## Fumbles and putting points on the board

So, the Packers are losing at the moment--what a shock. (Update: They won in the end!)

Here are my thoughts on the Democrats' misteps and what the Republicans need to do about it:

One team may fumble, but unless the other team scores during their possession, it's meaningless. Conservatives need to press the advantage, but I see the usual Republican/conservative ineptness.

It's not enough for people to see that Obamacare is failing, they need to see that any Obamacare-like plan will fail; that the failure is baked into the very idea of a big government solution.

We need to press home the point that hope for growth and prosperity is misdirected when placed in the hands of the government. If you want growth and prosperity, then you better hope for private enterprise and individuals to provide it, and for the government to stand back and let them do it.

If you want good schools and for the next generation to be educated and able, then you need to rethink how the government is providing free-but-abysmal education for all. The solution is not a top-down, regimented and regulated government solution; but a bottom-up percolation of ideas and experiments devised by individuals and individuals schools and districts.

If you want good-quality, affordable health insurance; then you shouldn't look for the government to write thousands of pages of regulations in an attempt to wish such insurance into being. People need to understand that it is the free choices of 300 million Americans that will build a strong insurance system--with each American looking for the best coverage for the best price, each choosing to enter freely into a contract with an insurance provider that meets their needs. Before Obamacare, government regulations were preventing free choice and free markets from working in the insurance market. Obamacare made it worse.

The choice the Democrats present is a false one: either you have government, or you have chaos and viciousness--it is only the government that can help, only the government that can create peace. Conservatives need to press home the point that the American people are fundamentally charitable and kind. That we seek to help those who are truly unable to help themselves; that we do want to help those who have fallen and need to rebuild their lives; but that we do not want a blank check for every whim a Congressman can dream up.

Not every problem can be solved.
Not every problem with a solution can be solved by group action.
Not every group action should be done by the government.
Not every government action should be done at the federal level.

Some things should be left to individuals, to private enterprise and charity, and to local and state governments.

The Democrats have fumbled, but the ball is still on their side of the 50-yard-line--and the referees are all in their pocket; unless we drive the ball back over to the other side of the field and really change the way Americans think about what the government should and can do, we're wasting our chance.

## Honor

So the insurance companies, which are so evil that we should abolish them entirely and bring in single-payer, are actually so completely trustworthy that we can run Obamacare solely on the honor system.
Health plans will estimate how much they are owed, and submit that estimate to the government. Once the system is built, the government and insurers can reconcile the payments made with the plan data to "true up" payments, he said.
In addition, was that paragraph simply in serious need of editing, or was the phraseology actually intentional? I don't think my health plan, or any health plan, is capable of independent thought. A health plan is a contract, a series of agreed-upon words which bind the insurer and insured in a money-for-services exchange. You can print off your health plan and read it. If it suddenly came to life in my hands and engaged me in a conversation about my premiums and government subsidies, I would be more than a little freaked. On the other hand, the phrasing might have been intentional; after all, most Americans like their health plan, they'd like to keep their health plan; but those nasty, money-grubbing, insurance companies are another matter entirely. Sock it to them, I say!

An editor should have rephrased it:
Insurance companies will estimate how much they are owed, and submit that estimate to the government....
But I think people's negative reactions to that sentence would be much stronger than the original.So, why was one phrase chosen over the other? Inadvertently?  or intentionally?

Shhhh...everything's fine...go back to sleep...

## Give me my gluten!

Continuing the flour/food theme:
The great gluten-free scam

Once, pasta and bread were store cupboard staples. Now, many of us are replacing them with ‘healthier’ gluten-free foods. But are they really better for us?

... [Nutritionist Ian] Marber predicts that these voices will only grow louder. “Our attention will turn to other diet trends, but the gluten-free craze will grow and grow.” Following a gluten-free diet isn’t actively harmful, he adds. “If it makes you happy, do it!” he laughs. “By buying that expensive stuff, you’ll certainly be making someone else very happy.”
I always laugh when I see something like a box of rice or a package of deli meat labeled "gluten-free"; it's an obvious marketing appeal to idiots. The article points out that really only about 1/100 have a true gluten disease, the rest are just wishfully thinking that gluten-free will make them thinner and give them more energy.

And the idea of labeling such obviously gluten-free foods such as rice and meat is just laughable. I swear our kids already know that gluten comes from wheat, while apparently much of the buying public is clueless--despite jumping on the gluten-free bandwagon.

Marketers are just surfing the tide of the latest craze.

## Semolina vs. Farina, aka Sooji

We eat a lot of Indian food at home, and often look up recipes online. Common ingredients include semolina and farina. Indian words for farina include sooji and rava, and it is also commonly referred to as Cream of Wheat, though this is a brand name and not exactly the same thing. Strange then that many expert Indian cooks don't seem to recognize the difference between these ingredients! I see the ingredients referred to incorrectly everywhere on the web.

What most American cooks call semolina is not sooji. Semolina is yellow, is made from hard durum wheat, and is the primary ingredient of Italian pasta. The American word for sooji is farina. Farina is white, is made from soft wheat, and is the primary ingredient of Cream of Wheat. If you make a semolina cake with farina, the result will be mushy. And what you want for upma is not semolina, it's farina, i.e. sooji or rava. It is a difference that matters. Indian stores tend to sell both products. That's another reason why it is strange that so many experts don't seem to know the difference!

