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Uncertainty and the conditional variance

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  • 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

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    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. Shangari, Dhruv & Chen, Jiahua, 2012. "Partial monotonicity of entropy measures," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1935-1940.
    2. 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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