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<h2 class="hd hd-2 unit-title">10.1 Bayesian methods for discrete variables</h2>
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<h3 class="hd hd-2">Video</h3>
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<h2 class="hd hd-2 unit-title">10.2 Bayesian predictive probability</h2>
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<h3 class="hd hd-2">Video</h3>
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<h2 class="hd hd-2 unit-title">10.3 Bayesian methods for continuous variables</h2>
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<h2 class="hd hd-2 unit-title">Chapter 10 Homework</h2>
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<p style="margin:0in;text-align:justify;text-justify:inter-ideograph"><b style="mso-bidi-font-weight:normal"><span style="mso-bidi-font-size:16.0pt;
font-family:"Times New Roman",serif;mso-fareast-font-family:DengXian;
mso-fareast-theme-font:minor-fareast;mso-font-kerning:12.0pt">Problem:</span></b><span style="mso-bidi-font-size:16.0pt;font-family:"Times New Roman",serif;
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
mso-font-kerning:12.0pt"> The presence of cracks in a shield tunnel can be modeled through a Poisson process with a mean rate of <i>v</i> as follows<o:p></o:p></span></p>
<p style="margin:0in;text-align:justify;text-justify:inter-ideograph"><img height="63" width="124" src="/assets/courseware/v1/428397ff61c496be3bdebe32f5b7e4bd/asset-v1:ISSMGE+TC304-105+2021+type@asset+block/chapter-10-equation.JPG" alt="" /></p>
<p style="margin:0in;text-align:justify;text-justify:inter-ideograph"><span style="mso-bidi-font-size:16.0pt;font-family:"Times New Roman",serif;
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
mso-font-kerning:12.0pt">where <i>x</i> is the number of the cracks and <i>t</i> is the length of the shield tunnel. Based on past experiences, <i>v</i> is uniformly distributed between 1 crack/km to 10 cracks/km. Suppose a field inspection during the first 200 m of a shield tunnel reveals no cracks. What is the posterior distribution of <i>v</i>? <o:p></o:p></span></p>
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