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