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Chapter3_MCMC/Chapter3.ipynb

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"When I say MCMC intelligently searches, I really am saying MCMC will *hopefully* converge towards the areas of high posterior probability. MCMC does this by exploring nearby positions and moving into areas with higher probability. Again, perhaps \"converge\" is not an accurate term to describe MCMC's progression. Converging usually implies moving towards a point in space, but MCMC moves towards a *broader area* in the space and randomly walks in that area, picking up samples from that area.\n",
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"####Why Thousands of Samples?\n",
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"#### Why Thousands of Samples?\n",
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"At first, returning thousands of samples to the user might sound like being an inefficient way to describe the posterior distributions. I would argue that this is extremely efficient. Consider the alternative possibilities:\n",
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Chapter6_Priorities/Chapter6.ipynb

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"Eliciting priors from non-technical experts is especially difficult. Rather than introduce the notion of probability distributions, priors, etc. that may scare an expert, there is a much simpler solution. \n",
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"###Trial roulette method \n",
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"### Trial roulette method \n",
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"The *trial roulette method* [8] focuses on building a prior distribution by placing counters (think casino chips) on what the expert thinks are possible outcomes. The expert is given $N$ counters (say $N=20$) and is asked to place them on a pre-printed grid, with bins representing intervals. Each column would represent their belief of the probability of getting the corresponding bin result. Each chip would represent an $\\frac{1}{N} = 0.05$ increase in the probability of the outcome being in that interval. For example [9]:\n",

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