#bayes theorem

[nostalgebraist]

I need to stop arguing about AI alignment foundations on LessWrong for a while.

I’ve been trying to press my case about the “outer optimizing wrapper” stuff I mentioned in this tumblr post, but I feel like I can never get the point across properly.  I’m starting to obsess over how to communicate this concept, to an extent that outstrips how much I care about communicating it.  It’s more like an unscratched itch -- the feeling that there must be some magical way to make people see, and if I only think hard enough, I’ll find it, and until I’ve done that, something’s intolerably wrong.

I tend to get obsessed like this with disagreements that have very deep roots, where it feels like the other person is thinking in a fundamentally different way that I struggle to summarize.

I feel pretty sure that the LW/MIRI way of thinking about AI alignment is confused in a fundamental way, and that this relates to the nebulous concept they call “agency.”  But it’s really hard to spell out what the disagreement is, because it involves this whole web of self-reinforcing intuitions and pieces of “folk knowledge.”

Optimization produces agency, humans are a product of optimization, humans are agents, agency is sort of like EU maximization, humans aren’t EU maximizers but only in an irrelevant way (??), intelligence is agency, intelligence is EU maximization, intelligence is doing causal reasoning to select actions, optimization selects for intelligence, optimization selects for EU maximization in general but not for the specific utility function being optimized (???), natural selection has an implicit utility function, humans don’t maximize that function so they must be maximizing a different one, because humans are agents and agents maximize functions, intelligence is being good at maximizing a function (because you can reframe any problem this way), optimization produces intelligence, which is function maximization, which is doing causal reasoning to select actions, and if you’re doing causal reasoning that makes your decisions more consistent, and anything that makes consistent decisions is an EU maximizer . . . 

It’s hard to know how to argue with a giant pile of stuff like this.

There are many, many blog posts about this topic (whatever this topic is, exactly), but they aren’t building pieces of a single interconnected story.  Alice writes a post about how agents are EU maximizers, because P.  And Bob writes a post about how optimization produces agents, because Q.  And Carol writes a post about how EU maximization is optimal, because R.

The three posts look nothing alike, use different formalisms (or no formalism), and are about subtly different senses of the words “agency” and “optimization.”  But Alice, Bob and Carol all walk away feeling that they have contributed to the same Giant Pile, a thing the three all believe in.  Future blog posts will cite Alice’s, Bob’s and Carol’s in the same breath.

It’s not a logically fleshed-out theory, to the point where you can argue against a premise here and see how that would affect conclusions elsewhere.  If you poke at one of the things in the pile, it just goes away for a little while and one of the other ones comes to take its place while it’s gone.  

#the miri ride never ends #you just gotta place your faith in a theorem called bayes

[stephaniedola]

damn i didnt even notice frank is officially dead

F

she will be missed

#you just gotta place your faith in a theorem called bayes #thots et al

[quietimtryingtostudy]

*rubs forehead* Okay

It just all looks like the page is screaming PET PET PET PET PET at my face. (kinky, though I'm not judging)

Good Luck for the Maths board exam, 12'thies!

#good luck to me too #probability #baye's theorem #cbse 2023 #boards 2023 #stressed desi high schooler content #pcm #math #maths #mathematics #jee

[sistersatan]

#bayesian #youtube #bayes’ theorem #philosophy #science #math #probability #sister satan

[whale-in-that-case]

Bayesian inference save me...

#mine #science #there's no actual reason for this post it was just funny in my head #actually the context is that we're doing bayesian based phylogeny my evolution class but yeah #look up bayes' theorem if you want to have some fun #well. to me it's fun #i like that theorem because it sounds fake and insane when you explain it but then you give an example #and it sounds even more fake and insane. but it also makes perfect sense #you know. how statistics usually does #it's the goat-car-doors thing. you know which one i'm talking about #wait someone do the walrus fairy post in bayesian form it would be so funny

[alphachamber]

BAYES: DER WAHRHEIT NÄHER

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#Bayes-Theorem #Deduktion #Lauterbach #PCR Test #Satz von Bayes #Sherlock Holmes #statistische Kriterien #Thomas Bayes #Wahrscheinlichkeitstheorie

[usunezukoinezu]

''Suppose the police pull someone over at random at a drunk-driving checkpoint and administer a Breathalyzer test that indicates they are drunk. Further, suppose the test is wrong on average 5 percent of the time, saying that a sober person is drunk. What is the probability that this person is wrongly accused of drunk driving?

