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Chapter3_MCMC/IntroMCMC.ipynb

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"In our case, $A$ represents $L_x = 1$ and $X$ is the evidence we have: we observe that $x = 175$. For a particular sample set of parameters for our posterior distribution, $( \\mu_0, \\sigma_0, \\mu_1, \\sigma_1, p)$, we are interested in asking \"Is the probability that $x$ is in cluster 1 *greater* than the probability it is in cluster 0?\", where the probability is dependent on the chosen parameters.\n",
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"\n",
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"\\begin{align}\n",
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"& P(L_x = 1| x = 175 ) \\gt P( (L_x = 0| x = 175 ) \\\\\\\\[5pt]\n",
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"& P(L_x = 1| x = 175 ) \\gt P(L_x = 0| x = 175 ) \\\\\\\\[5pt]\n",
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"& \\frac{ P( x=175 | L_x = 1 )P( L_x = 1 ) }{P(x = 175) } \\gt \\frac{ P( x=175 | L_x = 0 )P( L_x = 0 )}{P(x = 175) }\n",
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"\\end{align}\n",
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"\n",

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