and
$$ -\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2. +\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\boldsymbol{y}}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2. $$ -The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37. +
The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 38. Explain what the terms mean and discuss their interpretations.
diff --git a/doc/Projects/2023/Project1/html/Project1-bs.html b/doc/Projects/2023/Project1/html/Project1-bs.html index 24af4358b..905d9da71 100644 --- a/doc/Projects/2023/Project1/html/Project1-bs.html +++ b/doc/Projects/2023/Project1/html/Project1-bs.html @@ -499,10 +499,10 @@ $$and
$$ -\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2. +\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\boldsymbol{y}}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2. $$ -The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37. +
The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 38. Explain what the terms mean and discuss their interpretations.
diff --git a/doc/Projects/2023/Project1/html/Project1.html b/doc/Projects/2023/Project1/html/Project1.html index 41ec77b79..9e087eae6 100644 --- a/doc/Projects/2023/Project1/html/Project1.html +++ b/doc/Projects/2023/Project1/html/Project1.html @@ -535,10 +535,10 @@ $$and
$$ -\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2. +\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\boldsymbol{y}}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2. $$ -The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37. +
The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 38. Explain what the terms mean and discuss their interpretations.
diff --git a/doc/Projects/2023/Project1/ipynb/Project1.ipynb b/doc/Projects/2023/Project1/ipynb/Project1.ipynb index 467bad587..e28db853b 100644 --- a/doc/Projects/2023/Project1/ipynb/Project1.ipynb +++ b/doc/Projects/2023/Project1/ipynb/Project1.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "7424fea1", + "id": "ee871b85", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "c9ca1d90", + "id": "de647a13", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "3e4164b6", + "id": "f0094ea8", "metadata": { "editable": true }, @@ -63,7 +63,7 @@ }, { "cell_type": "markdown", - "id": "dd4dcdf5", + "id": "9d47e07f", "metadata": { "editable": true }, @@ -85,7 +85,7 @@ }, { "cell_type": "markdown", - "id": "71ddc478", + "id": "13b3c63c", "metadata": { "editable": true }, @@ -100,7 +100,7 @@ }, { "cell_type": "markdown", - "id": "d4184afb", + "id": "588eb391", "metadata": { "editable": true }, @@ -133,7 +133,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "62880fe6", + "id": "2b565e88", "metadata": { "collapsed": false, "editable": true @@ -185,7 +185,7 @@ }, { "cell_type": "markdown", - "id": "6f7e7c97", + "id": "5a80d8fa", "metadata": { "editable": true }, @@ -207,7 +207,7 @@ }, { "cell_type": "markdown", - "id": "7377112f", + "id": "2b8a75d3", "metadata": { "editable": true }, @@ -220,7 +220,7 @@ }, { "cell_type": "markdown", - "id": "72f83fe7", + "id": "de8e68ca", "metadata": { "editable": true }, @@ -232,7 +232,7 @@ }, { "cell_type": "markdown", - "id": "7a3578ff", + "id": "70a2795e", "metadata": { "editable": true }, @@ -244,7 +244,7 @@ }, { "cell_type": "markdown", - "id": "e0aef819", + "id": "07d74c94", "metadata": { "editable": true }, @@ -254,7 +254,7 @@ }, { "cell_type": "markdown", - "id": "c7f751af", + "id": "cb7a1688", "metadata": { "editable": true }, @@ -266,7 +266,7 @@ }, { "cell_type": "markdown", - "id": "c026a4bd", + "id": "0c273378", "metadata": { "editable": true }, @@ -295,7 +295,7 @@ }, { "cell_type": "markdown", - "id": "2635bcbd", + "id": "b6aa07e9", "metadata": { "editable": true }, @@ -313,7 +313,7 @@ }, { "cell_type": "markdown", - "id": "92892df2", + "id": "4c297a7f", "metadata": { "editable": true }, @@ -330,7 +330,7 @@ }, { "cell_type": "markdown", - "id": "35987aab", + "id": "9b65abbd", "metadata": { "editable": true }, @@ -346,7 +346,7 @@ }, { "cell_type": "markdown", - "id": "e61048c2", + "id": "9f2c97bc", "metadata": { "editable": true }, @@ -358,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "5ef456d4", + "id": "1390caea", "metadata": { "editable": true }, @@ -369,7 +369,7 @@ }, { "cell_type": "markdown", - "id": "52e6fbad", + "id": "757a87d4", "metadata": { "editable": true }, @@ -381,7 +381,7 @@ }, { "cell_type": "markdown", - "id": "db6028a0", + "id": "cf182a2a", "metadata": { "editable": true }, @@ -393,7 +393,7 @@ }, { "cell_type": "markdown", - "id": "9477ad5e", + "id": "c7f15f3d", "metadata": { "editable": true }, @@ -405,7 +405,7 @@ }, { "cell_type": "markdown", - "id": "8c2aeccd", + "id": "70c8c4e9", "metadata": { "editable": true }, @@ -416,7 +416,7 @@ }, { "cell_type": "markdown", - "id": "6a774b74", + "id": "3879a5b4", "metadata": { "editable": true }, @@ -428,7 +428,7 @@ }, { "cell_type": "markdown", - "id": "98fde9b7", + "id": "17191387", "metadata": { "editable": true }, @@ -441,7 +441,7 @@ }, { "cell_type": "markdown", - "id": "87a4d11d", + "id": "a7e3a698", "metadata": { "editable": true }, @@ -453,7 +453,7 @@ }, { "cell_type": "markdown", - "id": "b4844f1e", + "id": "93fc4a12", "metadata": { "editable": true }, @@ -463,7 +463,7 @@ }, { "cell_type": "markdown", - "id": "f7662ade", + "id": "85d336ad", "metadata": { "editable": true }, @@ -475,7 +475,7 @@ }, { "cell_type": "markdown", - "id": "1d61362e", + "id": "869ed780", "metadata": { "editable": true }, @@ -486,7 +486,7 @@ }, { "cell_type": "markdown", - "id": "74bbb4ab", + "id": "88502fe8", "metadata": { "editable": true }, @@ -519,7 +519,7 @@ }, { "cell_type": "markdown", - "id": "ac939724", + "id": "db4583da", "metadata": { "editable": true }, @@ -531,7 +531,7 @@ }, { "cell_type": "markdown", - "id": "4066d012", + "id": "da3a0dfc", "metadata": { "editable": true }, @@ -550,7 +550,7 @@ }, { "cell_type": "markdown", - "id": "7e5c5ef4", + "id": "07b53a45", "metadata": { "editable": true }, @@ -562,7 +562,7 @@ }, { "cell_type": "markdown", - "id": "690337b9", + "id": "1d8bc8d4", "metadata": { "editable": true }, @@ -576,7 +576,7 @@ }, { "cell_type": "markdown", - "id": "92dabf3c", + "id": "7f06bfd3", "metadata": { "editable": true }, @@ -588,7 +588,7 @@ }, { "cell_type": "markdown", - "id": "7da90966", + "id": "5624047e", "metadata": { "editable": true }, @@ -598,7 +598,7 @@ }, { "cell_type": "markdown", - "id": "33a81d54", + "id": "1b26ef35", "metadata": { "editable": true }, @@ -610,7 +610,7 @@ }, { "cell_type": "markdown", - "id": "abb9bd28", + "id": "6319fcec", "metadata": { "editable": true }, @@ -620,24 +620,24 @@ }, { "cell_type": "markdown", - "id": "5b4668fd", + "id": "2253bb98", "metadata": { "editable": true }, "source": [ "$$\n", - "\\mathrm{var}[\\tilde{y}]=\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2.\n", + "\\mathrm{var}[\\tilde{y}]=\\mathbb{E}\\left[\\left(\\tilde{\\boldsymbol{y}}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]\\right)^2\\right]=\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2.\n", "$$" ] }, { "cell_type": "markdown", - "id": "b453f8fc", + "id": "d08baf03", "metadata": { "editable": true }, "source": [ - "The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37.\n", + "The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 38.\n", "Explain what the terms mean and discuss their interpretations.