mhjensen
460 lines
26 KiB
HTML
460 lines
26 KiB
HTML
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs001.html#___sec0" style="font-size: 80%;"> To do list</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs002.html#___sec1" style="font-size: 80%;"> Domains and probabilities</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs003.html#___sec2" style="font-size: 80%;"> Tossing the dice</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs004.html#___sec3" style="font-size: 80%;"> Stochastic variables</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs005.html#___sec4" style="font-size: 80%;"> Stochastic variables and the main concepts, the discrete case</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs006.html#___sec5" style="font-size: 80%;"> Stochastic variables and the main concepts, the continuous case</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs007.html#___sec6" style="font-size: 80%;"> The cumulative probability</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs008.html#___sec7" style="font-size: 80%;"> Properties of PDFs</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs009.html#___sec8" style="font-size: 80%;"> Important distributions, the uniform distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs010.html#___sec9" style="font-size: 80%;"> Gaussian distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs011.html#___sec10" style="font-size: 80%;"> Exponential distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs012.html#___sec11" style="font-size: 80%;"> Expectation values</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs013.html#___sec12" style="font-size: 80%;"> Stochastic variables and the main concepts, mean values</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs014.html#___sec13" style="font-size: 80%;"> Stochastic variables and the main concepts, central moments, the variance</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs015.html#___sec14" style="font-size: 80%;"> Probability Distribution Functions</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs016.html#___sec15" style="font-size: 80%;"> Probability Distribution Functions</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs017.html#___sec16" style="font-size: 80%;"> The three famous Probability Distribution Functions</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs018.html#___sec17" style="font-size: 80%;"> Probability Distribution Functions, the normal distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs019.html#___sec18" style="font-size: 80%;"> Probability Distribution Functions, the normal distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs020.html#___sec19" style="font-size: 80%;"> Probability Distribution Functions, the cumulative distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs021.html#___sec20" style="font-size: 80%;"> Probability Distribution Functions, other important distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs022.html#___sec21" style="font-size: 80%;"> Probability Distribution Functions, the binomial distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs023.html#___sec22" style="font-size: 80%;"> Probability Distribution Functions, Poisson's distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs024.html#___sec23" style="font-size: 80%;"> Probability Distribution Functions, Poisson's distribution</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs025.html#___sec24" style="font-size: 80%;"> Meet the covariance!</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs026.html#___sec25" style="font-size: 80%;"> Meet the covariance in matrix disguise</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs027.html#___sec26" style="font-size: 80%;"> Covariance</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs028.html#___sec27" style="font-size: 80%;"> Meet the covariance, uncorrelated events</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs029.html#___sec28" style="font-size: 80%;"> Numerical experiments and the covariance</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs030.html#___sec29" style="font-size: 80%;"> Numerical experiments and the covariance</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs031.html#___sec30" style="font-size: 80%;"> Numerical experiments and the covariance, actual situations</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs032.html#___sec31" style="font-size: 80%;"> Numerical experiments and the covariance, our observables</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs033.html#___sec32" style="font-size: 80%;"> Numerical experiments and the covariance, the sample variance</a></li>
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|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs034.html#___sec33" style="font-size: 80%;"> Numerical experiments and the covariance, central limit theorem</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs035.html#___sec34" style="font-size: 80%;"> Definition of Correlation Functions and Standard Deviation</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs036.html#___sec35" style="font-size: 80%;"> Definition of Correlation Functions and Standard Deviation</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs037.html#___sec36" style="font-size: 80%;"> Definition of Correlation Functions and Standard Deviation</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs038.html#___sec37" style="font-size: 80%;"> Definition of Correlation Functions and Standard Deviation</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs039.html#___sec38" style="font-size: 80%;"> Definition of Correlation Functions and Standard Deviation, sample variance</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs040.html#___sec39" style="font-size: 80%;"> Definition of Correlation Functions and Standard Deviation</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs041.html#___sec40" style="font-size: 80%;"> Code to compute the Covariance matrix and the Covariance</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs042.html#___sec41" style="font-size: 80%;"><b>Random Numbers</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs043.html#___sec42" style="font-size: 80%;"><b>Random Numbers, better name: pseudo random numbers</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs044.html#___sec43" style="font-size: 80%;"><b>Random number generator RNG</b></a></li>
