mhjensen
243 lines
12 KiB
HTML
243 lines
12 KiB
HTML
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<title>Data Analysis and Machine Learning: Introduction and Representing data</title>
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'sections': [('What is Machine Learning?', 2, None, '___sec0'),
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('Types of Machine Learning', 2, None, '___sec1'),
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('Different algorithms', 2, None, '___sec2'),
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('Representing data, more examples', 2, None, '___sec8'),
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('Case study from Hudson bay', 2, None, '___sec10'),
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('Hares and lynx in Hudson bay from 1900 to 1920',
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('Why now create a computer model for the hare and lynx '
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('The traditional (top-down) approach', 2, None, '___sec15'),
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('Basic dynamics of the population of hares',
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<a class="navbar-brand" href="How2ReadData-bs.html">Data Analysis and Machine Learning: Introduction and Representing data</a>
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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="._How2ReadData-bs001.html#___sec0" style="font-size: 80%;">What is Machine Learning?</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs002.html#___sec1" style="font-size: 80%;">Types of Machine Learning</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs003.html#___sec2" style="font-size: 80%;">Different algorithms</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs004.html#___sec3" style="font-size: 80%;">Software and needed installations</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs005.html#___sec4" style="font-size: 80%;">Python installers</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs006.html#___sec5" style="font-size: 80%;">Installing R, C++, cython or Julia</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs007.html#___sec6" style="font-size: 80%;">Installing R, C++, cython or Julia</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs008.html#___sec7" style="font-size: 80%;">Introduction to Jupyter notebook and available tools</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs009.html#___sec8" style="font-size: 80%;">Representing data, more examples</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs010.html#___sec9" style="font-size: 80%;">Predator-Prey model from ecology</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs011.html#___sec10" style="font-size: 80%;">Case study from Hudson bay</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs012.html#___sec11" style="font-size: 80%;">Hudson bay data</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs013.html#___sec12" style="font-size: 80%;">Plotting the data</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs014.html#___sec13" style="font-size: 80%;">Hares and lynx in Hudson bay from 1900 to 1920</a></li>
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<!-- navigation toc: --> <li><a href="#___sec14" style="font-size: 80%;">Why now create a computer model for the hare and lynx populations?</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs016.html#___sec15" style="font-size: 80%;">The traditional (top-down) approach</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs017.html#___sec16" style="font-size: 80%;">Basic mathematics notation</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs018.html#___sec17" style="font-size: 80%;">Basic dynamics of the population of hares</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs019.html#___sec18" style="font-size: 80%;">Basic dynamics of the population of lynx</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs020.html#___sec19" style="font-size: 80%;">Evolution equations</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs021.html#___sec20" style="font-size: 80%;">Adapt the model to the Hudson Bay case</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs022.html#___sec21" style="font-size: 80%;">The program</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs023.html#___sec22" style="font-size: 80%;">The plot</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs024.html#___sec23" style="font-size: 80%;">Linear regression in Python</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs025.html#___sec24" style="font-size: 80%;">Linear Least squares in R</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs026.html#___sec25" style="font-size: 80%;">Non-Linear Least squares in R</a></li>
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</ul>
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</li>
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<a name="part0015"></a>
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<h2 id="___sec14" class="anchor">Why now create a computer model for the hare and lynx populations? </h2>
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<div class="panel panel-default">
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<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
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We see from the plot that there are indeed fluctuations.
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We would like to create a mathematical model that explains these
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population fluctuations. Ecologists have predicted that in a simple
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predator-prey system that a rise in prey population is followed (with
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a lag) by a rise in the predator population. When the predator
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population is sufficiently high, then the prey population begins
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dropping. After the prey population falls, then the predator
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population falls, which allows the prey population to recover and
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complete one cycle of this interaction. Thus, we see that
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qualitatively oscillations occur. Can a mathematical model predict
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this? What causes cycles to slow or speed up? What affects the
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amplitude of the oscillation or do you expect to see the oscillations
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damp to a stable equilibrium? The models tend to ignore factors like
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climate and other complicating factors. How significant are these?
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<ul>
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<li> We see oscillations in the data</li>
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<li> What causes cycles to slow or speed up?</li>
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<li> What affects the amplitude of the oscillation or do you expect to see the oscillations damp to a stable equilibrium?</li>
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<li> With a model we can better <em>understand the data</em></li>
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<li> More important: we can understand the ecology dynamics of
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predator-pray populations</li>
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</ul>
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</div>
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<p>
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