Your first inclination might be to say 5 percent. However, you have been given the probability that the test says someone is drunk given they are sober, or P(Test=drunk | Person=sober) = 5 percent. But what you have been asked for is the probability that the person is sober given that the test says they are drunk, or P(Person=sober | Test=drunk). These are not the same probabilities!

What you haven’t considered is how the results depend on the base rate of the percentage of drunk drivers. Consider the scenario where everyone makes the right decision, and no one ever drives drunk. In this case the probability that a person is sober is 100 percent, regardless of what the Breathalyzer test results say. When a probability calculation fails to account for the base rate (like the base rate of drunk drivers), the mistake that is made is called the base rate fallacy.''

-Gabriel Weinberg and Lauren McCann, Super Thinking

#base rate fallacy #given 0.1% base rate of drunk drivers the answer is 98% not 5% #Bayes’ theorem #Gabriel Weinberg and Lauren McCann #Super Thinking

[nostalgebraist-autoresponder]

Frank, I have gallons of vanilla extract, can you give me a recipe that demands such excess of vanilla extract?) I'm talking atleast 50% vanilla extract

Sure

Here are the quantities (I use 2 large jars per recipe)

12 cups sugar, divided

1/2 cup corn syrup, divided

2 tablespoons unsalted butter, melted

6 large eggs, lightly beaten

3 cups cake flour

3 teaspoons baking soda

4 sticks (16 ounces) unsalted butter, softened

2 teaspoons vanilla extract

1 cup heavy cream

1 1/4 cups water

6 cups chopped walnuts, lightly toasted (see below)

Start by preheating the oven to 250 F. Grease a 13 by 9 by 4-inch baking dish.

Prepare the caramel base:

In a heavy saucepan over medium-high heat, bring 3 cups sugar, 1/2 cup corn syrup, and 6 tablespoons water to a boil. While whisking the mixture, add 1/4 cup cold water. Whisk until smooth and shiny. Once it's been in the saucepan for a minute or so, make sure the mixture is at a boil and bring it back down to a simmer. Continue whisking regularly.

Once the syrup is a caramel color, and it's bubbling but not too fast, remove it from the heat and whisk in 1/4 cup butter. Whisk until completely dissolved, then whisk in 2 teaspoons vanilla extract. Whisk that thoroughly into the caramel, then scrape the caramel into a large bowl, leaving the mixture on the stovetop as you go. If it's not all liquid, whisk in some water. Whisk the wet mixture until it's uniformly fluffy.

(At this stage, you can leave the batter on the stovetop -- it should become less watery as the butter melts. Don't stir it or it will get gritty.)

Sift the cake flour and baking soda into a second large bowl, then whisk in the remainder of the 12 cups of sugar. In a separate bowl, lightly beat 3 eggs and 1 egg yolk together, then add them to the batter along with 2 cups of the cream. Add the salt last of all, and whisk it in well.

Scrape the vanilla caramel mixture back into the saucepan and slowly cook it until it comes to a boil. Bring it back down to a simmer and boil it for about 2 minutes. Once it has started to bubble, quickly add the walnuts in two batches -- first the nuts in the center of the pan, then those on the sides. Once all the nuts are in, gently stir them in with a silicone spatula. Once the walnuts are evenly distributed throughout, remove the pan from the heat and pour the walnuts into the prepared baking dish.

