# Statistical Inference Theory

A Statistical Inference Theory is a Statistical Theory that attempts to create meta-models for Stochastic Processes.

## References

### 2014

• (Wikipedia, 2011) ⇒ http://en.wikipedia.org/wiki/Statistical_inference
• In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation.[2] Initial requirements of such a system of procedures for inference and induction are that the system should produce reasonable answers when applied to well-defined situations and that it should be general enough to be applied across a range of situations. Inferential statistics are used to test hypotheses and make estimations using sample data. Whereas descriptive statistics describe a sample, inferential statistics infer predictions about a larger population than the sample represents.

The outcome of statistical inference may be an answer to the question "what should be done next?", where this might be a decision about making further experiments or surveys, or about drawing a conclusion before implementing some organizational or governmental policy.

1. Trevor Hastie, Robert Tibshirani, Jerome Friedman (2009) The Elements of Statistical Learning, Springer-Verlag .
2. Upton, G., Cook, I. (2008) Oxford Dictionary of Statistics, OUP. ISBN 978-0-19-954145-4

### 2008

• (Vapnik, 2008) ⇒ Vladimir N. Vapnik. (2008). “COLT interview - Vladimir Vapnik." http://www.learningtheory.org/
• My current research interest is to develop advanced models of empirical inference. I think that the problem of machine learning is not just a technical problem. It is a general problem of philosophy of empirical inference. One of the ways for inference is induction. The main philosophy of inference developed in the past strongly connected the empirical inference to the inductive learning process. I believe that induction is a rather restrictive model of learning and I am trying to develop more advanced models. First, I am trying to develop non-inductive methods of inference, such as transductive inference, selective inference, and many other options. Second, I am trying to introduce non-classical ways of inference.

### 2000

• (Vapnik, 2000) ⇒ Vladimir N. Vapnik. (2000). “The Nature of Statistical Learning Theory (2nd Edition).” Springer. ISBN:0387987800