Chapter 5: Summary added #50
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| We use the Julia library Turing.jl to instantiate a model where we set the prior probability and the distribution of the outcomes of our experiment. Then we use the Markov Chain Monte Carlo algorithm for sampling and saw how our posterior distribution updates with the input of new outcomes. | ||
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| Finally, we experiment on how changes in our prior distributions affect the results we obtain" |
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change: experiment on
for: experiment with
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| In this chapter, we gave an introduction to probabilistic programming languages exploring the classic coin flipping example in a Bayesian way. | ||
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| First, we saw that in this kind of Bernoulli trial scenario, where the experiment has two possible outcomes 0 or 1, it is a good idea to set our likelihood to have a binomial distribution. |
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set our likelihood to a binomial distribution.
| In this chapter, we gave an introduction to probabilistic programming languages exploring the classic coin flipping example in a Bayesian way. | ||
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| First, we saw that in this kind of Bernoulli trial scenario, where the experiment has two possible outcomes 0 or 1, it is a good idea to set our likelihood to have a binomial distribution. | ||
| We also learned what sampling is and saw why we use it to make an update on our beliefs. |
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to update our beliefs
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| First, we saw that in this kind of Bernoulli trial scenario, where the experiment has two possible outcomes 0 or 1, it is a good idea to set our likelihood to have a binomial distribution. | ||
| We also learned what sampling is and saw why we use it to make an update on our beliefs. | ||
| Then we used the Julia library Turing.jl to create a probabilistic model setting our prior probability to be a uniform distribution and the likelihood to have a binomial one. |
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setting our prior probability to a uniform distribution
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and the likelihood to a binomial one
| Then we used the Julia library Turing.jl to create a probabilistic model setting our prior probability to be a uniform distribution and the likelihood to have a binomial one. | ||
| So we sampled our model with the Markov chain Monte Carlo algorithm and saw how the posterior probability was updated every time we input a new coin flip result. | ||
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| Finally, we created a new model with the prior probability set to a normal distribution centered on *p* equals 0.5 which gave us more accurate results. |
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centered on p = 0.5
| md" ### Bayesian Bandits " | ||
| md" ### Summary | ||
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| In this chapter, we gave an introduction to probabilistic programming languages exploring the classic coin flipping example in a Bayesian way. |
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In this chapter, we gave an introduction to probabilistic programming languages and explored the classic coin flipping example in a Bayesian way.
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| First, we saw that in this kind of Bernoulli trial scenario, where the experiment has two possible outcomes 0 or 1, it is a good idea to set our likelihood to a binomial distribution. | ||
| We also learned what sampling is and saw why we use it to update our beliefs. | ||
| Then we used the Julia library Turing.jl to create a probabilistic model setting our prior probability to a uniform distribution and the likelihood to a binomial one. |
There was a problem hiding this comment.
probabilistic model, setting
| First, we saw that in this kind of Bernoulli trial scenario, where the experiment has two possible outcomes 0 or 1, it is a good idea to set our likelihood to a binomial distribution. | ||
| We also learned what sampling is and saw why we use it to update our beliefs. | ||
| Then we used the Julia library Turing.jl to create a probabilistic model setting our prior probability to a uniform distribution and the likelihood to a binomial one. | ||
| So we sampled our model with the Markov chain Monte Carlo algorithm and saw how the posterior probability was updated every time we input a new coin flip result. |
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We sampled our model
(delete So)
…edback-to-do-messages Chapter 5: Added feedback and to do messages
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- Fix
In the previous chapter we introduced some of the basic mathematical tools we are going to make use of throughout the book. We talked about histograms, probability, probability distributions and the Bayesian way of thinking.
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We will start this chapter by discussing
- Remove unnecessary italics and capitalization, fix typo in "probabilistic", remove apostrophe in PPLs, add fragment:
another useful tool, that is, probabilistic programming, and more specifically, how to apply it using probabilistic programming languages or PPLs.
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There are a few occurrences of "PPL's" change them all for "PPLs"
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These are systems, usually embedded inside a programming language,
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We will be focusing on some examples
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We are going now to tackle a well known example, just to settle some ideas: flipping a coin. But this time, from a Bayesian perspective.
By:
Let's revisit the old example of flipping a coin, but from a Bayesian perspective, as a way to lay down some ideas.
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To answer these questions we are going to build a simple model, with the help of Julia libraries that add PPL capabilities.
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Do we know anything else? Let's skip that question for the moment and suppose we don't know anything else about
$p$ . This complete uncertainty also constitutes information we can incorporate into our model. How so? Because we can assign equal probability to each value of$p$ while assigning 0 probability to the remaing values. This just means we don't know anything and that every outcome is equally likely. Translating this into a probability distribution, it means that we are going to use a uniform (NO CAPS, NO ITALICS) prior distribution for$p$ , and the function domain will be all numbers between 0 and 1.
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@martinacantaro i made the corrections you mention |
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