🧱 Grid Sampling

Grid sampling is a simple way to obtain samples of some random variable from a distribution . The main idea is to discretize by evaluating it along a grid of values, then sampling from the values proportionally.

The procedure is as follows:

1. Select a grid of values for .
2. For each grid value, calculate .
3. Sample a grid value with probability .

Finding an appropriate grid can often be trial-and-error, and ideally, the grid should cover all values of with non-zero probability, and it shouldn’t contain many values with zero probability.

Multi-Dimensional Sampling §

If we have multiple variables, we can select a grid of values for each and loop over all joint probabilities. For example, with two parameters and :

1. Select a grid of values for and another grid for .
2. For each pair, compute .
3. Calculate marginal probabilities .
4. Calculate conditional probabilities .
5. Sample using .
6. Sample using .