But if they are having children until they have one of each, the probability of the different observations does depend on the prior events!
292 karma · joined June 14, 2013
P(pb > 0.5 | "Six girls and one boy") = (P("Six girls and one boy" | pb > 0.5) * P(pb > 0.5)) / P("Six girls and one boy")
Applying Bayes theorem thus requires us to calculate P("Six girls and one boy" | pb > 0.5). How do you suggest that we do this? Why is your answer the unique correct solution?
In world one, I use bayesian update on the model P(# boys | Bias) = Mutltinomial(n = 7, p = Bias)
In world two, I use bayesian update on the model P(# children | Bias) = Geometric(p = Bias)
Might-have-beens and didn't happens do play in, in my choice of model. I should choose the one that I believe, and if I'm not certain, I should use an even more complicated model that incorporates my beliefs about what models might be appropriate.
Since her hypothesis test is designed to help answer the question of whether or not the mean population height is 65 inches, why should we expect it to tell us anything about the mean population height other than whether or not it being 65 is consistent with the data observed?
I would argue the true distinguishing feature of a "lambda function" in a PL is that it is first-class, nest-able, and lexically-scoped (that is, it captures bindings from its definition site).
A closure is simply a way of implementing lexical scope for functions.
A variable is a "free variable" not because it is "freed" from its lifetime, but because it is not bound by its enclosing lambda. (It would still be a free variable even if the function and the variable binding had the same lifetime.)
As far as private savings, those disappear almost immediately in the face of a medical disaster.
Things are pretty grim indeed without the government programs (Social Security and Medicare).
Don't forget there is still counter-party risk on the side that is sending Bitcoin in exchange for goods as well.
Uh...
They went through all the trouble of making a website. Maybe use https and just show me the password on the website?
Imagine you are a scientist and want to find out whether the hypothesis that men are on average taller than women is true. If you could just exactly measure and take the average of the entire male and female populations you wouldn't need a hypothesis test.
Since you can't, you can do an experiment where you take a random sample of men and women. Now, you can do the average in the same way, but you need something to help figure out whether to trust the results. That's where the p-value comes in. The reason you need to be careful to select hypotheses in advance is because in order for statistics to help you account for error you need the noise in the data to be uncorrelated with the result you are trying to assess---which it won't be if you chose the result because it was the one that looked best after you account for the noise.
The equal probability you are describing is for the p-value itself being more extreme, not the result.
A fairly standard definition of the p-value (from wikipedia) says: "In statistics, the p-value is a function of the observed sample results (a statistic) that is used for testing a statistical hypothesis. Before the test is performed, a threshold value is chosen, called the significance level of the test, traditionally 5% or 1% and denoted as α."
What this description is missing though is the crucial importance of the fact that the threshold value is chosen before doing the analysis. And moreover, that the entire analysis plan has been chosen before doing the analysis. Because what the p-value is really telling you is the probability that on repeating the experiment (and its accompanying analysis!) you would see a result as or more extreme than what you observed.
If your experiment comprises "try all of the combinations of variables to see what gives me the best answer", the p-value you compute would need to be some very fancy test that took that into account... and you would see your analysis as having much less statistical power.
For a simple example, look at a statistically rigorous method for dealing with multiple hypothesis testing when you plan it in advance: https://en.wikipedia.org/wiki/Bonferroni_correction.
Of course p-hacking is bad. The problem isn't frequentist statistics or p-values though, its scientists not understanding the statistics that they use. If you want to use a p-value to help make a decision about a hypothesis, you have to commit to your analysis plan in advance.
edit: Furthermore, p-values were designed to deal with experimental data. If you're doing an observational study, perhaps you should use statistical tools designed for that purpose.
To sum up: when you have people who have no idea what they're doing do statistics, they will do it badly.
Basically, the key idea is that you can manage the debugging information yourself. So for simple tail recursion, you can have the first call push a marker on the stack and subsequent calls update a count on the marker (if you care about the depth). For more complicated interactions, you can record whatever debugging information you need, even a full stack by associating the information with a cell under the top-most stack frame. (Of course, this debugging information may grow with the depth of recursion, depending on whether you try to keep the full stack or not, but will still be more space efficient than keeping around all of the stack frames.)
The main point is that keeping track of your execution context doesn't have to be done by walking the call stack, you just need to have a protocol for maintaining whatever state you want on entry/exit.
You can even try it out in Racket.
Edit: to clarify, my parenthetical was meant to say tail call optimization is not an optimization but a matter of correctness (so best to call it elimination instead), not to make a distinction between the two.
Also, that isn't quite the right paper but I don't have time to find the one I meant right now...
We picked the name Shill because it sounds a lot like shell, but is a bit of an in-joke because it is built on Racket, which is a descendant of Scheme. All three have slightly negative connotations: schemers, racketeers, shills.