Rejection sampling Puns

Suppose I have a target distribution 𝜋(𝜃|𝑥)∝𝑃(𝑥|𝜃)𝑃(𝜃) (e.g. the unnormalized posterior). I would like to use rejection sampling to obtain many samples {𝜃𝑖} from the posterior. Rejection sampling requires the use of a proposal distribution, 𝑔(𝜃), such that 𝑐⋅𝑔(𝜃)≥𝜋(𝜃|𝑥), ∀ 𝜃 (so 𝑐⋅𝑔(𝜃)c⋅g(θ) envelopes the unnormalized posterior).

My question is: Can I get samples from 𝜋(𝜃|𝑥)by setting 𝑔(𝜃)=𝑃(𝜃)? In other words, can my proposal distribution be my prior (times a constant), which I then compare to the likelihood 𝑃(𝑥|𝜃)? e.g. my proposed algorithm is as follows:

1. Sample 𝜃𝑖 from 𝑃(𝜃)
2. Sample 𝑈𝑖 from 𝑈𝑛𝑖𝑓(0,1)
3. If 𝑈𝑖⋅(𝐶⋅𝑃(𝜃𝑖))≤𝑃(𝑥|𝜃𝑖)), accept 𝜃𝑖. Otherwise reject.
4. Repeat many times

Will the resulting samples follow the posterior 𝜋(𝜃|𝑥)? Thank you!

Given this dataset:

https://preview.redd.it/xxedsq3ae8k61.png?width=1610&format=png&auto=webp&s=f4032971afb79d88f2c0153fa38de7b04af8fbb1

And this set up: https://imgur.com/LX0L6Sp

***And these questions:***https://imgur.com/MK4iVtq

1. How do I even approach defining the MLE
2. How do I create the sampling distribution for theta using python in order to do the rejection sampling?

Thanks for any help

https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.25.8422&rep=rep1&type=pdf

I’m trying to understand NTRU signatures. My understanding goes something like this:

In RSA you work with prime numbers. ECC you work with modular elliptic curve points with a peculiar addition rule.

In NTRU you work with polynomials (e.g. f(x)= x^3 - 2x) except everything is modulo (x^N -1). N is a parameter, a number, e.g. 503.

You never specify x, but conceptually for any given value of x, your polynomials evaluate to integers and you are just adding and multiplying modulo some concrete integer x_i ^N - 1.

You encrypt a message m by calculating:

3φ·h + m (mod q)

φ is a random polynomial, h is the public key polynomial. q is a fixed parameter, also a number, maybe 2048.

Now for key exchange you’re good to go. But for digital signatures there’s some known attack.

This is where I think I need correcting:

Instead of accepting any random φ, you try lots of random φ polynomials until it satsifies some ‘secure’ property.

Is this generally correct? Is φ the thing we’re trying to randomly sample from a better distribution? Or does rejection sampling add an entirely new layer to the problem that I haven’t appreciated?

https://arxiv.org/abs/1810.06758

i've been getting a lot of these errors lately. What's going on or how do i fix it? It's been happening more and more lately.

If i look in the logs i'll see errors like this:

2021-12-19T18:44:38.247958889Z [Error] VideoFileInfoReader: Unable to parse media info from file: /downloads/complete/Movies-4k/Skyfall.2012.UHD.BluRay.2160p.DTS-HD.MA.5.1.DV.HEVC.REMUX-FraMeSToR.mkv-xpost/Skyfall.2012.UHD.BluRay.2160p.DTS-HD.MA.5.1.DV.HEVC.REMUX-FraMeSToR.mkv 
2021-12-19T18:44:38.248023094Z 
2021-12-19T18:44:38.248036148Z [v4.0.0.5607] FFMpegCore.Exceptions.FFMpegException: ffprobe exited with non-zero exit-code (1 - [matroska,webm @ 0x34ac780] 0x00 at pos 0 (0x0) invalid as first byte of an EBML number
2021-12-19T18:44:38.248045430Z [matroska,webm @ 0x34ac780] EBML header parsing failed
2021-12-19T18:44:38.248054283Z /downloads/complete/Movies-4k/Skyfall.2012.UHD.BluRay.2160p.DTS-HD.MA.5.1.DV.HEVC.REMUX-FraMeSToR.mkv-xpost/Skyfall.2012.UHD.BluRay.2160p.DTS-HD.MA.5.1.DV.HEVC.REMUX-FraMeSToR.mkv: Invalid data found when processing input)
2021-12-19T18:44:38.248063670Z    at FFMpegCore.FFProbe.GetStreamJson(String filePath, Int32 outputCapacity, FFOptions ffOptions)
2021-12-19T18:44:38.248088694Z    at NzbDrone.Core.MediaFiles.MediaInfo.VideoFileInfoReader.GetMediaInfo(String filename) in D:\a\1\s\src\NzbDrone.Core\MediaFiles\MediaInfo\VideoFileInfoReader.cs:line 131
2021-12-19T18:44:38.248098872Z 
2021-12-19T18:44:38.248106915Z 
2021-12-19T18:44:38.249291715Z [Error] DetectSample: Failed to get runtime from the file, make sure ffprobe is available 
2021-12-19T18:44:38.402492994Z [Error] VideoFileInfoReader: Unable to parse media info from file: /downloads/complete/Movies-4k/Skyfall.2012.UHD.BluRay.2160p.DTS-HD.MA.5.1.DV.HEVC.REMUX-FraMeSToR.mkv-xpost/Skyfall.2012.UHD.BluRay.2160p.DTS-HD.MA.5.1.DV.HEVC.REMUX-FraMeSToR.mkv 
2021-12-19T18:44:38.402600306Z 
2021-12-19T18:44:38.402620502Z [v4.0.0.5607] FFMpegCore.Exceptions.FFMpegException: ffprobe exited with non-zero exit-code (1 - [matroska,webm @ 0x26bd780] 0x00 at pos 0 (0x0) invalid as first byte of an EBML number
2021-12-19T18:44:38.402632121Z [matroska,webm @ 0x26bd780] EBML header parsing failed
2021-12-19T18:44:38.402641065Z /downloads/complete/Movies-4k/Skyfall.2012.UHD.BluRay.2160p.DTS-HD.MA.5.1.DV.HEVC.REMUX-FraMeSToR.mkv-xpost/Skyfall.2012.UHD.BluRay.2160p.DTS-HD.MA.5.1.DV.HEVC.REMUX-FraMeSToR.mkv: Invalid data found when processing input)

