I do not understand Bayes Theorem

[Fruiteloop]

Ok so It's not that I do not understand its definition I just do not see how you implement it mathematically.

The definition is: update your believes with new data

But that is not going to tell you anything useful unless you use a network of beliefs.

The reason bell curves work is that they can be calculated by hand.

You need a supercomputer to calculate a network thus cannot be done by hand.

(A|B) as the main example: it actually looks like this:



How that F are you supposed to calculate that by hand?

It is why I never learned Bayes theorem by the memes like all other memes I learn math from. because it is not about Math. it only looks like its math.

If I could program a computer things be different but I cannot and I do not have money to buy easy to use software. Bayes theorem is useless in that case for me.

 

[aeon]

If you try to understand Bayesian thinking mathematically, you are guaranteed to not understand it.

Cheers,
Ian

 

[Wyote]

Somethin ain't computin here

 

[aeon]

But that is not going to tell you anything useful unless you use a network of beliefs.

If that is the case, you have already lost the plot, and dispensed with the Bayesian approach.

Meaning is always holonic, and subjective, yes, but belief is not necessary, and indeed, invariably leads to error.

The Bayesian approach must be fluid, without constants. Beliefs are thus.

So dispense with them. Hold only those things conditionally known in the moment. Conditional, because new information might come in which leads to refinement, or perhaps wholesale replacement. That allows room for your own nature, and fallibility, and the nature of the ever-changing world.

Cheers,
Ian

 

[Fruiteloop]

Google says that Frequentism and Bayesianism are used for different things.

That neither is better or worse than the other in absolute terms.

If you need to build a bridge and have absolute certainty over a long time in its integrity you use frequencies maths.

If you need some kind of adaptive system you use bayesian method.

Bayesian is just confusing because if this is true then what you need is dynamic structure in the math to do the calculation.

So it be like you make a car that has dynamic structures in it that must be places one on top another or the engine doesn't function.

A bridge is more of a fixed computation.

A car can swap out parts and be resigned in so many ways and do much more than a bridge.

But neither is better or worse.

A car does what a car does and a bridge does what a bridge does.

The computations are different.

 

[Fruiteloop]

When looking at the updating rule:

Conditional entropy must first be known otherwise you cannot do the calculations.

If you want to sample a pond for how many fish exist you must first know how many fish exist.

So it is backwards.

The thing I wanted to know is how many fish in the pond there are by taking a sample but according to all videos on bayes theorem you need to know how many fish exist FIRST. That is why I had trouble. I want to do the calculations to find the answer but you must assume the answer first to do to calculation so sampling is useless to find answers it is assumed you already know the answer. Holy Fuck.

Conditional entropy means you cannot do any calculations at all.

Stats Quest presented it this way

3 blue 1 brown presented it this way

all memes present it this way

how am I supposed to sample a pond to find the number of fish?

machine learning I think I could do some of that stuff because the calculations methods exist.

 

[aeon]

If you need to build a bridge and have absolute certainty over a long time in its integrity you use frequencies maths.

If you need some kind of adaptive system you use bayesian method.

Every time a bridge is built, Bayesian thought is used, because improvements are always made, and sometimes new approaches.

That said, improvements and approaches are always referenced to best-practices engineering standards and known material science.

Despite human consciousness defaulting to dualism, life is not so black and white, or this versus that.

Nor can it be reduced to ideations of the mind.

And for what it is worth, Bayesian Theory is just that. It might take quite a lot of testing to see if it is true, and useful.

Of course, it might not be true, yet still useful in finite contexts.

Cheers,
Ian

 

[aeon]

You do not need to know how many fish exist. How could you, or anyone?

You must make a presumption, and then test against the presumption with data.

YouTube is good for a lot of things, but I am not sure if this is one of them, inasmuch as I have not watched any of them.

Cheers,
Ian

 

[aeon]

https://www.infjs.com/threads/omnia-vincit-amor.31889/post-1474295

Cheers,
Ian

 

[Fruiteloop]

You do not need to know how many fish exist. How could you, or anyone?

You must make a presumption, and then test against the presumption with data.

YouTube is good for a lot of things, but I am not sure if this is one of them, inasmuch as I have not watched any of them.

