<img width="888" height="99" alt="Image" src="https://github.com/user-attachments/assets/7b4dfd18-f1bb-429e-8f8e-86ead63a1dad" /> this should probably be y^_{1:t-1}? <img width="360" height="54" alt="Image" src="https://github.com/user-attachments/assets/9fe7e9a3-3556-4595-9027-3baac13e0716" />
