E5. To be completed after lesson 22

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Exercise 5.1

Describe in words the difference between a parametric and nonparametric bootstrap for computing confidence intervals of maximum likelihood estimates.

Exercise 5.2

You may have heard that curve fitting involves “minimizing the sum of the square of the residuals.” If indeed finding the MLE for the pertinent parameters is equivalent to minimizing the sum of the square of the residuals, what underlying assumptions are there in the statistical model?

Exercise 5.3

Why can’t we use scipy.optimize.least_squares() on the Singer data for mRNA counts from smFISH experiments?

Exercise 5.4

In your mind, is there a fundamental difference between maximum likelihood estimation for variate-covariate models and the other parametric models we have encountered before?

Exercise 5.5

Write down any questions or points of confusion that you have.