nhaliday + dependence-independence   19

Vladimir Novakovski's answer to What financial advice would you give to a 21-year-old? - Quora
Learn economics and see that investment and consumption levels (as percentages) depend only marginally on age and existing net worth and mostly on your risk preferences and utility function.
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10 weeks ago by nhaliday
Variance of product of multiple random variables - Cross Validated
prod_i (var[X_i] + (E[X_i])^2) - prod_i (E[X_i])^2

two variable case: var[X] var[Y] + var[X] (E[Y])^2 + (E[X])^2 var[Y]
nibble  q-n-a  overflow  stats  probability  math  identity  moments  arrows  multiplicative  iidness  dependence-independence 
october 2017 by nhaliday
Pearson correlation coefficient - Wikipedia
https://en.wikipedia.org/wiki/Coefficient_of_determination
what does this mean?: https://twitter.com/GarettJones/status/863546692724858880
deleted but it was about the Pearson correlation distance: 1-r
I guess it's a metric

https://en.wikipedia.org/wiki/Explained_variation

http://infoproc.blogspot.com/2014/02/correlation-and-variance.html
A less misleading way to think about the correlation R is as follows: given X,Y from a standardized bivariate distribution with correlation R, an increase in X leads to an expected increase in Y: dY = R dX. In other words, students with +1 SD SAT score have, on average, roughly +0.4 SD college GPAs. Similarly, students with +1 SD college GPAs have on average +0.4 SAT.

this reminds me of the breeder's equation (but it uses r instead of h^2, so it can't actually be the same)

https://www.reddit.com/r/slatestarcodex/comments/631haf/on_the_commentariat_here_and_why_i_dont_think_i/dfx4e2s/
stats  science  hypothesis-testing  correlation  metrics  plots  regression  wiki  reference  nibble  methodology  multi  twitter  social  discussion  best-practices  econotariat  garett-jones  concept  conceptual-vocab  accuracy  causation  acm  matrix-factorization  todo  explanation  yoga  hsu  street-fighting  levers  🌞  2014  scitariat  variance-components  meta:prediction  biodet  s:**  mental-math  reddit  commentary  ssc  poast  gwern  data-science  metric-space  similarity  measure  dependence-independence 
may 2017 by nhaliday
Mixing (mathematics) - Wikipedia
One way to describe this is that strong mixing implies that for any two possible states of the system (realizations of the random variable), when given a sufficient amount of time between the two states, the occurrence of the states is independent.

Mixing coefficient is
α(n) = sup{|P(A∪B) - P(A)P(B)| : A in σ(X_0, ..., X_{t-1}), B in σ(X_{t+n}, ...), t >= 0}
for σ(...) the sigma algebra generated by those r.v.s.

So it's a notion of total variational distance between the true distribution and the product distribution.
concept  math  acm  physics  probability  stochastic-processes  definition  mixing  iidness  wiki  reference  nibble  limits  ergodic  math.DS  measure  dependence-independence 
february 2017 by nhaliday
Guess the Correlation
some basic rules?
- more trouble w/ high than low end (maybe because I'm just guessing slope/omitting outliers?)
- should try out w/ correlated Gaussians to get some intuition
games  learning  stats  intuition  thinking  hmm  street-fighting  correlation  instinct  mental-math  nitty-gritty  simulation  operational  todo  spock  quantitative-qualitative  dependence-independence 
july 2016 by nhaliday

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