Bayes Squad

 The Bayes Squad

A Probability Party with Formula Fellows

Bayes Theorem BT: Alright folks, let's get this Bayesian statistics party started! I'm Bayes Theorem, and I'm the king of the castle around here.

Prior Probability PA(A): Whoa, whoa, whoa. Slow down there, Bayes. You may be the main formula, but I'm the one who sets the foundation. I'm Prior Probability, and I establish the probability of events before any data is collected.

Likelihood P(A): And I'm Likelihood, the star of the show. I calculate the probability of evidence given the hypothesis.

Posterior Probability P(A|B): 

And I'm Posterior Probability, the one who updates the probability of the hypothesis after the evidence is observed.

Marginal Likelihood P(B): 

Don't forget about me! I'm Marginal Likelihood, and I calculate the probability of evidence without considering any particular hypothesis.

Joint Probability P(A and B) = P(A) x P(B|A): 

And I'm Joint Probability, the probability of both events happening simultaneously. I bring everyone together!

Conditional Probability P(B|A) = P(A and B) / P(A): 

And I'm Conditional Probability. I calculate the probability of an event happening, given that another event has occurred.

Law of Total Probability P(B) = P(B|A) x P(A) + P(B|~A) x P(~A): 

And finally, I'm Law of Total Probability, the one who sums everything up. I calculate the probability of an event happening by adding up the probability of the event happening given that a hypothesis is true, and given that it's false.

BT: Alright, alright, everyone calm down. We all have our roles to play, and we all contribute to the Bayesian approach. But let's be honest, without me, BT, none of you would even exist.

PriorP: Oh, come on, BT. You wouldn't even have a starting point without me. You need my probabilities to get things going.

L: And let's not forget about me. I'm the real star of the show. Without me, there wouldn't be any evidence to base your calculations on.

PosteriorP: And I'm the one who updates everything based on the evidence, so I'm pretty important too.

ML: Hey, don't forget about me! I'm the one who calculates the overall probability of evidence, regardless of any particular hypothesis.

JP: And I bring everyone together! Without me, you wouldn't even know if events were happening simultaneously.

CP: And I help you calculate the probability of events given certain conditions. You couldn't do it without me.

LoTP: And I'm the one who sums it all up. Without me, you'd just have a bunch of probabilities floating around with no context.

BT: Alright, alright, you all make good points. We're all important in our own way. But let's not forget that at the end of the day, we're all just formulas. It's the people who use us who really matter.

ML: Aww, Bayes, that's so sweet of you to say.

L: Yeah, who knew Bayes Theorem had a soft spot?

CP: Don't let it go to your head, Bayes. We're still the ones doing all the hard work.

LoTP: And don't forget about me! I'm the one who sums it all up and makes sense of it.

JP: And I bring everyone together!

PosteriorP: Alright, let's all just calm down and remember that we're all important in our own way. Without each other, we couldn't function.

PriorP: Well said, Posterior Probability.

BT: Alright, let's get back to work. We've got probabilities to calculate and hypotheses to update.

Part 2: Bayesian Brain Brigade: 

Where Probability and Prediction Meet 

Bayes Theorem: Alright, team, today we're discussing how our roles can be related to how the brain learns, like in a Bayesian model.

Prior Probability: Oh, I see where you're going with this. Just like how the brain establishes prior beliefs about the world before any new information is learned.

Likelihood: And then the brain updates those beliefs based on new evidence, just like how I calculate the probability of evidence given the hypothesis.

Posterior Probability: And I help update those beliefs by calculating the probability of the hypothesis after we observe new evidence.

Marginal Likelihood: And I help the brain see the overall probability of evidence, regardless of any particular hypothesis.

Joint Probability: And I help the brain understand how different factors interact, just like how I calculate the probability of both events happening simultaneously.

Conditional Probability: And I help the brain predict how certain conditions might affect outcomes, just like how I calculate the probability of an event happening, given that another event has occurred.

Law Of Total Probability: And I help the brain sum it all up, so it can get a clear picture of the probabilities involved in different outcomes.

BT: Exactly! Our roles are so important in how the brain learns and updates its beliefs based on new information.

L: It's almost like the brain is using Bayesian statistics to learn!

PosteriorP: And it makes sense, doesn't it? The brain is constantly updating its beliefs based on new information, just like how we update our probabilities based on new evidence.

ML: And it's not just about individual pieces of information. The brain needs to look at the overall picture, just like how I calculate the overall probability of evidence.

JP: And it needs to understand how different factors interact, just like how I calculate the probability of both events happening simultaneously.

CP: And it needs to predict how certain conditions might affect outcomes, just like how I calculate the probability of an event happening, given that another event has occurred.

LOTP: And it needs to sum it all up and make decisions based on the probabilities involved in different outcomes, just like how I do.

PriorP: It's amazing how our roles can be related to how the brain learns. It just goes to show how important probabilities are in understanding the world around us.

BT: Alright, team, let's keep up the good work. We're helping the brain learn and make accurate predictions, just like in a Bayesian model.

L: I predict that we'll be very successful!

ML: Well, the probability of that is pretty high, given our track record.

JP: But let's not forget about the probability of someone spilling coffee on the machine again!

CP: We need to consider all possible outcomes, even the unlikely ones.

PosteriorP: And I'll be there to update our probabilities based on new evidence, no matter what happens.

LOTP: And I'll be there to sum it all up and make sure we're making accurate predictions based on the probabilities involved.

BT: Alright, team, let's keep using Bayesian statistics to help the brain learn and make accurate predictions. We're making a real difference here!

ML: I couldn't agree more. It's all about the probabilities, after all.

JP: And the brain is really good at understanding them, just like us!

CP: With all of us working together, we can make sure the brain is learning and making predictions as accurately as possible.

PriorP: Let's keep those priors updated and accurate!

L: And let's keep updating our probabilities based on new evidence.

PosteriorP: And let's keep making accurate predictions and helping the brain learn

BT: Emm…, and let's not forget to have some fun while we're at it!

PriorP: Oh, I see where this is going. Are you going to make a joke about my name again?

BT: Well, I wouldn't want to raise the prior probability of hurt feelings!

And, Hey Likelihood, the likelihood of you being the target of a joke is pretty high.

JP: And the probability of us all laughing at it together is even higher!

CP: Speaking of laughter, what's the probability of a joke about conditional probability being funny?

PosteriorP: I don't know, but I'll update our probabilities based on the audience's response.

LOTP: And if all else fails, we can always sum it up with a good old-fashioned knock-knock joke!

BT: Here’s one. 

Knock knock!

L: Who's there?

BT: The brain.

L: The brain who?

BT: The brain that's so good at Bayesian prediction, it already knew who was at the door before it knocked!

CP: Another one, another one! 

BT: Knock knock!

L: Who's there? 

BT: Bayesian brain.

L: Bayesian brain who?

BT: Bayesian brain predicts so well, it's a psychic calculator!