Statistical & Financial Consulting by Stanford PhD

Home Page

Naive Bayes is a classification method. Suppose the data are split into
classes and we observe
variables
_{ }
We conveniently assume that in each class the variables are independent (hence the term "naive"). We estimate densities of the continuous variables and probability mass functions of the discrete variables as
_{ }
in each class
Then, whenever we see a data point with unknown class membership and known
_{ }
we apply the Bayes rule. We estimate the probability of class
membership as

where

Naive Bayes performs well in many settings but fails completely in situations where the classes are distinguished by the codependency structure of

Here the two variables

Barber, D. (2014). Bayesian Reasoning and Machine Learning. Cambridge University Press.

Han, J., Kamber, M. & Pei, J. (2012). Data mining: Concepts and Techniques (3rd ed). Morgan-Kaufman.

Hastie, T., Tibshirani, R., & Friedman, J. H. (2008). The elements of statistical learning: Data mining, inference, and prediction. New York: Springer.

Bishop, C. M. (2006) Pattern Recognition and Machine Learning. New York: Springer.

Witten, I. H., Frank, E., Hall, M., A., & Pal, C. J. (2017). Data Mining: Practical Machine Learning Tools and Techniques (4th ed). New York: Morgan-Kaufmann.

Duda, R. O., Hart, P. E., & Stork, D. G. (2000). Pattern Classification (2nd ed). New York: Wiley-Interscience.

- Detailed description of the services offered in the areas of statistical and financial consulting: home page, types of service, experience, case studies, payment options and statistics tutoring
- Directory of financial topics