\n", "\n", "Perform then a bias-variance analysis of the Franke function by\n", @@ -651,7 +651,7 @@ }, { "cell_type": "markdown", - "id": "6fe323b0", + "id": "d06c2f80", "metadata": { "editable": true }, @@ -676,7 +676,7 @@ }, { "cell_type": "markdown", - "id": "5fd2f486", + "id": "2a957aee", "metadata": { "editable": true }, @@ -704,7 +704,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "e88e39ea", + "id": "1c0d6323", "metadata": { "collapsed": false, "editable": true @@ -716,7 +716,7 @@ }, { "cell_type": "markdown", - "id": "29817da1", + "id": "183f2666", "metadata": { "editable": true }, @@ -728,7 +728,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "560fc9f4", + "id": "3ccf3ab9", "metadata": { "collapsed": false, "editable": true @@ -754,7 +754,7 @@ }, { "cell_type": "markdown", - "id": "3fc05383", + "id": "cf6cdda9", "metadata": { "editable": true }, @@ -779,7 +779,7 @@ }, { "cell_type": "markdown", - "id": "bb21261e", + "id": "f28a3bdf", "metadata": { "editable": true }, @@ -793,7 +793,7 @@ }, { "cell_type": "markdown", - "id": "c5ab9dbf", + "id": "ed920879", "metadata": { "editable": true }, @@ -823,7 +823,7 @@ }, { "cell_type": "markdown", - "id": "7d0dbb14", + "id": "f2bef519", "metadata": { "editable": true }, @@ -845,7 +845,7 @@ }, { "cell_type": "markdown", - "id": "e301049d", + "id": "e1891d3f", "metadata": { "editable": true }, diff --git a/doc/Projects/2023/Project1/ipynb/ipynb-Project1-src.tar.gz b/doc/Projects/2023/Project1/ipynb/ipynb-Project1-src.tar.gz index c50634476..da81f8033 100644 Binary files a/doc/Projects/2023/Project1/ipynb/ipynb-Project1-src.tar.gz and b/doc/Projects/2023/Project1/ipynb/ipynb-Project1-src.tar.gz differ diff --git a/doc/Projects/2023/Project1/pdf/Project1.p.tex b/doc/Projects/2023/Project1/pdf/Project1.p.tex index b886c97c4..c87a4528d 100644 --- a/doc/Projects/2023/Project1/pdf/Project1.p.tex +++ b/doc/Projects/2023/Project1/pdf/Project1.p.tex @@ -459,9 +459,9 @@ with \] and \[ -\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2. +\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\bm{y}}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2. \] -The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37. +The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 38. Explain what the terms mean and discuss their interpretations. Perform then a bias-variance analysis of the Franke function by diff --git a/doc/Projects/2023/Project1/pdf/Project1.pdf b/doc/Projects/2023/Project1/pdf/Project1.pdf index 513a3164d..a3466707a 100644 Binary files a/doc/Projects/2023/Project1/pdf/Project1.pdf and b/doc/Projects/2023/Project1/pdf/Project1.pdf differ diff --git a/doc/Projects/2023/Project1/pdf/Project1.tex b/doc/Projects/2023/Project1/pdf/Project1.tex index 0381df84e..2db7584c0 100644 --- a/doc/Projects/2023/Project1/pdf/Project1.tex +++ b/doc/Projects/2023/Project1/pdf/Project1.tex @@ -429,9 +429,9 @@ with \] and \[ -\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2. +\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\bm{y}}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2. \] -The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37. +The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 38. Explain what the terms mean and discuss their interpretations. Perform then a bias-variance analysis of the Franke function by diff --git a/doc/src/Projects/2023/Project1/Project1.do.txt b/doc/src/Projects/2023/Project1/Project1.do.txt index 8e58048f9..a1053a8f2 100644 --- a/doc/src/Projects/2023/Project1/Project1.do.txt +++ b/doc/src/Projects/2023/Project1/Project1.do.txt @@ -336,10 +336,10 @@ with and !bt \[ -\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2. +\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\bm{y}}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2. \] !et -The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37. +The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 38. Explain what the terms mean and discuss their interpretations. Perform then a bias-variance analysis of the Franke function by