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Bayesian inference is a method of statistical inference that relies on treating the model parameters as random variables and applying Bayes' theorem to deduce subjective probability statements about the parameters or hypotheses, conditional on the observed dataset.

10
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Going off of your NIPS workshop link, Yee Whye Teh had a keynote speech at NIPS on Bayesian Deep Learning (video: https://www.youtube.com/watch?v=LVBvJsTr3rg, slides: http://csml.stats.ox.ac.uk/news … /2017-12-08-ywteh-breiman-lecture/). I think at some point in the talk, Teh summarized Bayesian deep learning as applying the Bayesian framework to ideas from deep learning (like learning a posterior …
answered Jan 4 '18 by aleshing
2
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The best book for Gaussian Processes is Gaussian Processes for Machine Learning, of which there's a free pdf online: http://www.gaussianprocess.org/gpml/. For most other aspects of Bayesian
answered Feb 9 '18 by aleshing
3
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Your question is ill-posed, it doesn't make sense to "infer" a prior. Let's say you have a likelihood $p(x|\theta)$, where $x$ is the data and $\theta$ are some parameters. In bayesian inference … priors). In an empirical bayes setup you already posit a prior distribution, and use the data to set the hyperparameters of this prior. The point of reference/Jeffrey's priors (and objective bayesian inference) is to construct a prior using just the assumed likelihood. …
answered Nov 15 '17 by aleshing
4
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1answer
This might be a dumb question. I'm working on 2.11 in BDA (page 2 in this pdf http://www.uio.no/studier/emner/matnat/math/STK4021/h16/undervisningsmateriale/presentation_jariek.pdf). The problem is to …
asked Dec 21 '17 by aleshing
0
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You only put prior mass on the region that you want the posterior to have mass over. So in your situation, if you want the posterior of $b$ to only take on positive values, you'd specify a prior for $ …
answered Dec 27 '17 by aleshing
2
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0answers
I'm reading through a tutorial on the Dirichlet process (http://www.stats.ox.ac.uk/~teh/research/npbayes/Teh2010a.pdf) and have a small question. Given a draw from a Dirichlet process $G\sim\textsf{DP …
asked Sep 7 '17 by aleshing
2
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2answers
So I'm trying out a toy problem of inferring the mixing weights of a K-component Gaussian mixture model (just the weights, so I'm assuming the parameters of each Gaussian is known). My posterior is $\ …
asked Sep 5 '17 by aleshing
1
vote
1answer
If you have a binomial likelihood, $y|n,p\sim\textsf{Bin}(n,p)$, the Jeffreys' prior for the proportion $p$ is $\textsf{Beta}(1/2,1/2)$. If we instead reparameterize the proportion as the log odds $\p …
asked Dec 21 '17 by aleshing
1
vote
For question 1, to explicitly show how it follows from Bayes rule, we'd write $$p(w|y,x)=\frac{p(y|w,x)p(w|x)}{p(y|x)},$$ but we can just assume $w$ and $x$ are independent and write $$p(w|y,x)\prop …
answered Dec 1 '17 by aleshing
7
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0answers
Does anyone know of any references that look at the relationship between the Laplace approximation and variational inference (with normal approximating distributions)? Namely I'm looking for something …
asked Dec 26 '17 by aleshing
8
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When transforming a uniform distribution on $\log(\sigma)$ to a distribution on $\sigma$ you need to take into account the Jacobian of the transformation. This corresponds, as you correctly intuited, …
answered Jan 19 '18 by aleshing
2
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This tutorial (https://chrisdxie.files.wordpress.com/2016/06/in-depth-variational-inference-tutorial.pdf) answers most of your questions, and would probably be easier to understand than the original S …
answered Dec 23 '17 by aleshing
2
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The second expression is correct as this is an improper distribution, i.e. it doesn't integrate to $1$. Thus it doesn't have a density and you can only specify it up to proportionality.
answered Jan 31 '18 by aleshing
2
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From the picture, it looks like the prior is $p\sim\textsf{Beta}(1,1)$ for the unknown proportion $p$, which is the same as $p\sim\textsf{Unif}(0,1)$, and thus using a binomial likelihood with $k$ suc …
answered Dec 27 '17 by aleshing
0
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I don't know if you actually want to calculate a credible region for all three parameters jointly (it makes things more complicated). Instead you can calculate the credible intervals for each paramete …
answered Dec 24 '17 by aleshing