Bayes’ Theorem in the 21st Century (2013) [pdf]
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Bayes’ Theorem in the 21st Century (2013) [pdf]
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Re: Bayes’ Theorem in the 21st Century (2013) [pdf]
#2I truly believe that Bayesian inference is the statistics of the 21st century. Recent advances in MCMC (e.g., NUTS, Stan [1]) and variational inference (e.g., ADVI [2], VAE [3], etc.) + more computing power than ever promise a near future in which Bayesian inference is the default inference engine.
Prior distribution is a beautiful and logical mechanism for adding regularization, domain-specific knowledge to our model.
[1] Stan, a platform for statistical modeling http://mc-stan.org/
[2] Automatic Differentiation Variational Inference https://arxiv.org/abs/1603.00788
[3] Auto-Encoding Variational Bayes https://arxiv.org/abs/1312.6114
Re: Bayes’ Theorem in the 21st Century (2013) [pdf]
#3Bayesian theorem made more sense once I started seeing the conditional (if statement) in conditional probability.
Re: Bayes’ Theorem in the 21st Century (2013) [pdf]
#4Bayesian theorem made more sense once I started seeing the conditional (if statement) in conditional probability.
Yep. Baye's theorem is actually a generalization of contrapositivity (if A implies B, then "not B" implies "not A") to stochastic settings. It's not usually taught in an intuitive way.
Re: Bayes’ Theorem in the 21st Century (2013) [pdf]
#5For those who are new to Bayesian Statistics and not to eager to dive into the maths right away I recommend Think Bayes [0]. It gives a nice introduction for those who know programming (Python). The ebook is available for free (see link).
Re: Bayes’ Theorem in the 21st Century (2013) [pdf]
#6Bayesian theorem made more sense once I started seeing the conditional (if statement) in conditional probability.
Yep. Baye's theorem is actually a generalization of contrapositivity (if A implies B, then "not B" implies "not A") to stochastic settings. It's not usually taught in an intuitive way.
Yeah, I had to figure some of this out on my own. Do you have a good book/resource on this?
Re: Bayes’ Theorem in the 21st Century (2013) [pdf]
#7I truly believe that Bayesian inference is the statistics of the 21st century. Recent advances in MCMC (e.g., NUTS, Stan [1]) and variational inference (e.g., ADVI [2], VAE [3], etc.) + more computing power than ever promise a near future in which Bayesian inference is the default inference engine. Prior distribution is a beautiful and logical mechanism for adding regularization, domain-specific knowledge to our mode…
Curious if there is any work to build ecosystem to run complex models on ML accelerators, like some layers for TF for example..
Re: Bayes’ Theorem in the 21st Century (2013) [pdf]
#8I truly believe that Bayesian inference is the statistics of the 21st century. Recent advances in MCMC (e.g., NUTS, Stan [1]) and variational inference (e.g., ADVI [2], VAE [3], etc.) + more computing power than ever promise a near future in which Bayesian inference is the default inference engine. Prior distribution is a beautiful and logical mechanism for adding regularization, domain-specific knowledge to our mode…
Curious if there is any work to build ecosystem to run complex models on ML accelerators, like some layers for TF for example..
There are several libraries. PyMC4 [1], the next version of PyMC3, will introduce TF as a backend. Tensorflow probability [2] from Google. PYRO [3], from Uber, uses Pytorch backend.
[1]: https://github.com/pymc-devs/pymc4
[2]: https://www.tensorflow.org/probability/
[3]: http://pyro.ai/
Re: Bayes’ Theorem in the 21st Century (2013) [pdf]
#9Earlier quoted context omitted.
Yep. Baye's theorem is actually a generalization of contrapositivity (if A implies B, then "not B" implies "not A") to stochastic settings. It's not usually taught in an intuitive way.
Yeah, I had to figure some of this out on my own. Do you have a good book/resource on this?
Probability Theory the Logic of Science is an excellent textbook on math and theory. Note the title even references cultus' point.
Unfortunately it predates many of the modern developments in methods / computation, but if you want to dive deep, I strongly recommend it. It takes the perspective of designing a reasoning robot to make the most effective decisions.
Another resource, eg Stan's manual, can get you up and running on computation/inference. Your choice in computation tool should reflect the type and size of of problems you're interested in, and languages you're comfortable with. Stan has bindings for many scripting languages. R also offers Nimble, Python PyMC3 and Edward, and Julia has DynamicHMC and Turing. (EDIT: xcodevn has better Python recommendations: https://news.ycombinator.com/item?id=18213923 )
Re: Bayes’ Theorem in the 21st Century (2013) [pdf]
#10"The prior can generally only be understood in the context of the likelihood"
https://arxiv.org/abs/1708.07487