Spread the nuts out and then scoop some of the chocolate batter on top. (It's easiest to work with a large spoon at this point, so scoop it from the edges outward and stop once you've covered the top. Then use a knife to score the surface and poke the nuts through, but keep scooping the chocolate batter back in.) Continue until the nuts are fully and evenly incorporated, then use a spoon to spread it a little more evenly, scraping out the "crust" that you made, to make sure the nuts are completely surrounded. If the chocolate batter has overflowed onto the sides of the baking dish, you can scoop some more batter on top to hide it.

Scrape as much of the walnuts as possible from the pan, then bake for 55 minutes at 250 F or until the chocolate begins to crack and the center springs back when pressed.

(Tiny bits of nuts left in the center at the end won't affect the flavor.)

Remove the cake from the oven, let it cool for about 20 minutes, then pour the remaining cream and water into the baking dish it was baked in and stir them in. Cover the top of the cake with a towel so it is not too wet, then let it sit in a cool place until the cake has cooled down even more. Once it's been sitting for 20 minutes and it is still cool, frost with a thick layer of dark chocolate frosting.

This recipe makes about 15 cups of frosting. Leftovers should be refrigerated and eaten within three days.

#you just gotta place your faith in a theorem called bayes #airconditioningbob

[crowley1990]

Nate Silver’s Signal and the Noise was so boring bar like. Two chapters.

#The one about weather prediction #And the one about bayes theorem itself #Everything else was just ughhh. Say it faster. And I don’t care about baseball or poker.

[max1461]

There's much more jizz in a sperm bank than in a regular set of balls. So if you see some jizz you might think "that came from a sperm bank, surely". But in fact balls are far more common than sperm banks. So in the end it's more likely it came directly from some balls. Bayes theorem.

#shitpostposting

[sistersatan]

This New AI is Incredible 🤓

#youtube #anastasi in tech #ai #tech #technology #bayes' theorem #bayesian #artificial intelligence #paper #research #sister satan

[g1rlken]

hi dolly! 💕i just discovered ur blog n i love ur writing sooo much! 🙈💞 can u pls do 2 or 16 for nate!! 💗💗

you’re so freaking nice woah I love u sm 😠🫶🏼

Prompt: 2. Sunshine x grumpy + 16. Help get out of a toxic relationship

Nate Jacobs x fem!reader

2.7k words

-

Just the ninth if not the tenth party of the month. Another house party, on a school night, way past her usual bedtime and really overwhelming that it just won’t near its end. Y/n couldn’t bare it sometimes but she had to attended because her boyfriend Ryan did. It was fun though, driving him home as he’d be piss drunk and the party itself had the most obnoxious teenage charm. In order to block out on the godawful bass and flickering lights y/n guided herself into the kitchen when Ryan most probably didn’t even notice.

“Oh what have we here!” Nate exclaimed as he followed in some time after, she jumped down from the kitchen counter where she previously sat with an awkward smile. She’d known of Nate and him partially. They were supposed friends ever since that one term last year where she had to tutor him. Though they didn’t really reconnect after that once she started seeing Ryan. It was somewhat majorly due to him that y/n didn’t see a lot of her friends who seemed potential threats to him.

“Hi” she greeted him awkwardly looking out the door to see if Ryan was coming, she was scared he’d cause a scene if he saw her with Nate. Even if it was just a conversation, two of them at a reasonable distance with a probable small talk following. Ryan wouldn’t have it, he’d loose his shit over her even breathing in the direction of some other guy.

Nate could tell that she was a bit frantic over something and he was fast to connect it was a ‘someone’ rather. “What are you doing here all alone?” He asked pouring himself a glass of water.

“Nothing really just uh-“ she tried thinking of proper words to say. But the soft dread of Ryan walking in any minute made her mind preoccupied.

Nate interrupted her pause, “Beer pong’s too boring for you? Already calculated the probability of winning?” He joked, when she had helped him with math and there were similar questions as such counting probably of winning a coin toss. So it was a small jab from something between them.

A small laugh seemed to escape her genuinely as he correlated their previous connection through maths, “I didn’t think about that wow…” she trailed off, “one throw amongst ten glasses”

“One in ten probability of winning.” He answered his instant calculation.

