Precision (statistics)

In statistics, the precision matrix or concentration matrix is the matrix inverse of the covariance matrix or dispersion matrix, $P=\Sigma ^{-1}$ .^[1]^[2]^[3] For univariate distributions, the precision matrix degenerates into a scalar precision, defined as the reciprocal of the variance, $p={\frac {1}{\sigma ^{2}}}$ .^[4]

Other summary statistics of statistical dispersion also called precision (or imprecision^[5]^[6]) include the reciprocal of the standard deviation, $p={\frac {1}{\sigma }}$ ;^[3] the standard deviation itself and the relative standard deviation;^[7] as well as the standard error^[8] and the confidence interval (or its half-width, the margin of error).^[9]

^ DeGroot, Morris H. (1969). Optimal Statistical Decisions. New York: McGraw-Hill. p. 56.
^ Davidson, Russell; MacKinnon, James G. (1993). Estimation and Inference in Econometrics. New York: Oxford University Press. p. 144. ISBN 0-19-506011-3.
^ ^a ^b Dodge, Y. (2003). The Oxford Dictionary of Statistical Terms. Oxford University Press. ISBN 0-19-920613-9.
^ Bolstad, W.M.; Curran, J.M. (2016). Introduction to Bayesian Statistics. Wiley. p. 221. ISBN 978-1-118-59315-8. Retrieved 2022-08-13.
^ Natrella, M.G. (2013). Experimental Statistics. Dover Books on Mathematics (in Italian). Dover Publications. p. 21-PA14. ISBN 978-0-486-15455-8. Retrieved 2022-08-14.
^ Balakrishnan, N. (2009). Methods and Applications of Statistics in the Life and Health Sciences. Methods and Applications of Statistics. Wiley. p. 537. ISBN 978-0-470-40509-3. Retrieved 2022-08-14.
^ Ellison, S.L.R.; Farrant, T.J.; Barwick, V. (2009). Practical Statistics for the Analytical Scientist: A Bench Guide. Valid Analytical Measurement. Royal Society of Chemistry. p. 145. ISBN 978-0-85404-131-2. Retrieved 2022-08-14.
^ Wilburn, A.J. (1984). Practical Statistical Sampling for Auditors. Statistics: A Series of Textbooks and Monographs. Taylor & Francis. p. 62. ISBN 978-0-8247-7124-9. Retrieved 2022-08-14.
^ Cumming, G. (2013). Understanding The New Statistics: Effect Sizes, Confidence Intervals, and Meta-Analysis. Multivariate Applications Series. Taylor & Francis. p. 366. ISBN 978-1-136-65918-8. Retrieved 2022-08-14.

[1] DeGroot, Morris H. (1969). Optimal Statistical Decisions. New York: McGraw-Hill. p. 56.

[2] Davidson, Russell; MacKinnon, James G. (1993). Estimation and Inference in Econometrics. New York: Oxford University Press. p. 144. ISBN 0-19-506011-3.

[dodge-3] Dodge, Y. (2003). The Oxford Dictionary of Statistical Terms. Oxford University Press. ISBN 0-19-920613-9.

[Bolstad_Curran_2016_p._221-4] Bolstad, W.M.; Curran, J.M. (2016). Introduction to Bayesian Statistics. Wiley. p. 221. ISBN 978-1-118-59315-8. Retrieved 2022-08-13.

[Natrella_2013_p._21-PA14-5] Natrella, M.G. (2013). Experimental Statistics. Dover Books on Mathematics (in Italian). Dover Publications. p. 21-PA14. ISBN 978-0-486-15455-8. Retrieved 2022-08-14.

[Balakrishnan_2009_p._537-6] Balakrishnan, N. (2009). Methods and Applications of Statistics in the Life and Health Sciences. Methods and Applications of Statistics. Wiley. p. 537. ISBN 978-0-470-40509-3. Retrieved 2022-08-14.

[Ellison_Farrant_Barwick_2009_p._145-7] Ellison, S.L.R.; Farrant, T.J.; Barwick, V. (2009). Practical Statistics for the Analytical Scientist: A Bench Guide. Valid Analytical Measurement. Royal Society of Chemistry. p. 145. ISBN 978-0-85404-131-2. Retrieved 2022-08-14.

[Wilburn_1984_p._62-8] Wilburn, A.J. (1984). Practical Statistical Sampling for Auditors. Statistics: A Series of Textbooks and Monographs. Taylor & Francis. p. 62. ISBN 978-0-8247-7124-9. Retrieved 2022-08-14.

[Cumming_2013_p._366-9] Cumming, G. (2013). Understanding The New Statistics: Effect Sizes, Confidence Intervals, and Meta-Analysis. Multivariate Applications Series. Taylor & Francis. p. 366. ISBN 978-1-136-65918-8. Retrieved 2022-08-14.

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