I can create a video to send to them to prove your sample is the correct one!

Being fairly new to frags, I've recently bought a ton of samples/discovery sets to figure out what I want to buy a bottle of down the road, and I've ended up with a lot of one and done "rejects", but it seems wasteful to just toss them e.g. a few sprays gone from a 2ml sample. Do you keep them around and revisit them later to see if your tastes changed or toss them? Curious what people who go through a lot of samples do.

I have sent two samples to 23andme with both being rejected. I made sure I followed their instructions without deviation. After the second rejection, I had to sign a contract that they will give me a refund if I never buy another kit from them.

I went to Ancestry and they have also rejected my samples twice even if I strictly follow the instructions. Why won’t my saliva work?!?!?

I’m f/25/5’5/ 150. I recently started a new job and didn’t have any preemployment drug testing and the policy is that they only test on suspicion... so I’ve gone back to smoking pretty much every day for 3 months. I took about a month off 4 or 5 months ago but other than that I’ve been smoking almost daily for two years (and mostly pretty high quality cuz I was in a legal state). Found out an hour before today that I’d be tested for a government contractor badge (I smoked last night because I wasn’t even warned there was a possibility).

First sample I did quick fix and it was the right temperature but wasn’t accepted because it didn’t foam and didn’t smell like pee. Is it possible that I could still get in trouble for the bad first sample even though the tester didn’t say anything? Has anyone had success with mixing quick fix and real piss because that’s what I ended up doing (yes, I know the company says not to...)? When I got home I took a dollar tree thc test and it was negative (but I was a bit more hydrated than I was when I took the actual test).

Do they tell me or my employer the results first?

The test will also test positive for other things cuz of my prescribed meds: adderall, benzos, Wellbutrin, and abilify (also of course took acid only 3 days ago). Could any of these help explain positive results (I know Wellbutrin and abilify can cause false positives for amphetamines).

Any advice/ personal experiences with these things would be greatly appreciated!

Suppose I have a target distribution 𝜋(𝜃|𝑥)∝𝑃(𝑥|𝜃)𝑃(𝜃) (e.g. the unnormalized posterior). I would like to use rejection sampling to obtain many samples {𝜃𝑖} from the posterior. Rejection sampling requires the use of a proposal distribution, 𝑔(𝜃), such that 𝑐⋅𝑔(𝜃)≥𝜋(𝜃|𝑥), ∀ 𝜃 (so 𝑐⋅𝑔(𝜃)c⋅g(θ) envelopes the unnormalized posterior).

My question is: Can I get samples from 𝜋(𝜃|𝑥)by setting 𝑔(𝜃)=𝑃(𝜃)? In other words, can my proposal distribution be my prior (times a constant), which I then compare to the likelihood 𝑃(𝑥|𝜃)? e.g. my proposed algorithm is as follows:

1. Sample 𝜃 from 𝑃(𝜃)
2. Sample 𝑈𝑖 from 𝑈𝑛𝑖𝑓(0,1)
3. If 𝑈𝑖⋅(𝐶⋅𝑔(𝑥𝑖))≤𝑃(𝑥𝑖|𝜃𝑖), accept 𝑥𝑖. Otherwise reject.
4. Repeat many times

Will the resulting samples follow the posterior 𝜋(𝜃|𝑥)? Thank you!