## Hypothetical Statistics Question

Let $$\phi(x,\mu,\sigma)$$ denote the normal distribution with mean $$\mu$$ and standard deviation $$\sigma$$ evaluated at $$x.$$ Consider the model distribution $$p(x,\mu)=(1-t)\cdot \phi(x,\mu-3t,1)+t\cdot \phi(x,\mu+3\cdot(1-t),t^2),$$ for some known, fixed, but very small $$t>0.$$ Since $$t$$ is small, $$p$$ looks very much like a normal distribution with variance $$1$$ and mean $$\mu,$$ except for a tall spike around $$\mu+3.$$ See the picture below. The mean of $$p$$ is $$\mu.$$ Note in the last term, the variance is $$t^4.$$ The total mass of the spike is $$t,$$ thus small, and so the cumulative distribution for $$p$$ will look very much like the standard cumulative distribution for $$\phi(x,\mu,1).$$

Suppose we have a sample $$x_0,$$ assumed to be from a distribution $$p$$ of the form above, but of unknown mean. To repeat, $$t$$ is known. Consider the hypothesis: $$H_0: \mu=x_0-3\cdot(1-t)$$ Do we reject $$H_0$$?

If $$H_0$$ is true, then $$p(x_0,\mu)\approx t \cdot \phi(x_0,x_0,t^2) = 1/(t \sqrt{2\pi}),$$ and this is very large, about $$1/t$$ times larger than $$p(\mu,\mu).$$ Indeed, $$x_0-3\cdot(1-t)$$ is very close to the maximum likelihood estimate for $$\mu.$$ These seem to be reasons not to reject $$H_0.$$

On the other hand, the overall mass of the spike is small, and the entire spike is well out on the tail of $$p.$$ Thus it is in some sense unlikely to get an $$x_0$$ out there, assuming $$H_0$$ is true. Since the cumulative distribution looks very much like the normal cumulative distribution for $$\phi(x,\mu,1),$$ it makes sense to apply the usual test and reject $$H_0.$$

I find that not rejecting in this case is the right thing to do, but I am not sure what others might think. I also wonder how often such a question is relevant.

## Clueless

Our kid's school has a "Smart Lab", which is a place where kids, generally in 6th-8th grade, can play with technology.

Here is a transcript-by-memory of a conversation I had with the instructor:
Me: Do any of the kids do any actual programming?

Instructor: Oh, yeah. Have you heard of Scratch?

Me: Yes. That's basically like MindStorms; you tell it to move the figure three steps this way, two steps that way. I mean actual coding.

Ins: Sure! Some kids even make webpages.

Me (trying very hard not to laugh in his face): No, I mean actual programming, like goto subroutine, if this then that.

Ins: Oh, no, not really.
Me: (Beating my head against the wall)...

What's amazing is that the technology teacher didn't even know what I meant when I said either "programming" or "coding".

Meanwhile, I asked the other kid's 8th grade computer programming teacher whether they taught any other languages than Java, and if students were taught to document their code. Answers: Other languages are offered later, in high school (the AP test is only Java, so that's the emphasis), and documenting is not stressed in the level 1 class, but in the second class they do.

## What is an Unusual Event?

My random thoughts on random events posted as a blog comment:

Suppose we have disjoint events $$(E_1,E_2,\dots,E_N),$$ and corresponding probabilities for these events $$(p_1,p_2,\dots,p_N),$$ where $$p_n=\mbox{Prob}(E_n)$$ and $$\sum_{n=1}^N p_n=1.$$ If a particular event $$E_k$$ occurs, what would make us think this was in some sense "unusual" or perhaps "suspicious"? It's not enough that $$p_k$$ be small, since for large $$N$$, even a uniform distribution on the $$E_n$$ will have $$p_k=1/N$$ small. Nor is it enough that $$p_k$$ be much less than $$\max_n p_n,$$ since it is possible that all $$p_n$$ are equal except for one event having many times larger yet still tiny probability. It's not enough if $$p_k$$ is less than nearly all the other $$p_n$$, because all the $$p_n$$ could be very nearly equal.

What does seem to work in the cases I can think of is to choose some factor $$R \gt 1$$, calculate $$\sum\{p_n: p_n \gt R p_k\}$$, and see if this is close to $$1.$$ To work this into a hypothesis test, we could reject the null hypothesis $$H_0$$ if $$\sum\{p_n: p_n\gt R p_k\} \gt (1-1/R),$$ though the expression on the right-hand side is rather arbitrary. With this setup, what value should $$R$$ be? Let $$x_0$$ be a sample we have collected, and consider the standard normal and the $$p=.05$$ rule, where $$\mbox{Prob}(|x_0|\gt 1.96)=0.05.$$ Then $$R=3.71,$$ since $$3.71\cdot \phi(1.96) = \phi(1.1),$$ and $$\mbox{Prob}(|x_0|\gt 1.1)=1/3.71.$$ If we wanted $$R=20,$$ we would need to use a cutoff $$|x_0|\gt 3.135749,$$ which corresponds to a very small standard $$p$$-value of $$0.001714.$$

Clearly, given any $$p$$ cutoff, a.k.a $$\alpha$$, we can find a corresponding factor $$R,$$ and vice-versa. Since the $$p=.05$$ rule is arbitrary, I don't see what difference it makes for the most common cases. Thus, $$p$$-value analysis seems generally ok to me in practice. My concern here is with its justification.