Vinícius L
4.2K posts

Vinícius L
@viniliff
PhD student in statistics in Madrid, Spain. Interested in causal inference, statistical dependence and friendships. Posts mainly in Portuguese and English.







Not only does causation NOT imply correlation, it doesn’t even imply statistical dependence! Here’s a snippet from my friend @viniliff master’s thesis on copulas & causality, showing variables can be causally connected yet completely independent. 👇




We usually repeat that correlation doesn’t imply causation, which is true. But the reverse, causation doesn’t imply correlation, is ALSO true. Let X~N(0,1) and Y=X^2. In this example, X causes Y. But the correlation between X and Y is Corr(X,Y)=Corr(X,X^2)=Cov(X,X^2)/(σ_X*σ_(X^2))=(E[X*X^2]-E[X]*E[X^2])/(σ_X*σ_(X^2))=0. Why?👇 The function h(x)=x^3 is odd: (-x)^3=-x^3 and the distribution is symmetric around 0, f is even: f(x)=f(-x) Thus (x^3)*f(x) is odd (odd*even=odd function) and the integral of an odd function over a symmetric interval is 0. Thus E[X^3]=∫X^3*f(x)dx=0 (the integral is from -♾️ to ♾️) The same occurs with the function g(x)=x because g(-x)=-x=-g(x) (it’s odd). So E[X]=∫X*f(x)dx=0 (the integral is again from -♾️ to ♾️) Thus Corr(X,Y)=0 because Cov(X,X^2)=0. Thus we have proven that causation DOES NOT IMPLY correlation. Q. E. D. ▪️


Not only does causation NOT imply correlation, it doesn’t even imply statistical dependence! Here’s a snippet from my friend @viniliff master’s thesis on copulas & causality, showing variables can be causally connected yet completely independent. 👇





Em cursos de econometria padrão, variáveis colisoras quase nunca aparecem. Por isso, fiz um exercício bobinho derivando o viés de colisão num modelo linear, direto dos parâmetros estruturais. Uma forma simples de ver o que geralmente fica de fora.


Tem uma pergunta q da pra vc fazer pra um estudante de "exatas" q diz muito sobre o tipo de estudante q ele é O q vc acha q é a matemática? É uma descoberta da humanidade, a lingua do universo? Ou é uma invenção, construída socialmente pra descrever certos conceitos da realidade?



Languages I speak: 🇲🇱 French 🇰🇪 English 🇲🇰 Albanian Basic understanding: 🇸🇷 Dutch 🇱🇺 German Languages I would like to learn: 🇨🇺 Spanish 🇨🇭 Italian

languages I speak: 🇧🇷 portuguese 🇦🇷 spanish 🇺🇸 english I can sustain a conversation 🇮🇹 italian 🇩🇪 german basic understanding 🇫🇷 french would like to learn 🇮🇷 farsi 🇱🇧 arabic 🍝 latin 🇵🇾🇧🇷 guaraní 🇵🇪🇧🇴 quechua


