Exponential families! The secret magic at the heart of traditional statistics.

Exponential families are (sorta) probability distributions that *just work*, in the sense that and the things you would *hope* you can do with them, you can.

Noted here so I have somewhere to dump notes, but not something I am going to go into right now.

Most interesting models are not exponential families. There are curved exponential families which generalise exponential families in some way that I have not looke into.

## Refs

- ShHY04: (2004) Adaptive Model Selection and Assessment for Exponential Family Distributions.
*Technometrics*, 46(3), 306–317. DOI - AlSH04: (2004) Exponential Families for Conditional Random Fields. In Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence (pp. 2–9). Arlington, Virginia, United States: AUAI Press
- Brow86: (1986)
*Fundamentals of statistical exponential families: with applications in statistical decision theory*. Hayward, Calif: Institute of Mathematical Statistics - WaJo08: (2008)
*Graphical models, exponential families, and variational inference*(Vol. 1). - BrCZ10: (2010) Nonparametric regression in exponential families.
*The Annals of Statistics*, 38(4), 2005–2046. DOI - JeMø91: (1991) Pseudolikelihood for Exponential Family Models of Spatial Point Processes.
*The Annals of Applied Probability*, 1(3), 445–461. DOI - Efro78: (1978) The Geometry of Exponential Families.
*The Annals of Statistics*, 6(2), 362–376. DOI - JuSH12: (2012) The RKHS Approach to Minimum Variance Estimation Revisited: Variance Bounds, Sufficient Statistics, and Exponential Families.
*ArXiv:1210.6516 [Math, Stat]*. - TPSR15: (2015) Vector-Space Markov Random Fields via Exponential Families. In Journal of Machine Learning Research (pp. 684–692).