a parameter of probability distribution govern the probabilities associated with different conditions in that distribution. It is usually a vector:

For instance, for uniform \(Uni(\alpha, \beta)\), parameter \(\theta = [\alpha, \beta]\).

importantly, for a discrete distribution system with 6 parameters, we only need 5 independent parameters to be able to satisfy the entire system. This is because a probability distribution must sum to 1.

however, for a conditional probability:

\begin{equation} p(x|a) \end{equation}

we need to specificity \((n-1)m\) parameters, whereby \(m\) is the number of states \(a\) can take, and \(n\) the number of states \(n\) can take. Each group of \(m\) has to add up to \(1\).

We want to learn a Baysian Network’s parameters from data.

• unbiased parameter learning
• Maximum Likelihood Parameter Learning
• Baysian Parameter Learning

If we want to do it in a Bayes Net:

parameter learning in Baysian Network

1. tag EEG by data type (what mental stage does it come from?)
2. per region, per data type, we take a band-power series
3. calculate statistics per series
4. shove the results into something interpretable

Conclusion

N1 results performs the best across brain regions; where the data came from didn’t change performance by much.

PARRY is if ELIZA had mental states such as fear, anger, and mistrust. Mentions of various things in the user turn increases or decreases each variable

Differential Equations in more than one independent variable:

\begin{equation} f(x_1, \dots, x_{n}) \end{equation}