# Eleisha's Segment 22: Uncertainty of Derived Parameters

To Compute:

1. In lecture slide 3, suppose (for some perverse reason) we were interested in a quantity $\displaystyle f = b_3/b_5$ instead of $\displaystyle f = b_3b_5$ . Calculate a numerical estimate of this new $\displaystyle f$ and its standard error.

The variance of $\displaystyle f$ can be calculated as:

$\displaystyle \text{Variance} = \bigtriangledown f \Sigma \bigtriangledown f^T$ In this case:

$\displaystyle \bigtriangledown f = (0, 0, \frac{1}{b_5}, 0, \frac{-b_3}{b_5^2} )$

2. Same set up, but plot a histogram of the distribution of $\displaystyle f$ by sampling from its posterior distribution (using Python, MATLAB, or any other platform).

Histogram: