This is a pretty nice video thank you so much!!! I feel like I understood a lot of things much better after listening to the video. But there's also homework to prepare for if one wants to fully appreciate the content in the video. One should understand mostly about Bayesian statistics, and terms like normalizing factors. If not, checking around Wikipedia might be a good option.
Great video! Still wondering, can you perhaps further explain why the terms that cancel are equal for a normal distribution at 7:21? Can't wait for the next video coming out!
A normal distribution is symmetric about the mean. So, to put some numbers on it, let's say that the proposed theta (theta_star) was one sigma to the right of theta_(i-1). This of course means that theta_(i-1) is one sigma to the left of theta_star. So q(theta_star | theta_(i-1)) is equal to the normal distribution density at +1 sigma. In the divisor, you have q(theta_(i-1) | theta_star) which is equal to the normal distribution density at -1 sigma. But the normal distribution is symmetric about 0, so those values are equal and cancel each other out.
Posterior probability of new theta / Posterior probability of old theta. You need to understand bayesian statistics for continuous distributions for this.
There's a slight abuse of notation. q(theta* | theta_{i-1}) means 2 things here. It means both the probability density function for theta* (the candidate value) given the current state of theta; and it also represents the distribution theta* | theta_{i-1}. As mentioned, a commonly used proposal distribution is the Normal distribution. q(theta* | theta _{i-1}) would then be the Normal probability density function with mean theta_{i-1}, i.e. the current value, evaluated at the candidate value theta*, which is also drawn from this Normal distribution. Note that a Normal distribution also needs a variance. That is a tricky thing to set, even when a Normal proposal is indeed suitable. One reason the Normal proposal is commonly used is that those q factors end up cancelling, due to symmetry, so you don't actually compute the proposal densities. Though, you still sample from the proposal distribution.
@@maximmarchal9991 just look at the movie Metropolis from 1927 or listen to welcome to the machine from pink Floyd and know what's going on. ..this are the bad guys. That's all
Can't believe how good your backwards handwriting is ;)
This is a pretty nice video thank you so much!!! I feel like I understood a lot of things much better after listening to the video. But there's also homework to prepare for if one wants to fully appreciate the content in the video. One should understand mostly about Bayesian statistics, and terms like normalizing factors. If not, checking around Wikipedia might be a good option.
How does this guy write backwards?
same question. I looked it up and apparently it involves writing on glass in front of camera + flipping the video horizontally.
but how did you write in reverse?
he didn't, they just reverse the video afterward
@@frozenburrito9313 that cant be right. What is filmed is a mirror reflection.
PureLogic right, that's the correct word
Very nice and conscise presentation, thanks!
Thank you. Great set you got there for presenting it, almost convinced me you're actually left-handed lololol
explained everything super clear, thank you
Brilliant explanation!!! this is the best one
Where is the next vedio?
are you writing backwards?! very nice video, thank you for sharing.
Great video! Still wondering, can you perhaps further explain why the terms that cancel are equal for a normal distribution at 7:21? Can't wait for the next video coming out!
A normal distribution is symmetric about the mean. So, to put some numbers on it, let's say that the proposed theta (theta_star) was one sigma to the right of theta_(i-1). This of course means that theta_(i-1) is one sigma to the left of theta_star. So q(theta_star | theta_(i-1)) is equal to the normal distribution density at +1 sigma. In the divisor, you have q(theta_(i-1) | theta_star) which is equal to the normal distribution density at -1 sigma. But the normal distribution is symmetric about 0, so those values are equal and cancel each other out.
Could you explain the intuitions behind the formula for alpha?
How about totalitair communism? ? Plain in side. .right in front of your 👀
Posterior probability of new theta / Posterior probability of old theta.
You need to understand bayesian statistics for continuous distributions for this.
Do you have more video of the tutor??
Just a very good video!
where is the next?
can we have an example of programming this example on Matlab.
Dear Professor, what is "q" here?
There's a slight abuse of notation. q(theta* | theta_{i-1}) means 2 things here. It means both the probability density function for theta* (the candidate value) given the current state of theta; and it also represents the distribution theta* | theta_{i-1}. As mentioned, a commonly used proposal distribution is the Normal distribution. q(theta* | theta _{i-1}) would then be the Normal probability density function with mean theta_{i-1}, i.e. the current value, evaluated at the candidate value theta*, which is also drawn from this Normal distribution. Note that a Normal distribution also needs a variance. That is a tricky thing to set, even when a Normal proposal is indeed suitable. One reason the Normal proposal is commonly used is that those q factors end up cancelling, due to symmetry, so you don't actually compute the proposal densities. Though, you still sample from the proposal distribution.
you got me at the first sentence
I still did not understand. I will wait for the next video. Thank you anyway !
Soon we will upload the next video
@@MachineLearningTV But when?! Great video by the way.
@@maximmarchal9991 just look at the movie Metropolis from 1927 or listen to welcome to the machine from pink Floyd and know what's going on. ..this are the bad guys. That's all
Nothing more than repeated the Wiki, you didn't specify what's theta_0, how the "draw" candidate, not even one example.
You miss an example. Without example this looks like science fiction
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