Exercise 21.2 - Laplace approximation to normal-gamma

Answers

This is the same with exercise 21.1 when the prior is uniformative. Note that:

\begin{align} \sum_{n = 1}^{N} {(y_{n} - μ)}^{2} = & \sum_{n = 1}^{N} {((y_{n} - ȳ) - (μ - ȳ))}^{2} \\ = & \sum_{n = 1}^{N} {(y_{n} - ȳ)}^{2} + \sum_{n = 1}^{N} {(μ - ȳ)}^{2} + 2 (μ - ȳ) \cdot \sum_{n = 1}^{N} (y_{n} - ȳ) \\ = & N s^{2} + N {(μ - ȳ)}^{2}, \end{align}

where $s^{2} = \frac{1}{N} \sum_{n = 1}^{N} {(y_{n} - ȳ)}^{2}$

Conclusions for all problems (a), (b) and (c) have been included in those of the previous exercise.

solour_lfq

2021-03-24 13:42