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Uncertainty and the conditional variance

Author

Listed:
  • Chen, Jiahua
  • van Eeden, Constance
  • Zidek, James
Abstract
Statisticians have long viewed the quest for more information, for example through the acquisition of additional data, as being central to the goal of reducing uncertainty about some aspect of the world. This paper explores that objective through the variance, a common way of quantifying uncertainty. In particular, it examines the relationship between information and uncertainty. Surprisingly it shows that increasing the amount of information can in some cases increase the variance while in others it can decrease it. Which of these occurs is not explained by the seductive thesis that it depends simply on whether that uncertainty is merely aleatory-due to chance alone-or epistemic-due to lack of knowledge. Through examples it shows the relationship to be complex and a general theory elusive.

Suggested Citation

  • Chen, Jiahua & van Eeden, Constance & Zidek, James, 2010. "Uncertainty and the conditional variance," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1764-1770, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1764-1770
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    References listed on IDEAS

    as
    1. Burdett, Kenneth, 1996. "Truncated means and variances," Economics Letters, Elsevier, vol. 52(3), pages 263-267, September.
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    Cited by:

    1. Jiahua Chen, 2013. "A Partial Order on Uncertainty and Information," Journal of Theoretical Probability, Springer, vol. 26(2), pages 349-359, June.
    2. Shangari, Dhruv & Chen, Jiahua, 2012. "Partial monotonicity of entropy measures," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1935-1940.
    3. Alexis Hannart & Michael Ghil & Jean-Louis Dufresne & Philippe Naveau, 2013. "Disconcerting learning on climate sensitivity and the uncertain future of uncertainty," Climatic Change, Springer, vol. 119(3), pages 585-601, August.
    4. Gupta, Nitin & Bajaj, Rakesh Kumar, 2013. "On partial monotonic behaviour of some entropy measures," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1330-1338.

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