Unbiased estimators in a Monty Hall problem

In my previous post, I talked about the German Tank Problem. And while discussing the frequentist approach, I defined the “unbiased” estimator. But seriously, unbiased estimators are really weird. Let me show you an example, in the form of a Monty-Hall-like problem.

Suppose that I’ve set up three closed doors A, B, and C, each with a prize behind it. Two of them have $1000, and one has $2000. Doors A and B don’t really matter, your prize is behind door C. How much is this prize worth to you? But before you answer, please, look behind one of the other doors, A or B.

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The German Tank Problem

The German Tank Problem supposes that there are N tanks with ID numbers from 1 to N. We don’t know what N is, but have looked at a single tank’s ID number, which we’ll denote m. How would you estimate N?

This is a well-known problem in statistics, and you’re welcome to go over to Wikipedia and decide that Wikipedia is a better resource than I am and, you know, fair. But, the particular angle I would like to take, is using this problem to understand the difference between Bayesian and frequentist approaches to statistics.

I’m aware of the popular framing of Bayesian and frequentist approaches as being in an adversarial relationship. I’ve heard some people say they believe that one approach is the correct one and the other doesn’t make any sense. I’m not going to go there. My stance is that even if you’re on Team Bayes or whatever, it’s probably good to understand both approaches at least on a technical level, and that’s what I seek to explain.

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Origami: Giggling Skull

Giggling skull

Skull by Jo Nakashima, and Skeleton Hand by Jeremy Shafer

The other day, my mother said that she didn’t celebrate Halloween growing up, they only had All Saints Day.  I think she’s a lot more enthusiastic about Halloween than I am.  Anyway, here’s a Halloween themed origami I made once, as part of the local origami club.  I think the skull is supposed to be made with one-sided black paper, to contrast the color of the eyes with the rest, but clearly I didn’t plan ahead.  Another fortuitous accident, is that once we had the skull and the hand, everyone’s skull was giggling.

Logic puzzles, overexplained

By “logic puzzle”, I don’t just mean puzzles involving logic, but rather a specific genre of puzzles, whose most famous types are Sudoku and Picross. There are many other types of such puzzles, and creators of logic puzzles can create entirely new types, if they are so inclined. If you’re not sure what I’m talking about, or if you’re just interested in finding logic puzzles, at the bottom of this post I’ve included a list of places you can find them.

I’m fairly good at logic puzzles. I’ve done the US Puzzle Championship for over a decade, and I placed in the top 25 once? So not like top-of-the-world good, but decent. And I’m a generalist, which is to say that relatively speaking I’m not very good with Sudoku, and I do better with other types of puzzles, including entirely new types.

My goal here is to overexplain my understanding of logic puzzles, and solving strategy. I am not confident that this is actually helpful to someone trying to get better at solving logic puzzles, but that’s not really the point. The point is to explicitly describe what would otherwise only be understood intuitively.

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Double standards in art

Some double standards in art are taken completely for granted. For instance, parents are expected to appreciate shows or concerts put on by young kids—as long as their own children are involved. And if you’ve ever enjoyed obscure or non-commercial art, such as fanfic, comics, music, videos, blogs, or just random people on social media, we tend to embrace its flaws and limitations, even when the same flaws and limitations may be unacceptable in mainstream media.

Another example, is the way that we often judge sequels in terms of the original. We might say that a video game sequel is worse than the first one, because it didn’t improve much on the original. Logically, if it improves on the original game by a nonzero amount, it’s a better game, but that’s not the logic we tend to follow.

And why is that? What theories of “goodness” are people using that allow these apparent double standards?  Here are several ideas for what might make the difference.

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Link Roundup: October 2021

In case you missed it, I published a couple articles on The Asexual Agenda this month: The search for an Asian ace masculinity, and I hate “A is not for Ally”.

On Doing Your Own Research | The Weekly Sift – Doug Muder talks about how experts can be wrong, but doing your own research can be even worse, depending on your own knowledge base.  In agreement with Doug, I think having a PhD certainly helps, because you understand what it’s like to understand something that only a few people in the world understand, and you also understand the kind of biases and mistakes experts make.  But what strategy could I recommend to most people who don’t have PhDs?  Are you just epistemically SOL?

I know what scientists are like, and that makes scientific conspiracy theories extremely unbelievable to me.  On the other hand, scientific frauds, persistent errors, and plain miscommunications are far more believable.  I’m reminded of an article in Wired that traced the 6-feet rule about COVID to old irrelevant arguments about the transmission of measles.  I can’t vouch that this story is 100% accurate, but it’s very true to my understanding of scientist behavior.  While the scientific ideal is to update your theories with the evidence, in practice scientists are financially incentivized to expound upon the value of their previously published work, even if that means perpetuating error.  And this causes a whole bunch of problems, most of which are far too mundane to ever make it into the news.

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Origami: Coronavirus

Coronavirus origami

Coronavirus, an original design by me

Let me tell a story.  Although I’ve continued posting monthly origami photos, I’ve made very little origami in the past year.  I just have a really large backlog of photos (all on my Flickr, if you can find it).  Although being stuck at home all the time doesn’t seem like it would interfere with origami (and indeed, I was already stuck at home in previous years due to unemployment), there was more of a psychological shift, as I felt less motivated to pursue certain interests.

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