Cheers,
Ian

sampling is a math method to find something

but with bayesian assumptions you cannot do those calculations?

or maybe you can but condition entropy is no the way

 

[Fruiteloop]

Not sure how bayesian thinking is in any way different from normal thinking.

Yes people update beliefs but people did that before bayes so why do you need a formula if the formula has no calculation practicality.

 

[aeon]

Not sure how bayesian thinking is in any way different from normal thinking.

It’s not—at least for a reasonable individual with critical faculties.

Yes people update beliefs but people did that before bayes so why do you need a formula if the formula has no calculation practicality.

You’re still thinking it is math. This is why you do not understand it.

Cheers,
Ian

 

[Fruiteloop]

It’s not—at least for a reasonable individual with critical faculties.

You’re still thinking it is math. This is why you do not understand it.

Cheers,
Ian

If it is not math.

Then neither is frequentism

Neither is good or bad they just differ in what they are used for.

So why would people fight about it?

Is frequency thinking bad?

I assume if it is a way of thinking and not math then it is bad because it does not update it beliefs?

That is why I think is should only be about math because why would people think that way?

"You are think by not updating your beliefs" is such an insult but if it only about the math then it is not an insult.

 

[Fruiteloop]

Frequentism is just a way of saying someone is stupid because "The thinking does not update itself".

So if math no longer has anything to do with it.

It is just a way to insult people.

 

[Fruiteloop]

To me math as a framework should not be about insulting people.

But then is comes down to epistemology of statistics.

If statistics really is math or not?

 

[John K]

It’s a mathematical formalisation of an everyday process. We all make assumptions about something then refine those assumptions based on real life experience. The Baysian approach simply formulates this with mathematical precision for quantifiable situations. So if you think a dice is biased, estimate the probability of a 6 then keep on revising that estimate by repeated experiments. The formula will settle down eventually to a steady state which gives the best probability of a 6.

Edit to get rid of a spurious ‘to’

 

[Fruiteloop]

It’s a mathematical formalisation of an everyday process. We all make assumptions about something then refine those assumptions based on real life experience. The Baysian approach simply formulates this with mathematical precision for quantifiable situations. So if you think a dice is biased to estimate the probability of a 6 then keep on revising that estimate by repeated experiments. The formula will settle down eventually to a steady state which gives the best probability of a 6.

This is good for a simple number.

And simple numbers are closer to frequentism.

But I wonder how you incorporate that into a multiple variables framework.

A model that has to be updated also requires a structure depending on what is to be modeled.

That becomes more of a simulation with a memory involved to track where things have been and make inferences on the future.

The electric grid or anything to do with city systems / factories and supermarkets economics . Those be larger systems needing projections.

I want to make model of cognition and a way of seeing what it does in an environment.

The environment is most complicated to build. So many ways to build them and so many ways to have interactions inside them.

There'd need to be a general way to do it to sum up results. Sampling some distributions more than others.

 

[John K]

This is good for a simple number.

And simple numbers are closer to frequentism.

But I wonder how you incorporate that into a multiple variables framework.

A model that has to be updated also requires a structure depending on what is to be modeled.

That becomes more of a simulation with a memory involved to track where things have been and make inferences on the future.

The electric grid or anything to do with city systems / factories and supermarkets economics . Those be larger systems needing projections.

I want to make model of cognition and a way of seeing what it does in an environment.

The environment is most complicated to build. So many ways to build them and so many ways to have interactions inside them.

There'd need to be a general way to do it to sum up results. Sampling some distributions more than others.

That sounds like a very interesting aim. The starting point I’d guess is to adopt or to develop a theory of cognition upon which a model of it can be built. That would then need to be subject to the hypothesis / test / refine process which is at the heart of all scientific method. I don’t think Baysian techniques would be central to this though they may help to establish the likelihood of validity of some of your premises that underlie the model.

You might also be able to use Baysian techniques to predict the likelihood of how the model will react in repeated situations. I wonder whether this is likely though because there there may not be a stable probability for a particular event happening in the very rich context of cognition.

Even more complicated in real life is feedback trouble. Real people can behave quite differently if they know they are being monitored and predicted than if they don’t. That can be a swine to model because it leads to non-linearity and difficult / unanticipated effects.