Bayesian Statistics: Bernoulli example

Course Q&A Math for Machine Learning Probability & Statistics for Machine Learning &...
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I am a bit confused here specifically why theta is a continuous random variable?

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Hi @Musab_Bin_Gulfam,

\theta shows the probability of success, and although the outcomes (0 and 1) are discrete, \theta is treated as a continuous random variable here.

We use a prior distribution to represent our initial uncertainty about \theta, and after observing data, we update this to a posterior distribution, which is the probabilities of different \theta values.

Hope this helps, feel free to ask if you need further help!

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Thank you.

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You’re welcome! happy to help :raised_hands:

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Hi Alireza:
Thanks for your answer, I encountered this as well in this lesson. So I’m clear, P(H) is a random variable a priori only, and becomes a discrete variable a posteriori? This seems pretty critical, just want to make sure I’m grasping the concept.

Thanks,
Tom

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Hi @tfoss78 ,

P(H) is treated as a continuous random variable both prior and a posteriori. Because, we use a prior distribution to show uncertainty about \theta . Then, we update this to a posterior distribution, which still counts \theta as a continuous variable.

Hope it helps! Feel free to ask if you need further assistance.