### Encoding and Decoding

• Encoding solves “how does a stimulus cause a pattern of responses?” ($P(\text{response}\|\text{stimulus})$).
• Decoding solves “what do these responses tell us about the stimulus?” ($P(\text{stimulus}\|\text{response})$).

### Basic Coding Model

In the following context, $s(\cdot)$ represents signal, $r(\cdot)$ represents response, $f(\cdot)$ represents filter and $g(\cdot)$ represents nonlinear function.

### Feature Selection

We want to sample the responses of the system to many stimuli so we can characterize what it is about the input that triggers responses.

### Variability

Kullback-Leibler divergence: difference between two probability distribution.

Tuning curve:

The Goodness measure between $P(s_{f}\|\text{spike})$ and $P(s_{f})$:

Distribution:

Mean:

Variance:

#### Poisson spiking

Distribution:

Mean:

Variance:

Fano factor:

Interval distribution: