Statistics Research Activity

AKA: Statistics Research, Theoretical Statistics, Mathematical Statistics.
Context:
- It can be supported by:
- It can range from being Applied Statistics Research to being Theoretical Statistics Research.
- It can support:
See: Statistics Research Area, Statistics Discipline, Machine Learning Research Activity, Data Mining Research Activity.

References

(Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Mathematical_statistics
- Mathematical statistics is the study of Statistics from a mathematical standpoint, using Probability Theory as well as other branches of Mathematics such as Linear Algebra and analysis. The term "mathematical statistics" is closely related to “Statistical Theory” but also embraces modelling for Actuarial Science and non-statistical Probability Theory.
- Statistics deals with gaining information from data. In practice, Data often contain some Randomness or Uncertainty. Statistics handles such data using methods of probability theory.
- Statistics is divided into:
  - Descriptive Statistics - the part of statistics that describes data, i.e. summarises the data and their typical properties
  - Inferential Statistics - the part of statistics that draws conclusions from data, i.e. checks whether the data fulfill some condition and gives guarantees on the involved uncertainty.
Master's Degree in Statistics at the University of Chicago. http://www.stat.uchicago.edu/admissions/ms-degree.html
- Mathematical Statistics: Focuses on theoretical statistics, probability and stochastic processes. Provides an excellent background for pursuing doctoral studies in statistics, finance and other disciplines in which probability and statistics are heavily used.

(Mitchell, 2006) ⇒ Tom M. Mitchell. (2006). “The Discipline of Machine Learning." Machine Learning Department technical report CMU-ML-06-108, Carnegie Mellon University.
- A Statistician asks: “What can be inferred from data plus a set of modeling assumptions, with what reliability?”

Joe Romano. (2005). http://www-stat.stanford.edu/brochure/part4.html#romano
- Statistics is concerned with making sense or inferences about the world based on limited information and uncertainties. In contrast, mathematics is exact. The goal is to prove theorems based on a well-defined set of assumptions. ... Mathematical statistics serves to precisely quantify and explain what can be learned through "experimentation," in spite of having to acknowledge our uncertainty in the process.