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Posts tagged with causality




Parameters

  • The shape of the continents depends on the global temperature. (Cold locks ice in polar caps.) Google “Morse theory”.
  • The price of housing always rises, until it doesn’t.
     
  • You develop a system of habits to discipline yourself; maxims for self-motivation; then the working world changes on you. Loyalty is no longer rewarded. Hard work is less valued than the ability to make PlentyOfFish.com.
  • For years the normal trading range of [insert spread, instrument, or security] is X, until one day sufficiently many (external) parameters shift. The market changes and you see a 20-sigma event. Heroes only.

  • Whoever coded your profile website (chi.mp, flavors.me, tumblr), wrote a route that takes a string as parameter. Entering the name isomorphismes into this function fetches this webdata. Entering your name fetches your webdata. All part of one and the same formula.
  • The Lotka-Volterra equations of a large ecosystem, dancing as the sliders shift around in their hypercube. Death and life hang in the balance. And it’s literally a balance. If the fulcrum moves so far that the lever hits the ground, a species will either become extinct or overpopulate the ecosystem (like an algal bloom)—either phase change being irreversible. (Er, at least anti-entropic.)
     
  • You think you know yourself, until you step into a new context—new country, new career, new city—and latent aspects of you become dominant.

    Who was I before? If I was her then and am this now, what is the underlying me?

    Self as a function of circumstance. Perhaps just as constant at root, but reactive; responsive; springy; primed for change.




Contrary to common folklore, causal relationships can be distinguished from spurious covariations using inductive reasoning.

Judea Pearl, Causality





You’ve run the regression.  You see the t’s, the β’s, and the p’s.  But what do they mean?  Don’t panic.  This book will tell you. [T]he estimators in common use almost always have a simple interpretation that is not heavily model dependent….  A leading example is linear regression, which provides useful information about the conditional mean function regardless of the shape of this function.  Likewise, instrumental variables estimate an average causal effect for a well-defined population even if the instrument does not affect everyone. Hooray!

You’ve run the regression.  You see the t’s, the β’s, and the p’s.  But what do they mean?  Don’t panic.  This book will tell you.

[T]he estimators in common use almost always have a simple interpretation that is not heavily model dependent….  A leading example is linear regression, which provides useful information about the conditional mean function regardless of the shape of this function.  Likewise, instrumental variables estimate an average causal effect for a well-defined population even if the instrument does not affect everyone.

Hooray!




Anscombes quartet The four data sets are different, yet they have the same “line of best fit” as computed by ordinary least squares regression.

Anscombes quartet

The four data sets are different, yet they have the same “line of best fit” as computed by ordinary least squares regression.


hi-res




extrapolation and interpolation The most important lesson I learned from this book:  regression is reliable for interpolation, but not for extrapolation.  Even further, your observations really need to cover the whole gamut of causal variables, intersections included, to justify faith in your regressions. Imagine you have two causal variables, A and B, that are causing X.  Maybe your data cover a wide range of observations of A — some high, some low, some in-between.  And you have, too, the whole gamut of observations of B — high, low, and medium.  It might still be the case that you haven’t observed A and B together (not seen ).  Or that you’ve only observed them together (not seen ).  In either case, your regression is effectively extrapolating to the other causal region and you should not trust it. Let’s keep the math sexy.  Say you meet an attractive member of your favourite sex.  This person A) likes to hunt, and B) is otherwise vegetarian.  Your prejudices  are that you don’t like hunters () and you do like vegetarians ().  By comparing the magnitudes of these preferences, you deduce that you should not get along with this attractive person, because the bad A part outweighs the good B part. However, since you haven’t observed both A and B positive at once, your preconceptions are not to be trusted.  Despite your instincts , you go out on a date with Mr or Ms (A>0, B>0) and have a fantastic time.  Turns out there was a positive interaction term in the  range, it also correlates positively with the noise (it wasn’t noise, just unknown knowledge), and you’ve found your soul mate.

extrapolation and interpolation

The most important lesson I learned from this book:  regression is reliable for interpolation, but not for extrapolation.  Even further, your observations really need to cover the whole gamut of causal variables, intersections included, to justify faith in your regressions.

Imagine you have two causal variables, A and B, that are causing X.  Maybe your data cover a wide range of observations of A — some high, some low, some in-between.  And you have, too, the whole gamut of observations of B — high, low, and medium.  It might still be the case that you haven’t observed A and B together (not seen ).  Or that you’ve only observed them together (not seen ).  In either case, your regression is effectively extrapolating to the other causal region and you should not trust it.

Let’s keep the math sexy.  Say you meet an attractive member of your favourite sex.  This person A) likes to hunt, and B) is otherwise vegetarian.  Your prejudices  are that you don’t like hunters () and you do like vegetarians ().  By comparing the magnitudes of these preferences, you deduce that you should not get along with this attractive person, because the bad A part outweighs the good B part.

However, since you haven’t observed both A and B positive at once, your preconceptions are not to be trusted.  Despite your instincts , you go out on a date with Mr or Ms (A>0, B>0) and have a fantastic time.  Turns out there was a positive interaction term in the  range, it also correlates positively with the noise (it wasn’t noise, just unknown knowledge), and you’ve found your soul mate.