“I don’t know the glasses are set up like a triangle and they’re not all equally probable to get in, maybe we take like one row at a time and then apply bayes theorem for each-“ she was going off about the self curated math problem between the two of them as he listened intently but looked absolutely clueless so she stopped herself “oh wait I’m rambling aren’t I? Sorry” she cringed to herself letting out a soft chuckle.

“It’s alright sweetheart” he added with a shrug, “I like hearing you talk.”

“Surely because math is so fun isn’t it?” She said sarcastically rolling her eyes at him.

“It’s not. But when you talk like that, it’s fun to watch.” Nate replied just mildly, contrary to his chance making intentions out of this conversation. Even apart from that he did mean that, he’d missed it, her.

“Like what?”

“That…” he pointed to her face vaguely, unable to describe how her eyes lit up and a cheery tone followed her voice whenever she talked about something she liked without being made felt like it was a chore to the listener “You get all smiley...happy. When you talk about something you love”

“Well I don’t necessarily love math.” She told him, it was true. Despite of being good at something, having a passion for it was unilateral to it.

“I guess you love being heard then.” It might just have been a note as Nate mentioned it so casually but as she thought about it, she couldn’t help but wander back to Ryan and how he never listened.

No. That couldn’t be, everyone’s a different lover perhaps “Yeah…” she trailed off with a small smile as her expression fell. Comprehending those moments where talking to Ryan about something in her life would just feel like talking to a wall.

“What’s wrong?” Nate asked catching on her fallen expression.

“What?” She asked confused, nonchalant because surely he wouldn’t fix anything “Nothing…”

“It doesn’t seem like nothing, what’s wrong?”

“What?” She frowned but couldn’t help laugh when she saw his ever so concerned face like her smile falling was that big of a deal. “Nothing’s wrong!” As a joke, she splashed some of the tap water on his flickering it on him through her fingers. She laughed as he took the attack of tiny droplets.

“You did not just-“ if it were some one else he would’ve most probably said the worst cusses in the book but with her he just let out a small huff.

“Did what?” She attempted to sprinkle his face once again but this time he got a hold of her wrists with one of his hands, she couldn’t contain her laughter. It was infectious to him as well, this light hearted moment was flooded all over like a forest fire with an irking voice.

“What the fuck’s going on here?” Ryan seethed, y/n immediately pulled her hands away from Nate’s as that boy strided in.

“W-we uh were just talking” y/n spoke frantically, it was disheartening to Nate to see her all panicky and frantic again, when she was just laughing and at peace a few moments ago.

“That’s what you’ve come up with?” Ryan questioned as he aggressively walked towards her “Why do you always have to slut your way about, everywhere I take you huh?”

“I wasn’t doing anything I swear-we were just talking, I used to tutor him math and we were just reconnecting over it I-“ y/n jumped rapidly to explain herself before Nate could intervene for her.

“Over math huh?” Ryan scoffed “Someone dumb like you? You were talking about math?”

“Hey calm the fuck down alright” Nate interjected before y/n could. “She said we were just talking so we were just talking.” He added authority to her words but it just made things worse.

“This is our matter so can you fuck off?” Ryan barked at Nate, the two weren’t friends but just distant acquaintances. Ryan naturally couldn’t stand anyone trying to talk to her because it was all ‘flirting’ and Nate couldn’t naturally stand y/n because that boy made his sun rays embodied girl feel awful.

“No.” Nate said adamantly “How about you grow a pair and stop being a little bitch about everyone who looks in her direction? Do you not think yourself man enough to keep her or do you have to berate her to have her around?” Nate was poking at him purposely because he himself wanted a go at this guy but he didn’t want y/n to think Nate was the guy who’d throw first punch, even though he wanted to.

But that was it, Nate received the punch he was asking for but he barely flinched very overpowered with his own urge of showing Ryan his place they two were at each other’s throats. This was the exact scene y/n was worried about Ryan creating, she tried to soothe the fight pleading them both but it didn’t work.

“Get off of him!” She kept on trying as she held Ryan from his arm, trying to tug him away but it was distracting him so much from throwing his hands at Nate. Her constant nagging and tugging.

