From a683057340eae7627757e22a9812f1bed8034466 Mon Sep 17 00:00:00 2001 From: rlouf Date: Thu, 23 Jan 2025 04:12:52 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20blackjax?= =?UTF-8?q?-devs/sampling-book@960dea0c33b7fd180c75c571ece4f142d0f25e5e=20?= =?UTF-8?q?=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- algorithms/mclmc.html | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/algorithms/mclmc.html b/algorithms/mclmc.html index c7dac27..27584d6 100644 --- a/algorithms/mclmc.html +++ b/algorithms/mclmc.html @@ -672,8 +672,8 @@

Validate the choice of \(\epsilon

A more complex example#

We now consider a more complex model, of stock volatility.

The returns \(r_n\) are modeled by a Student’s-t distribution whose scale (volatility) \(R_n\) is time varying and unknown. The prior for \(\log R_n\) is a Gaussian random walk, with an exponential distribution of the random walk step-size \(\sigma\). An exponential prior is also taken for the Student’s-t degrees of freedom \(\nu\). The generative process of the data is:

-
-(1)#\[\begin{align} +
+(1)#\[\begin{align} &r_n / R_n \sim \text{Student's-t}(\nu) \qquad &&\nu \sim \text{Exp}(\lambda = 1/10) \\ \nonumber &\log R_n \sim \mathcal{N}(\log R_{n-1}, \sigma) \qquad