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93 changes: 50 additions & 43 deletions 01-technical-background.html
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<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">


<title>1&nbsp; Technical background – Biological and Biomedical Data Science (DSAN 6150)</title>
<title>Appendix A — Technical background – Biological and Biomedical Data Science (DSAN 6150)</title>
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<nav class="quarto-page-breadcrumbs" aria-label="breadcrumb"><ol class="breadcrumb"><li class="breadcrumb-item"><a href="./01-technical-background.html"><span class="chapter-number">1</span>&nbsp; <span class="chapter-title">Technical background</span></a></li></ol></nav>
<nav class="quarto-page-breadcrumbs" aria-label="breadcrumb"><ol class="breadcrumb"><li class="breadcrumb-item"><a href="./01-technical-background.html">Appendices</a></li><li class="breadcrumb-item"><a href="./01-technical-background.html"><span class="chapter-number">A</span>&nbsp; <span class="chapter-title">Technical background</span></a></li></ol></nav>
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<h2 id="toc-title">Table of contents</h2>

<ul>
<li><a href="#software" id="toc-software" class="nav-link active" data-scroll-target="#software"><span class="header-section-number">1.1</span> Software</a></li>
<li><a href="#probability-distributions" id="toc-probability-distributions" class="nav-link" data-scroll-target="#probability-distributions"><span class="header-section-number">1.2</span> Probability distributions</a>
<li><a href="#software" id="toc-software" class="nav-link active" data-scroll-target="#software"><span class="header-section-number">A.1</span> Software</a></li>
<li><a href="#probability-distributions" id="toc-probability-distributions" class="nav-link" data-scroll-target="#probability-distributions"><span class="header-section-number">A.2</span> Probability distributions</a>
<ul class="collapse">
<li><a href="#exponential-distribution" id="toc-exponential-distribution" class="nav-link" data-scroll-target="#exponential-distribution"><span class="header-section-number">1.2.1</span> Exponential distribution</a></li>
<li><a href="#weibull-distribution" id="toc-weibull-distribution" class="nav-link" data-scroll-target="#weibull-distribution"><span class="header-section-number">1.2.2</span> Weibull distribution</a></li>
<li><a href="#gamma-distribution" id="toc-gamma-distribution" class="nav-link" data-scroll-target="#gamma-distribution"><span class="header-section-number">1.2.3</span> Gamma distribution</a></li>
<li><a href="#poisson-distribution" id="toc-poisson-distribution" class="nav-link" data-scroll-target="#poisson-distribution"><span class="header-section-number">1.2.4</span> Poisson distribution</a></li>
<li><a href="#exponential-distribution" id="toc-exponential-distribution" class="nav-link" data-scroll-target="#exponential-distribution"><span class="header-section-number">A.2.1</span> Exponential distribution</a></li>
<li><a href="#weibull-distribution" id="toc-weibull-distribution" class="nav-link" data-scroll-target="#weibull-distribution"><span class="header-section-number">A.2.2</span> Weibull distribution</a></li>
<li><a href="#gamma-distribution" id="toc-gamma-distribution" class="nav-link" data-scroll-target="#gamma-distribution"><span class="header-section-number">A.2.3</span> Gamma distribution</a></li>
<li><a href="#poisson-distribution" id="toc-poisson-distribution" class="nav-link" data-scroll-target="#poisson-distribution"><span class="header-section-number">A.2.4</span> Poisson distribution</a></li>
</ul></li>
<li><a href="#statistical-methods" id="toc-statistical-methods" class="nav-link" data-scroll-target="#statistical-methods"><span class="header-section-number">1.3</span> Statistical methods</a>
<li><a href="#statistical-methods" id="toc-statistical-methods" class="nav-link" data-scroll-target="#statistical-methods"><span class="header-section-number">A.3</span> Statistical methods</a>
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<li><a href="#hypthesis-testing-and-errors" id="toc-hypthesis-testing-and-errors" class="nav-link" data-scroll-target="#hypthesis-testing-and-errors"><span class="header-section-number">1.3.1</span> Hypthesis testing and errors</a></li>
<li><a href="#hypthesis-testing-and-errors" id="toc-hypthesis-testing-and-errors" class="nav-link" data-scroll-target="#hypthesis-testing-and-errors"><span class="header-section-number">A.3.1</span> Hypthesis testing and errors</a></li>
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<h1 class="title"><span class="chapter-number">1</span>&nbsp; <span class="chapter-title">Technical background</span></h1>
<h1 class="title">Appendix A — Technical background</h1>
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<p>This course requires fairly involved knowledge of statistics and probability. We’ll be introducing several new concepts through the semester, but we will provide refreshers of some basic concepts as a starting point for this course.</p>
<section id="software" class="level2" data-number="1.1">
