Scope: Lectures 11-12. Four questions; submit derivations and code/output where requested.
State units and model assumptions. Keep unrounded values in code and round only in your final communication. Revisions and resubmissions are encouraged.
Question 1
Report the normalized model growth factor at z=0, 0.5, and 1 from the supplied script. Describe the normalization and two omitted physical effects.
Work to show: equations, units, assumptions, and a reproducible computation where requested.
Question 2
Estimate f=d ln D/d ln a at z=0.5 with centered finite differences using h=0.01 and h=0.005. Compare the results and state a convergence criterion.
Work to show: equations, units, assumptions, and a reproducible computation where requested.
Question 3
For a Gaussian residual vector, derive the Cholesky-whitened expression for chi-square and explain why explicit matrix inversion is discouraged.
Work to show: equations, units, assumptions, and a reproducible computation where requested.
Question 4
Distinguish a likelihood contour from a marginalized posterior contour. Name one way a prior can affect the latter.
Work to show: equations, units, assumptions, and a reproducible computation where requested.