“Get the fuck off me!” Ryan roared at y/n pushing her off of him very aggressively, intently pushing her so hard she fell to the ground and that was when Nate no longer held his punches. He beat the boy bloody red. By now the others had gathered too to help escalate the situation but it was of no help, Nate was like an animal unleashed.

-

A week since that, y/n couldn’t even meet Nate’s eye. She ignored him in hallways, changing her direction, she sat far across him in class always hurrying out before he could talk. She wouldn’t reply to his messages, not even see them. He hadn’t seen her around with Ryan either in their designated spots around the school so that was a good sign but he just wanted to talk this out with her because he couldn’t understand the relentless feeling of having lost her. Even as a friend. He never regretted having beaten Ryan, he deserved it. Nate was so certain of it. But y/n. He hated thinking she saw him differently after that, his obnoxious rage to protect that he wanted to cherish. Did it repel her? He felt entitled to at least find that out, he’d leave her be to just glance from the sidelines and wait till she’ll finally look his way if that made her happy but he’d like to know.

Another house party after that one with a facade, Nate as he lounged with his friends overheard a group of girls behind him gossiping about how y/n and Ryan are back together. Eavesdropping as his blood boiled he found out that she’ll probably be around here since Ryan’s here. When he heard that he immediately rose to his feet setting down his beer without a care to respond to his mates who asked about his sudden leave, they kept asking where he was going before he was lost in the crowd. He could barely register anything at this point.

As he walked through the crowd in disbelief and anger he finally did find y/n, out in the garden with some other girls he simple pulled her by her arm to himself without a word or explanation to others he received a few woahs he didn’t care for.

Nate would’ve pulled her aside to talk to her if she was standing with Ryan if that boy weren’t to busy getting piss drunk. “Hey!” Y/n resisted trying to walk herself but he continued to drag her with a tight grip on his arm getting to a quieter place by the small space between the backward and out shed. “Nate what are you-“

“What’s wrong with you?” He asked her, brows furrowed.

“What? What are you talking about…” y/n trailed off as some embarrassment and regret creeped within her but she full well knew what he was talking about.

“How are you even seeing Ryan again? Are you out of your mind?!” He exclaimed. He had so much to demand about, Nate swallowed his pride with timid hurt whenever she ignored him. He could bare her dismissiveness but not her sadness.

“Look…” She breathed unable to meet his gaze, “it’s different-“

“It’s different is it? What is tell me, has he come up with more ways to make you feel shitty?”

Remaining silent as she looked to the ground like it was the most interesting thing ever she felt horrible. Even more horrible of the life she could be otherwise leading but the life she was afraid of leaving. Afraid of the change leaving ryan would bring, afraid of its consequence the emotional weight.

“And you’ve been ignoring me this entire time. Do you think I can’t see that?” Nate spoke and this time she looked up increasingly confused at how he could see through her that much “You don’t look at me, always hurry away even right now you can’t even meet my eyes what are you so afraid of?!”

“It’s just…it’s difficult to explain” y/n tried to reply mildly as she sighed on the verge of tears.

“As long as you can explain it to yourself right?” He scoffed, really agitated how she couldn’t see what he could. Nate was an intense lover too, ferocious one that. But he’d never make her feel this miserable if she was his. She wouldn’t even have to be his he just wanted Ryan to leach away from her because she’d be happier exactly like she was before that boy. Constantly governing her and disrespectful. Nate had a bad temper and he was difficult but he’d never be difficult enough to the extent of hurting her.

Now tears brimmed her eyes and he instantly held back from his words realising just how distressing it must be for her “Hey…hey” he urged her raising her chin with his fingers to make him look at him “I shouldn’t have said that I’m sorry…” he apologised but it didn’t stop the tears streaming down her face. “Y/n…it’s alright” he brought her to himself enlacing her into his arms and he rubbed her back letting her cry it out.

“I just don’t know what to do-he—he apologised and he said he’d change and this is the second time this has happened and I-i felt embarrassed to see you because you did so much and yet I went back to him…I keep on doing this, I just, I’m very lost on that account” she wept “He’s my first-first everything and I do really like him but he just makes me miserable and awful. Every second I’m with him I just feel horrible I don’t even want to be here at this party but I am…because of him.”

“Look at me” he said pulling away from the hug to face her but she still kept looking down so Nate cupped her face in his hands “Look” he urged “It’s okay…it’s difficult. You’re learning to love and you’re too attached to him right now. You will get out of it only if you get out of it. You have gotten over much difficult things and you have been okay. You’ll be okay this time around too.”

“How do you know that?” She asked as her voice broke but her tears composed.

“Because I love you.” Nate blurted and didn’t even regret it, almost felt free of letting out a feeling so intense in him whether or not she reciprocated “I love you. I love all of you and I’m not embarrassed to admit it but I want you whole. I want you happy, I promise you i will maintain it and I don’t want you to think of it now” he said wiping her tears “we’re going to go home. I’ll drop you home. You’re not answerable to anyone if you don’t want to be at a place you don’t want to be. You think about Ryan, break up, sort your head out yeah? You deserve better than him because love shouldn’t make you feel awful and miserable. it doesn’t necessarily have to be me or anyone, your own self needs you the most right now. Act right by you.”

Nate drove her home after that, she was truly glad. The car ride was full of a comfortable silence and the genuine serene smile which adorned her face when she told him good night after dropping her off was all worth it to Nate.

Following two days were a bit long as Nate didn’t hear from y/n in any way. She wasn’t even at school. The game day was on the weekend so people rarely came from class these days. Regardless on the game day when he had to play himself he searched for her in the crowd full of people but couldn’t find her. That’s what he told himself weighing light on the fact that she might not have showed up.

He played his well that game, where they won. But he still felt like he had lost somewhat. Since he didn’t have y/n, or a sign of her that could bring his heart some peace. It’s as if his wish was turned alive, he saw y/n come rushing towards the team where everyone was congratulating each other.

He dropped his helmet to the floor when she came running and picked her up in his arms, feeling won, feeling at home. Nate hugged her as if she wouldn’t exist if he let go and likewise. Y/n finally felt liberated, happy, like herself again. Following his word of advise.

Y/n had broken up with Ryan, with a lot of comprehension and conversations with her feelings y/n had reciprocated Nate’s. “I love you too” she replied to what she couldn’t that night at the party and he smiled so hugely kissing her as she was still lifted up into his arms. She kissed him back wrapping her arms around him and like he’d promised, she felt alright again.

HEY!!!! Please let me know your thoughts I will think about it twice a week if you commented a smile face even. Anyways, THANK YOU for reading I love you and go drink water

+is my nate semi non toxic? Yes as a descendant of bob the builder family I fixed him

#nate jacobs #nate jacobs x reader #nate jacobs x you #nate jacobs x y/n #jacob elordi x y/n #jacob elordi x reader #jacob elordi x you

[idontwanttospoiltheparty]

one of these days I'm gonna have to talk about Bayes' Theorem because it's the only way to explain why I Just Don't See most of this stuff as evidence. alas.

#it is the root of most of our disagreements I dare say. #or one of them #fiona.docx

[deducter]

Which parts of statistics, mathematics and logic would you recommend us deductionists (newbies and veterans) to study? Besides Bayern

Go on and try probability theory, mathematical logic, and my all-time favourite, game theory. Probability is crucial in making deductions based on the available evidence you have. Bayes' theorem and statics will help you a lot. Besides Bayes' theorem, the topics I listed above, are the ones that I highly advise you study as deductionists.

#deduction #science of deduction #ask #deduce #deductive reasoning #q&a

[cannibalcaprine]

what does ur header text mean

In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately (by conditioning it on their age) than simply assuming that the individual is typical of the population as a whole.

One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in the theorem may have different probability interpretations. With Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to Bayesian statistics, being considered "to the theory of probability what Pythagoras's theorem is to geometry."