<h2 data-number="1.1" class="anchored" data-anchor-id="software"><span class="header-section-number">1.1</span> Software</h2>
<section id="software" class="level2" data-number="A.1">
<h2 data-number="A.1" class="anchored" data-anchor-id="software"><span class="header-section-number">A.1</span> Software</h2>
<p>In this class, we will use <i class="fa-brands fa-r-project" aria-label="r-project"></i> as our primary software. We expect you to be familiar with the <code>tidyverse</code> packages, and <code>ggplot2</code> for visualization.</p>
<p>In this class, we will make extensive use of the <code>survival</code> package, as well as various specialized packages</p>
</section>
<section id="probability-distributions" class="level2" data-number="1.2">
<h2 data-number="1.2" class="anchored" data-anchor-id="probability-distributions"><span class="header-section-number">1.2</span> Probability distributions</h2>
<section id="probability-distributions" class="level2" data-number="A.2">
<h2 data-number="A.2" class="anchored" data-anchor-id="probability-distributions"><span class="header-section-number">A.2</span> Probability distributions</h2>
<p>You are probably familiar with the normal (Gaussian) distribution and the binomial distribution. We’ll introduce some new distributions that will be used in the class</p>
<section id="exponential-distribution" class="level3" data-number="1.2.1">
<h3 data-number="1.2.1" class="anchored" data-anchor-id="exponential-distribution"><span class="header-section-number">1.2.1</span> Exponential distribution</h3>
<section id="exponential-distribution" class="level3" data-number="A.2.1">
<h3 data-number="A.2.1" class="anchored" data-anchor-id="exponential-distribution"><span class="header-section-number">A.2.1</span> Exponential distribution</h3>
<p>The exponential distribution has one parameter, usually denoted by <span class="math inline">\(\lambda &gt; 0\)</span> , which is also the mean of the distribution. If <span class="math inline">\(X\sim Exp(\lambda)\)</span>, then</p>
<p><span class="math display">\[
P(X &gt; x) = e^{-\lambda x}\quad \text{for } x &gt; 0
\]</span></p>
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<section id="weibull-distribution" class="level3" data-number="1.2.2">
<h3 data-number="1.2.2" class="anchored" data-anchor-id="weibull-distribution"><span class="header-section-number">1.2.2</span> Weibull distribution</h3>
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<h3 data-number="A.2.2" class="anchored" data-anchor-id="weibull-distribution"><span class="header-section-number">A.2.2</span> Weibull distribution</h3>
<p>The Weibull distribution is a generalization of the Exponential distribution. It is a two-parameter distribution, with the parameters called shape (<span class="math inline">\(\alpha\)</span>) and scale ( <span class="math inline">\(\beta\)</span> ). For this distribution,</p>
<p><span class="math display">\[
P(X &gt; x ) = e^{-(x/\beta)^\alpha}
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<noscript>Please enable JavaScript to experience the dynamic code cell content on this page.</noscript>
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<section id="gamma-distribution" class="level3" data-number="1.2.3">
<h3 data-number="1.2.3" class="anchored" data-anchor-id="gamma-distribution"><span class="header-section-number">1.2.3</span> Gamma distribution</h3>
<section id="gamma-distribution" class="level3" data-number="A.2.3">
<h3 data-number="A.2.3" class="anchored" data-anchor-id="gamma-distribution"><span class="header-section-number">A.2.3</span> Gamma distribution</h3>
</section>
<section id="poisson-distribution" class="level3" data-number="1.2.4">
<h3 data-number="1.2.4" class="anchored" data-anchor-id="poisson-distribution"><span class="header-section-number">1.2.4</span> Poisson distribution</h3>
<section id="poisson-distribution" class="level3" data-number="A.2.4">
<h3 data-number="A.2.4" class="anchored" data-anchor-id="poisson-distribution"><span class="header-section-number">A.2.4</span> Poisson distribution</h3>
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</section>
<section id="statistical-methods" class="level2" data-number="1.3">
<h2 data-number="1.3" class="anchored" data-anchor-id="statistical-methods"><span class="header-section-number">1.3</span> Statistical methods</h2>
<section id="hypthesis-testing-and-errors" class="level3" data-number="1.3.1">
<h3 data-number="1.3.1" class="anchored" data-anchor-id="hypthesis-testing-and-errors"><span class="header-section-number">1.3.1</span> Hypthesis testing and errors</h3>
<section id="statistical-methods" class="level2" data-number="A.3">
<h2 data-number="A.3" class="anchored" data-anchor-id="statistical-methods"><span class="header-section-number">A.3</span> Statistical methods</h2>
<section id="hypthesis-testing-and-errors" class="level3" data-number="A.3.1">
<h3 data-number="A.3.1" class="anchored" data-anchor-id="hypthesis-testing-and-errors"><span class="header-section-number">A.3.1</span> Hypthesis testing and errors</h3>


</section>
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