Statistical Inference Algorithm

A statistical inference algorithm is an inference algorithm that can be implemented by a statistical inference system (to solve a statistical inference task).

• Context:
  • It can apply to a Statistical Model.
  • It can be analyzed by Statistical Inference Theory.
• Example(s):
  • a Statistical Hypothesis Testing Algorithm.
  • a Posterior Probability-based Inference Algorithm.
  • …
• Counter-Example(s):
  • a Logical Inference Task.
• See: Statistical Inference Task, Inductive Inference, Bayes Rule, Probability Function, Random Variable, Random Sample, Statistical Argument, Population Parameter Estimation, Probability Theory, Statistical Learning Task, Inductive Statistics.

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References

2013

• (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/Statistical_inference
  • In statistics, statistical inference is the process of drawing conclusions from data that is subject to random variation, for example, observational errors or sampling variation. More substantially, the terms statistical inference, statistical induction and inferential statistics are used to describe systems of procedures that can be used to draw conclusions from datasets arising from systems affected by random variation, such as observational errors, random sampling, or random experimentation. 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.

    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.

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Statistical_inference
  • Statistical inference or statistical induction comprises the use of Statistics and random sampling to make Inferences concerning some unknown aspect of a Population. It is distinguished from Descriptive Statistics.

    Statistical inference is inference about a population from a random sample drawn from it or, more generally, about a random process from its observed behavior during a finite period of time. It includes:

    • Point Estimation.
    • Interval Estimation.
    • Hypothesis Testing (or Statistical Significance testing)
    • Prediction – see Predictive Inference.
  • There are several distinct schools of thought about the justification of statistical inference. All are based on some idea of what real world phenomena can be reasonably modeled as Probability.
    • Frequency Probability.
    • Bayesian Probability.
    • Fiducial Probability.
  • The topics below are usually included in the area of statistical inference.
    • Statistical Assumptions.
    • Statistical Decision Theory.
    • Estimation Theory
    • Statistical Hypothesis Testing.
    • Revising Opinions in Statistics.
    • Design of Experiments, the Analysis of Variance, and Regression.
    • Survey Sampling.
    • Summarizing Statistical Data

2010

• (AMTA, 2010) ⇒ American Massage Theory Association. (2010). “Glossary of Research Terminology."
  • Inferential Statistics: The family of quantitative analysis techniques that allows one not only to test hypotheses in a study, but also to calculate effect sizes and confidence interval estimations as supplements to hypothesis testing.

2006

• (Dubnicka, 2006) ⇒ Suzanne R. Dubnicka. (2006). “Introduction to Statistics - Handout 11." Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
  • QUOTE: ... Ideally, we would like to use the sample to draw conclusions about the entire population; this is known as inference or statistical inference. ... Statistical inference is the process of drawing conclusions about a population from a sample. In particular, we typically have questions regarding the value of certain population parameters. We use statistical inference to answer these questions about parameters based on the information in the sample, specifically the values of statistics. Estimation and hypothesis testing are the two common forms of statistical inference. ...
• (Cox, 2006) ⇒ David R. Cox. (2006). “Principles of Statistical Inference." Cambridge University Press. ISBN:9780521685672

2002

• (Garthwaite et al., 2002) ⇒ Paul Garthwaite, Ian Jolliffe, and Byron Jones. (2002). “Statistical Inference." Oxford University Press. ISBN:0-19-857226-3

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