Multivariate binary probability distribution in the Grassmann formalism

We propose a probability distribution for multivariate binary random variables. The is expressed as principal minors of the parameter matrix, which matrix analogous to inverse covariance in Gaussian distribution. In our model, partition function, central moments, and marginal conditional distributions are analytically. That is, summation over all possible states not necessary obtaining function various expected values, problem with conventional Bernoulli proposed model has many similarities For example, terms its respectively. represents sort partial correlation. can be derived using Grassmann numbers, anticommuting numbers. Analytical expressions also useful generating numbers Hence, we investigated sampling estimates synthetic datasets. computational complexity maximum likelihood estimation from observed data proportional number unique states, required case empirically that appear consistent asymptotically normal.