Statistical Science

Statistical Inference: The Big Picture

Robert E. Kass

Full-text: Open access

Abstract

Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism, serves as a foundation for inference. Statistical pragmatism is inclusive and emphasizes the assumptions that connect statistical models with observed data. I argue that introductory courses often mischaracterize the process of statistical inference and I propose an alternative “big picture” depiction.

Article information

Source
Statist. Sci. Volume 26, Number 1 (2011), 1-9.

Dates
First available in Project Euclid: 9 June 2011

Permanent link to this document
http://projecteuclid.org/euclid.ss/1307626554

Digital Object Identifier
doi:10.1214/10-STS337

Mathematical Reviews number (MathSciNet)
MR2849898

Citation

Kass, Robert E. Statistical Inference: The Big Picture. Statist. Sci. 26 (2011), no. 1, 1--9. doi:10.1214/10-STS337. http://projecteuclid.org/euclid.ss/1307626554.


Export citation

References

  • Barnett, V. (1999). Comparative Statistical Inference, 3rd ed. Wiley, New York.
  • Behseta, S., Kass, R. E., Moorman, D. and Olson, C. R. (2007). Testing equality of several functions: Analysis of single-unit firing rate curves across multiple experimental conditions. Statist. Med. 26 3958–3975.
  • Brown, E. N. and Kass, R. E. (2009). What is statistics? (with discussion). Amer. Statist. 63 105–123.
  • Cox, D. R. (1990). Role of models in statistical analysis. Statist. Sci. 5 169–174.
  • DiMatteo, I., Genovese, C. R. and Kass, R. E. (2001). Bayesian curve-fitting with free-knot splines. Biometrika 88 1055–1071.
  • Freedman, D., Pisani, R. and Purves, R. (2007). Statistics, 4th ed. W. W. Norton, New York.
  • Freedman, D. and Ziesel (1988). From mouse-to-man: The quantitative assessment of cancer risks (with discussion). Statist. Sci. 3 3–56.
  • Glymour, C. (2001). Instrumental probability. Monist 84 284–300.
  • Hecht, S., Schlaer, S. and Pirenne, M. H. (1942). Energy, quanta and vision. J. Gen. Physiol. 25 819–840.
  • Kass, R. E. (2006). Kinds of Bayesians (comment on articles by Berger and by Goldstein). Bayesian Anal. 1 437–440.
  • Kass, R. E., Ventura, V. and Brown, E. N. (2005). Statistical issues in the analysis of neuronal data. J. Neurophysiol. 94 8–25.
  • Kass, R. E. and Wasserman, L. A. (1996). The selection of prior distributions by formal rules. J. Amer. Statist. Assoc. 91 1343–1370.
  • Lehmann, E. L. (1990). Model specification: The views of Fisher and Neyman, and later developments. Statist. Sci. 5 160–168.
  • Lenhard, J. (2006). Models and statistical inference: The controversy between Fisher and Neyman–Pearson. British J. Philos. Sci. 57 69–91.
  • Lovett, M., Meyer, O. and Thille, C. (2008). The open learning initiative: Measuring the effectiveness of the OLI statistics course in accelerating student learning. J. Interact. Media Educ. 14.
  • Moore, D. S. and McCabe, G. (2005). Introduction to the Practice of Statistics, 5th ed. W. H. Freeman, New York.
  • Olson, C. R., Gettner, S. N., Ventura, V., Carta, R. and Kass, R. E. (2001). Neuronal activity in macaque supplementary eye field during planning of saccades in response to pattern and spatial cues. J. Neurophysiol. 84 1369–1384.
  • Robert, C. P., Chopin, N. and Rousseau, J. (2009). Harold Jeffreys’ theory of probability revisited (with discussion). Statist. Sci. 24 141–194.
  • Rollenhagen, J. E. and Olson, C. R. (2005). Low-frequency oscillations arising from competitive interactions between visual stimuli in macaque inferotemporal cortex. J. Neurophysiol. 94 3368–3387.
  • Stanford, P. K. (2006). Exceeding Our Grasp. Oxford Univ. Press.
  • Wallstrom, G., Liebner, J. and Kass, R. E. (2008). An implementation of Bayesian adaptive regression splines (BARS) in C with S and R wrappers. J. Statist. Software 26 1–21.