Jeremiah

There is going to be a subjective risk factor of how much a person will be willing to gamble with. That will vary from person to person and doesn't sa...

You are only willing to make that traded because it is only 10 bucks. That is not much to lose in the first place. It is a subjective criteria and it ...

This is not a paradox and in fact the solution is straight forward and simple. This is an exercise in observational bias. Separating the objective and...

You never need to know the distribution or even guess at it. We have X=f(x_i) for some unknown population. Where x_i is some positive real number on a...

Repeating over and over that this is "not a statistics problem" is not a valid response to anything I am doing. That is nothing but blind categorical ...

How does this relate to what I am doing? As far as I can tell it doesn't.

I am not talking about a model of the probability, I am talking about modeling the problem. We build models for two reasons, to make a predictions or ...

Also even without a sample distribution a theoretical model can still be set up. That is where my interests are atm. However, sigma is still a problem...

The normal distribution is widely used to make probabilistic claims about unknown populations, which have discrete values and unknown limits. If you w...

Doesn't matter, I am not using it as proxy.

There is a problem with the third chance mechanism, the one where we get the chance to switch, and if it should be included in the model, as it is sub...

It may need two logical vectors.

My simulation can give a visualization of this.The resulting distribution from the process of filling the envelopes changes the possible outcomes from...

I actually have been thinking about how to model this problem and I believe I will need to include a logical true/false vector. The problem here is th...

I am not advocating for this approach but I think this is your best shot at estimating the median of the distribution from a single sample. People hav...

Here is a link for the emprical rule, which I think makes a normal distribution a better choice for a prior. https://www.investopedia.com/terms/e/empi...

I have to think about it more.

I was thinking you could use Y to justify your priors. It is the only information you have. Maybe include justification on the emprical rule which say...

My continue interest here is not in debating the different approaches, but in the modeling of X. If I was going to build a theoretical Baysian model I...

https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_introbayes_sect009.htm Highest Posterior Density (HPD) Interv...

The HDI is 95% of the area under the curve. It is a cut off range.

It'll be fine once we use a MCMC and get the HDI. You forgot the part of my argument where we need a sample distribution.

A normal distribution does not have to have a mid of 0, nor do they need negative values.

There are two mindsets here, people who hinge their expections on what is known and people who hinge their expections on what they feel they can safel...

When dealing with unknown populations even priors needs to be tempered with a sample distribution before you have a posterior distribution that is rel...

A normal prior would actually make more sense, as empirical investigations have shown it robust against possible skewness.

No, it is not.

A random variable is defined by a real world function.

Each observed x is an independent event.

It does not even matter, as the second chance mechanism transforms the distribution.

You use samples to make probabilistic inferences about an unknown population. I roll a die 10 times and 9 of those times get a 6. Now it is not imposs...

Claiming this case is "ideal" is an entirely subjective standard pumped full of observational bias.

The thing to recognized here is that we have a nested structure. There are three chance mechanisms, with each housed in the last. Let x_{ij}, i = 1, 2...

This is an important separation to keep in mind, as the conceptual difference between these approaches to probability is not the number of observation...

Calling me a troll is a personal attack.

Also. . . , Since I have already displayed in this thread that x can come from any number of continuous distributions, this means we have no clue how ...

Something else I would like to point out, is that assuming that the probability of any given x must come from a discrete distribution is not necessari...

That's because I accept that you use a different vernacular.

What is the difference between experimental data and observational data?

There are some interesting aspects to note if you diagram the 1.25X argument in comparison to the other two. Which clearly shows why it is a faulty ar...

I don't really think you know what I said. If you need clarification just ask .

I noted towards the start of the thread that this had more to with defining the sample space. Calculating expected returns is a futile effort if we ca...

I just said that. That is exactly what I said. I already posted the definition of an event from one of my books, which I will refer to over you. I wil...

You created a double standard. You can try to bury that in text, but that is what happened.

If you are using the principle of indifference then criticizing people for using the principle of indifference, that is hypocritical.

So you think you always have a 1.25 expected gain in every possible instance?

As far as I am concerned I already found the flaw. Take it or leave it, that is your choice.

Hey, if you feel lucky then switch, if you think you are close to the cap don't, feel this one out, but you are not going to be able to justly quantif...

You are guessing. Then trying to model your guesswork.

It is also rational to want ice-cream on a hot day. You still don't know anything about the distribution.