Homework 1 - Granger causality¶
When you observe a system over time, you find one variable B always follows another variable A. In other words, A's current value can very well predict B's future value after a specific amount of time, say 10 minutes. This pattern is consistently observed over a very long time, indicating sufficiently high statistical significance and no sign of cyclicity. Among the 5 relationships below, which is/are consistent with this observation? Provide one real-life example for each consistent case. Do not ChatGPT.
Homework 2 - Imperfect perturbation¶
What will go wrong if the perturbation is imperfect in P->A->B? Consider two scenarios:
- When the perturbation P has a separate way to influence B other than through A
- When a confounder D affects both perturbation P and gene B
Q1: For each scenario, draw the corresponding schematic diagram, write down the decomposition of distribution, and draw a plot between P and A and between P and B. Use them to explain why the imperfect perturbation will cause problems when estimating the effect of A on B. Tip: if a binary perturbation under confounder D is unclear to you, try a continuous perturbation instead.
Q2: The randomized double-blinded placebo-controlled trial avoids the two scenarios above. Why?