# Chapter 2 Hello bookdown

## 2.1 Integrating Gaussian Processes for \(\theta_{dkt}\)

To model \(\theta_{dkt}\) using a GP, you would generally follow these steps:

### 2.1.1 Define a Covariance Function:

Choose a covariance function that defines the temporal correlation structure for the GP. The choice of this function (e.g., squared exponential, Matérn) can significantly impact the smoothness and variability of the simulated paths.

### 2.1.2 Simulate GP Paths for Topic Probabilities:

For each individual and topic, simulate a GP path that represents the evolution of the activation probability over time. This simulation would replace the direct random generation of \(\theta_{dkt}\) – we can use a gaussian process with various mean functions as before values and ensure that the probabilities change in a continuous and smooth manner.