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Morten Hjorth-Jensen
2024-11-25 08:12:27 +01:00
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doc/LectureNotes/_build/html/statistics.html
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@@ -257,6 +257,9 @@
<li class="toctree-l1"><a class="reference internal" href="week47.html">Week 47: From Decision Trees to Ensemble Methods, Random Forests and Boosting Methods</a></li>
<li class="toctree-l1"><a class="reference internal" href="exercisesweek47.html">Exercise week 47</a></li>
<li class="toctree-l1"><a class="reference internal" href="week48.html">Week 48: Gradient boosting and summary of course</a></li>
<li class="toctree-l1"><a class="reference internal" href="exercisesweek48.html">Exercises week 48</a></li>
</ul>
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
<ul class="nav bd-sidenav">
@@ -938,27 +941,27 @@ uncorrelated.</p>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>1.4472072453812375
[[19.67682459 13.19317931 14.24528007 8.94643492 16.06820064 19.95552222
14.31817138 9.32718019 17.21017449 24.16728032]
[13.19317931 8.8459385 9.55136503 5.99852479 10.77362108 13.3800442
9.60023816 6.25381195 11.53930691 16.20399985]
[14.24528007 9.55136503 10.31304636 6.476882 11.63277222 14.44704666
10.36581693 6.75252724 12.45951828 17.49620093]
[ 8.94643492 5.99852479 6.476882 4.06766333 7.30570681 9.07314999
6.51002339 4.24077626 7.82492649 10.98810428]
[16.06820064 10.77362108 11.63277222 7.30570681 13.12137895 16.29578663
11.69229565 7.61662544 14.05392092 19.73513091]
[19.95552222 13.3800442 14.44704666 9.07314999 16.29578663 20.23816725
14.52097038 9.45928804 17.4539351 24.50957964]
[14.31817138 9.60023816 10.36581693 6.51002339 11.69229565 14.52097038
10.41885751 6.78707908 12.52327207 17.58572679]
[ 9.32718019 6.25381195 6.75252724 4.24077626 7.61662544 9.45928804
6.78707908 4.42125659 8.15794224 11.45573958]
[17.21017449 11.53930691 12.45951828 7.82492649 14.05392092 17.4539351
12.52327207 8.15794224 15.05273905 21.13771505]
[24.16728032 16.20399985 17.49620093 10.98810428 19.73513091 24.50957964
17.58572679 11.45573958 21.13771505 29.68250468]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>1.6630365942333707
[[ 2.9789621 5.29596775 9.61069934 8.94881093 7.29305818 5.06734969
8.35612808 9.50699066 6.58518977 5.96699567]
[ 5.29596775 9.41511622 17.08580103 15.90910271 12.96552275 9.00868142
14.85543733 16.90142882 11.70708167 10.60806265]
[ 9.61069934 17.08580103 31.00594727 28.87056912 23.52879528 16.34823563
26.95846133 30.67136331 21.2450769 19.25066495]
[ 8.94881093 15.90910271 28.87056912 26.88225436 21.90836824 15.2223334
25.10183335 28.55902794 19.78192944 17.92487255]
[ 7.29305818 12.96552275 23.52879528 21.90836824 17.85477485 12.40582286
20.45736943 23.27489698 16.12178015 14.608325 ]
[ 5.06734969 9.00868142 16.34823563 15.2223334 12.40582286 8.61979174
14.21415299 16.17182246 11.20170657 10.15013036]
[ 8.35612808 14.85543733 26.95846133 25.10183335 20.45736943 14.21415299
23.43933023 26.66755363 18.4717654 16.73770203]
[ 9.50699066 16.90142882 30.67136331 28.55902794 23.27489698 16.17182246
26.66755363 30.34038983 21.01582211 19.04293178]
[ 6.58518977 11.70708167 21.2450769 19.78192944 16.12178015 11.20170657
18.4717654 21.01582211 14.55699091 13.19043259]
[ 5.96699567 10.60806265 19.25066495 17.92487255 14.608325 10.15013036
16.73770203 19.04293178 13.19043259 11.95216188]]
</pre></div>
</div>
</div>
@@ -1226,15 +1229,15 @@ more practically oriented methods like the blocking technique.</p>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.14555142287587747
3.471032560330219
-0.36388945426885777
0.8471097389658617 8.314152725401152 16.209550199940885
2.467818446250011 2.622158030566299 8.055384838739426
[[ 0.84710974 2.46781845 2.62215803]
[ 2.46781845 8.31415273 8.05538484]
[ 2.62215803 8.05538484 16.2095502 ]]
[21.82751857 0.10066746 3.44262663]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.02067725499485532
4.1599466577177715
-0.010435324202206745
1.0573975468113945 11.60638779409259 34.06300749480313
3.3628139153668575 3.9755893793908617 13.085147027563798
[[ 1.05739755 3.36281392 3.97558938]
[ 3.36281392 11.60638779 13.08514703]
[ 3.97558938 13.08514703 34.06300749]]
[40.7125057 0.07536391 5.93892323]
</pre></div>
</div>
</div>
@@ -1502,7 +1505,7 @@ these limiting values.</p>
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<img alt="_images/2d32a16373526bea9bc6f4e8fe926f0ed4c4e23d38a4de33454551f6599a83cf.png" src="_images/2d32a16373526bea9bc6f4e8fe926f0ed4c4e23d38a4de33454551f6599a83cf.png" />
<img alt="_images/46a1fad1ccb7c31a75875feb55a5327e9f0ae2b02295543e814d1b2fc23ab459.png" src="_images/46a1fad1ccb7c31a75875feb55a5327e9f0ae2b02295543e814d1b2fc23ab459.png" />
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<p>Since our random numbers, which are typically generated via a linear congruential algorithm,
@@ -1564,10 +1567,10 @@ assumption for approximating <span class="math notranslate nohighlight">\(\sigma
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.028592327979280928 1.0458514144974842
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.0065879787737229524 1.0071299074549438
</pre></div>
</div>
<img alt="_images/8dd8c0fbf4c42ac2d98c5a66035e455e4d40a3c6c7114c3d05daba0ad8fdf4ba.png" src="_images/8dd8c0fbf4c42ac2d98c5a66035e455e4d40a3c6c7114c3d05daba0ad8fdf4ba.png" />
<img alt="_images/467927f86cd8a5304cb2f39dbf480015e72d87541abf390f2a0eb8672b465f1e.png" src="_images/467927f86cd8a5304cb2f39dbf480015e72d87541abf390f2a0eb8672b465f1e.png" />
</div>
</div>
<p>As can be seen from the plot, the first point gives back the variance and a value of one.