d336ad",
"id": "4f84b574",
"metadata": {
"editable": true
},
@@ -475,7 +475,7 @@
},
{
"cell_type": "markdown",
"id": "869ed780",
"id": "3077c7a2",
"metadata": {
"editable": true
},
@@ -486,7 +486,7 @@
},
{
"cell_type": "markdown",
"id": "88502fe8",
"id": "f82bcde0",
"metadata": {
"editable": true
},
@@ -519,7 +519,7 @@
},
{
"cell_type": "markdown",
"id": "db4583da",
"id": "3ff30b63",
"metadata": {
"editable": true
},
@@ -531,7 +531,7 @@
},
{
"cell_type": "markdown",
"id": "da3a0dfc",
"id": "61c75d7b",
"metadata": {
"editable": true
},
@@ -550,7 +550,7 @@
},
{
"cell_type": "markdown",
"id": "07b53a45",
"id": "829664c0",
"metadata": {
"editable": true
},
@@ -562,7 +562,7 @@
},
{
"cell_type": "markdown",
"id": "1d8bc8d4",
"id": "c3462fff",
"metadata": {
"editable": true
},
@@ -576,19 +576,19 @@
},
{
"cell_type": "markdown",
"id": "7f06bfd3",
"id": "10d717b5",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathrm{Bias}[y]+\\mathrm{var}[\\tilde{y}]+\\sigma^2,\n",
"\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathrm{Bias}[\\tilde{y}]+\\mathrm{var}[\\tilde{y}]+\\sigma^2,\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "5624047e",
"id": "5858f4a4",
"metadata": {
"editable": true
},
@@ -598,19 +598,19 @@
},
{
"cell_type": "markdown",
"id": "1b26ef35",
"id": "c3b75de4",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\mathrm{Bias}[y]=\\mathbb{E}\\left[\\left(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]\\right)^2\\right],\n",
"\\mathrm{Bias}[\\tilde{y}]=\\mathbb{E}\\left[\\left(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]\\right)^2\\right],\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "6319fcec",
"id": "b8cc130e",
"metadata": {
"editable": true
},
@@ -620,7 +620,7 @@
},
{
"cell_type": "markdown",
"id": "2253bb98",
"id": "1ae109c5",
"metadata": {
"editable": true
},
@@ -632,7 +632,7 @@
},
{
"cell_type": "markdown",
"id": "d08baf03",
"id": "6bd24bc3",
"metadata": {
"editable": true
},
@@ -651,7 +651,7 @@
},
{
"cell_type": "markdown",
"id": "d06c2f80",
"id": "4b962286",
"metadata": {
"editable": true
},
@@ -676,7 +676,7 @@
},
{
"cell_type": "markdown",
"id": "2a957aee",
"id": "8a4f9316",
"metadata": {
"editable": true
},
@@ -704,7 +704,7 @@
{
"cell_type": "code",
"execution_count": 2,
"id": "1c0d6323",
"id": "96232c73",
"metadata": {
"collapsed": false,
"editable": true
@@ -716,7 +716,7 @@
},
{
"cell_type": "markdown",
"id": "183f2666",
"id": "67545b6f",
"metadata": {
"editable": true
},
@@ -728,7 +728,7 @@
{
"cell_type": "code",
"execution_count": 3,
"id": "3ccf3ab9",
"id": "bad8a459",
"metadata": {
"collapsed": false,
"editable": true
@@ -754,7 +754,7 @@
},
{
"cell_type": "markdown",
"id": "cf6cdda9",
"id": "1e6a8f3f",
"metadata": {
"editable": true
},
@@ -779,7 +779,7 @@
},
{
"cell_type": "markdown",
"id": "f28a3bdf",
"id": "3e942cfc",
"metadata": {
"editable": true
},
@@ -793,7 +793,7 @@
},
{
"cell_type": "markdown",
"id": "ed920879",
"id": "5451b425",
"metadata": {
"editable": true
},
@@ -823,7 +823,7 @@
},
{
"cell_type": "markdown",
"id": "f2bef519",
"id": "b0aabc96",
"metadata": {
"editable": true
},
@@ -845,7 +845,7 @@
},
{
"cell_type": "markdown",
"id": "e1891d3f",
"id": "a6299b8f",
"metadata": {
"editable": true
},
doc/Projects/2023/Project1/ipynb/ipynb-Project1-src.tar.gz
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doc/Projects/2023/Project1/pdf/Project1.p.tex
+2 -2
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@@ -451,11 +451,11 @@ Show that you can rewrite this in terms of a term which contains the variance o
term which measures the deviation from the true data and the mean value of the model (the bias term) and finally the variance of the noise.
