Adam Bull


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Causal without correlation, how?

No, it's just causation without correlation; correlation is defined to be the aggregate effect.

What is Akaike statistics?

I wouldn't read too much into that quote, it seems pretty misleading to me. There are essentially two statistical paradigms, frequentism and Bayesianism, which you probably already know about.

The third item is referring to the likelihood principle, a philosophical position which states that inference should be based only on the likelihood. There are a small number of techniques in both frequentism and Bayesianism which have this property, but in general it's pretty restrictive, and I don't know of any practitioners who take it seriously.

You'll notice the fourth item is not referring to Akaike in general, but rather to the Akaike information criterion (AIC). This is a specific technique for model selection, which happens to depend only on the likelihood and the model size.

If you were the kind of person who enjoys armchair statistical philosophy, and has heard the likelihood principle is too restrictive, you might like to enlarge it to also allow dependence on the model size; you could then describe this as AIC-based statistics. It's not a term in common usage, and I think that principle is still too restrictive to be of much interest.

How to Lose a Fair Game

(Still not financial advice.)

Well, Kelly is optimal if you have infinite time, or logarithmic utility. In practice we all have finite time, and many of us are more risk-averse. Plus, as you mentioned earlier, Kelly is only optimal if you know the payoff distribution, which you don't.

I'm not saying leverage can't be a useful addition to a portfolio; just that there are also reasonable concerns about it. Yes, a leveraged mix of equities and bonds has done pretty well the past forty years. But the thirty before that, it was a disaster. Sure, the macroeconomic regime was different then; but in a world of negative interest rates, are you sure it won't change again?

How to Lose a Fair Game

(This is not financial advice.)

I'm not sure the linked article shows it to be false, exactly. If you look at the first graph, you can see that over 135 years of US data, 1x leverage returns about 4% annually, and 2x leverage about 5%, with double the risk. That's pretty bad, unless you're desperate for risk.

Now, that plot doesn't include dividends, which are an important part of the calculation. And using different countries or time periods will give different results, as they demonstrate later on. Still, if you're discussing a type of investment the SEC specifically warns people about, there might be more to say here?

The US Already Has A Wealth Tax

Most Western countries levy some form of CGT; to avoid it, you'd need to move to a low-tax jurisdiction like Switzerland or Singapore. It's certainly possible for founders and investors to do that, but it's a pretty big life change.

Moving from one US state to another, on the other hand, is pretty easy.

Maths writer/cowritter needed: how you can't distinguish early exponential from early sigmoid

In the simplest case where the errors are Gaussian, this would probably be covered by standard regression lower bounds? You'd show that exponentials and sigmoids can be made close in L² over a restricted domain, then deduce it requires many samples / low noise to distinguish them.

Or as Aaro says above, maybe better to parametrise the sigmoid, and take the Fisher information of the turning point parameter.