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|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs045.html#___sec44" style="font-size: 80%;"><b>Random number generator RNG and periodic outputs</b></a></li>
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|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs046.html#___sec45" style="font-size: 80%;"><b>Random number generator RNG and its period</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs047.html#___sec46" style="font-size: 80%;"><b>Random number generator RNG, other examples</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs048.html#___sec47" style="font-size: 80%;"><b>Random number generator RNG, other examples</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs049.html#___sec48" style="font-size: 80%;"><b>Random number generator RNG, RAN0</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs050.html#___sec49" style="font-size: 80%;"><b>Random number generator RNG, RAN0</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs051.html#___sec50" style="font-size: 80%;"><b>Random number generator RNG, RAN0</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs052.html#___sec51" style="font-size: 80%;"><b>Random number generator RNG, RAN0</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs053.html#___sec52" style="font-size: 80%;"><b>Random number generator RNG, RAN0 code</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs054.html#___sec53" style="font-size: 80%;"> Properties of Selected Random Number Generators</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs055.html#___sec54" style="font-size: 80%;"> Properties of Selected Random Number Generators</a></li>
|
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs056.html#___sec55" style="font-size: 80%;"> Properties of Selected Random Number Generators</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs057.html#___sec56" style="font-size: 80%;"> Simple demonstration of RNGs using python</a></li>
|
|
<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs058.html#___sec57" style="font-size: 80%;"> Properties of Selected Random Number Generators</a></li>
|
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs059.html#___sec58" style="font-size: 80%;"> Autocorrelation function</a></li>
|
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs060.html#___sec59" style="font-size: 80%;"> Correlation function and which random number generators should I use</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs061.html#___sec60" style="font-size: 80%;"><b>Which RNG should I use?</b></a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs062.html#___sec61" style="font-size: 80%;"> How to use the Mersenne generator</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs063.html#___sec62" style="font-size: 80%;"> Why blocking?</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs064.html#___sec63" style="font-size: 80%;"> Why blocking?</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs065.html#___sec64" style="font-size: 80%;"> Code to demonstrate the calculation of the autocorrelation function</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs066.html#___sec65" style="font-size: 80%;"> What is blocking?</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs067.html#___sec66" style="font-size: 80%;"> What is blocking?</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs068.html#___sec67" style="font-size: 80%;"> What is blocking?</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs069.html#___sec68" style="font-size: 80%;"> Implementation</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs070.html#___sec69" style="font-size: 80%;"> Actual implementation with code, main function</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs071.html#___sec70" style="font-size: 80%;"> The Bootstrap method</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs072.html#___sec71" style="font-size: 80%;"> Bootstrapping</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs073.html#___sec72" style="font-size: 80%;"> Bootstrapping, recipe</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs074.html#___sec73" style="font-size: 80%;"> Bootstrapping, "code":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/Programs/Sampling/analysis.py"</a></li>
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<!-- navigation toc: --> <li><a href="._Statistics.do.txt-bs075.html#___sec74" style="font-size: 80%;"> Jackknife, "code":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/Programs/Sampling/analysis.py"</a></li>
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<a name="part0000"></a>
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<!-- ------------------- main content ---------------------- -->
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<div class="jumbotron">
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<center><h1>Data Analysis and Machine Learning: Elements of Probability Theory and Statistical Data Analysis</h1></center> <!-- document title -->
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<p>
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<!-- author(s): Morten Hjorth-Jensen -->
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<center>
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<b>Morten Hjorth-Jensen</b> [1, 2]
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</center>
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<p>
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<!-- institution(s) -->
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<center>[1] <b>Department of Physics, University of Oslo</b></center>
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<p>
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<center><h4>Sep 20, 2020</h4></center> <!-- date -->
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<br>
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<p>
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<p><a href="._Statistics.do.txt-bs001.html" class="btn btn-primary btn-lg">Read »</a></p>
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<li class="active"><a href="._Statistics.do.txt-bs000.html">1</a></li>
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<!-- copyright --> © 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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