Points of significance: Bayesian statistics

Journal name:
Nature Methods
Volume:
12,
Pages:
377–378
Year published:
DOI:
doi:10.1038/nmeth.3368
Published online
Corrected online

Today's predictions are tomorrow's priors.

At a glance

Figures

  1. Prior probability distributions represent knowledge about the coin before it is tossed.
    Figure 1: Prior probability distributions represent knowledge about the coin before it is tossed.

    (a) Three different prior distributions of π, the probability of heads. (b) Toss outcomes are combined with the prior to create the posterior distribution used to make inferences about the coin. The likelihood is the probability of observing a given toss outcome, which is π3 for a toss of H3. The gray area corresponds to the probability that the coin is biased toward heads. The error bar is the 95% credible interval (CI) for π. The dotted line is the posterior mean, E(π). The posterior is shown normalized to 4π3 to make its area 1.

  2. Effect of choice of prior and amount of data collected on the posterior.
    Figure 2: Effect of choice of prior and amount of data collected on the posterior.

    All curves are beta(a,b) distributions labeled by their equivalent toss outcome, Ha−1Tb−1. (a) Posteriors for a toss outcome of H3T1 using weakly (H3T1) and strongly (H15T5) head-weighted priors. (b) The effect of a head-weighted prior, H3T1, diminishes with more tosses (4, 20, 100) indicative of a tail-weighted coin (75% tails).

Change history

Corrected online 24 September 2015
In the version of this article initially published, the curves (in red) showing the likelihood distribution in Figure 2 were incorrectly drawn in some panels. The error has been corrected in the HTML and PDF versions of the article.

References

  1. Puga, J.L., Krzywinski, M. & Altman, N. Nat. Methods 12, 277278 (2015).
  2. Kass, R.E. & Raftery, A.E. J. Am. Stat. Assoc. 90, 791 (1995).

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Author information

Affiliations

  1. Jorge López Puga is a Professor of Research Methodology at UCAM Universidad Católica de Murcia.

  2. Martin Krzywinski is a staff scientist at Canada's Michael Smith Genome Sciences Centre.

  3. Naomi Altman is a Professor of Statistics at The Pennsylvania State University.

Competing financial interests

The authors declare no competing financial interests.

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