That is, show that
\[
\mathbb{E}\left[(\bm{y}-\bm{\tilde{y}})^2\right]=\mathrm{Bias}[y]+\mathrm{var}[\tilde{y}]+\sigma^2,
\mathbb{E}\left[(\bm{y}-\bm{\tilde{y}})^2\right]=\mathrm{Bias}[\tilde{y}]+\mathrm{var}[\tilde{y}]+\sigma^2,
\]
with
\[
\mathrm{Bias}[y]=\mathbb{E}\left[\left(\bm{y}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right],
\mathrm{Bias}[\tilde{y}]=\mathbb{E}\left[\left(\bm{y}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right],
\]
and
\[
doc/Projects/2023/Project1/pdf/Project1.pdf
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doc/Projects/2023/Project1/pdf/Project1.tex
+2 -2
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@@ -421,11 +421,11 @@ Show that you can rewrite this in terms of a term which contains the variance o
term which measures the deviation from the true data and the mean value of the model (the bias term) and finally the variance of the noise.
That is, show that
\[
\mathbb{E}\left[(\bm{y}-\bm{\tilde{y}})^2\right]=\mathrm{Bias}[y]+\mathrm{var}[\tilde{y}]+\sigma^2,
\mathbb{E}\left[(\bm{y}-\bm{\tilde{y}})^2\right]=\mathrm{Bias}[\tilde{y}]+\mathrm{var}[\tilde{y}]+\sigma^2,
\]
with
\[
\mathrm{Bias}[y]=\mathbb{E}\left[\left(\bm{y}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right],
\mathrm{Bias}[\tilde{y}]=\mathbb{E}\left[\left(\bm{y}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right],
\]
and
\[
doc/pub/week35/ipynb/week35.ipynb
+464 -1323
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doc/pub/week38/ipynb/week38.ipynb
+4 -4
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doc/src/Projects/2023/Project1/Project1.do.txt
+2 -2
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@@ -324,13 +324,13 @@ term which measures the deviation from the true data and the mean value of the m
That is, show that
!bt
\[
\mathbb{E}\left[(\bm{y}-\bm{\tilde{y}})^2\right]=\mathrm{Bias}[y]+\mathrm{var}[\tilde{y}]+\sigma^2,
\mathbb{E}\left[(\bm{y}-\bm{\tilde{y}})^2\right]=\mathrm{Bias}[\tilde{y}]+\mathrm{var}[\tilde{y}]+\sigma^2,
\]
!et
with
!bt
\[
\mathrm{Bias}[y]=\mathbb{E}\left[\left(\bm{y}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right],
\mathrm{Bias}[\tilde{y}]=\mathbb{E}\left[\left(\bm{y}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right],
\]
!et
and
doc/src/week38/exercisesweek38.do.txt
+2 -2
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@@ -42,13 +42,13 @@ term which measures the deviation from the true data and the mean value of the m
That is, show that
!bt
\[
\mathbb{E}\left[(\bm{y}-\bm{\tilde{y}})^2\right]=\mathrm{Bias}[y]+\mathrm{var}[\tilde{y}]+\sigma^2,
\mathbb{E}\left[(\bm{y}-\bm{\tilde{y}})^2\right]=\mathrm{Bias}[\tilde{y}]+\mathrm{var}[\tilde{y}]+\sigma^2,
\]
!et
with
!bt
\[
\mathrm{Bias}[y]=\mathbb{E}\left[\left(\bm{y}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right],
\mathrm{Bias}[\tilde{y}]=\mathbb{E}\left[\left(\bm{y}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right],
\]
!et
and