diff --git a/lectures/multivariate_normal.md b/lectures/multivariate_normal.md index efe60e043..49aa0f9e9 100644 --- a/lectures/multivariate_normal.md +++ b/lectures/multivariate_normal.md @@ -1454,6 +1454,13 @@ y_{T} \alpha_{0}\\ \vdots\\ \alpha_{0} +\end{array}\right]}} +\underset{\equiv u}{\underbrace{\left[\begin{array}{c} +u_{1} \\ +u_2 \\ +u_3\\ +u_4\\ +\vdots\\ +u_T \end{array}\right]}} $$ diff --git a/lectures/prob_meaning.md b/lectures/prob_meaning.md index 87535257e..dfde21873 100644 --- a/lectures/prob_meaning.md +++ b/lectures/prob_meaning.md @@ -710,15 +710,13 @@ Typically, the functional form of the likelihood function determines the functio A natural question to ask is why should a person's personal prior about a parameter $\theta$ be restricted to be described by a conjugate prior? -Why not some other functional form that more sincerely describes the person's beliefs. +Why not some other functional form that more sincerely describes the person's beliefs? -To be argumentative, one could ask, why should the form of the likelihood function have *anything* to say about my -personal beliefs about $\theta$? +To be argumentative, one could ask, why should the form of the likelihood function have *anything* to say about my personal beliefs about $\theta$? A dignified response to that question is, well, it shouldn't, but if you want to compute a posterior easily you'll just be happier if your prior is conjugate to your likelihood. -Otherwise, your posterior won't have a convenient analytical form and you'll be in the situation of wanting to -apply the Markov chain Monte Carlo techniques deployed in {doc}`this quantecon lecture `. +Otherwise, your posterior won't have a convenient analytical form and you'll be in the situation of wanting to apply the Markov chain Monte Carlo techniques deployed in {doc}`this quantecon lecture `. We also apply these powerful methods to approximating Bayesian posteriors for non-conjugate priors in {doc}`this quantecon lecture ` and {doc}`this quantecon lecture `