Nicholas J. Barrowman and Ransom A. Myers.
"Raindrop Plots: A New Way to Display Collections of Likelihoods and Distributions".
In The American Statistician, vol. 57, no. 4, pp. 268--274, 2003.

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Abstract:

In a variety of settings, it is desirable to display a collection of likelihoods over a common interval. One approach is simply to superimpose the likelihood curves. However, where there are more than a handful of curves, such displays are extremely difficult to decipher. An alternative is simply to display a point estimate with a confidence interval, corresponding to each likelihood. However, these may be inadequate when the likelihood is not approximately normal, as can occur with small sample sizes or nonlinear models. A second dimension is needed to gauge the relative plausibility of different parameter values. We introduce the raindrop plot, a shaded figure over the range of parameter values having log-likelihood greater than some cutoff, with height varying proportional to the difference between the log- likelihood and the cutoff. In the case of a normal likelihood, this produces a reflected parabola so that deviations from normality can be easily detected. An analogue of the raindrop plot can also be used to display estimated random effect distributions, posterior distributions, and predictive distributions.

Bibtex:

@Article{        barrowman:2003:RDPD,
  author = 	 {Nicholas J. Barrowman and Ransom A. Myers},
  title = 	 {Raindrop Plots: A New Way to Display Collections of Likelihoods and Distributions},
  journal = 	 {The American Statistician},
  year = 	 {2003},
  volume = 	 {57},
  number = 	 {4},
  pages = 	 {268--274},
  month = 	 {November},
}

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References:

Agresti, A. (1990), Categorical Data Analysis, New York: Wiley.
Balanda, K. P., and MacGillivray, H. L. (1988), "Kurtosis: A Critical Review," The American Statistician, 42, 111-119.
Barrowman, N. J., and Myers, R. A. (2000), "Still More Spawner-Recruitment Curves: The Hockey Stick and its Generalizations," Canadian Journal of Fisheries and Aquatic Sciences, 57, 665-676.
Barrowman, N. J., Myers, R. A., Hilborn, R., Kehler, D. G., and Field, C. A. (2003), "The Variability Among Populations of Coho Salmon in the Maximum Reproductive Rate and Depensation," Ecological Applications, 13, 784-793.
Bates, D. M., and Watts, D. G. (1988), Nonlinear Regression Analysis and its Applications, New York: Wiley.
Box, G. E. P., and Tiao, G. C. (1973), Bayesian Inference in Statistical Analysis, New York: Wiley.
Cleveland, W. S. (1985), The Elements of Graphing Data, Monterey, CA: Wadsworth.
Cox, D. R., and Hinkley, D. V. (1974), Theoretical Statistics, London: Chapman & Hall.
Efron, B. (1996), "Empirical Bayes Methods for Combining Likelihoods," Journal of the American Statistical Association, 91, 538-565.
Gilks, W. R., Richardson, S., and Spiegelhalter, D. J. (eds.) (1996), Markov Chain Monte Carlo in Practice, London: Chapman & Hall.
Gilks, W. R., Thomas, A., and Spiegelhalter, D. J. (1994), "A Language and Program for Complex Bayesian Modelling," The Statistician, 43, 169-178.
Hintze, J. L., and Nelson, R. D. (1998), "Violin Plots: A Box Plot-Density Trace Synergism," The American Statistician, 52, 181-184.
Hyndman, R. J. (1996), "Computing and Graphing Highest Density Regions," The American Statistician, 50, 120-126.
Lee, J. J., and Tu, Z. N. (1997), "A Versatile One-Dimensional Distribution Plot: the BLiP Plot," The American Statistician, 51, 353-358.
Lerman, P. M. (1980), "Fitting Segmented Regression Models by Grid Search," Applied Statistics, 29, 77-84.
Lewis, S., and Clarke, M. (2001), "Forest Plots: Trying to See the Wood and the Trees," British Medical Journal, 322, 1479-1480.
Lindstrom, M. J., and Bates, D. M. (1990), "Nonlinear Mixed Effects Models for Repeated Measures Data," Biometrics, 46, 673-687.
Miettinen, O. S. (1985), Theoretical Epidemiology, New York: Wiley.
Morris, C. N. (1996), Comment on "Empirical Bayes Methods for Combining Likelihoods," Journal of the American Statistical Association, 91, 555-558.
Royall, R. M. (1997), Statistical Evidence: A Likelihood Paradigm, London: Chapman and Hall.
Sacks, H. S., Chalmers, T. C., Blum, A. L., Berrier, J., and Pagano, D. (1990), "Endoscopic Hemostasis, An Effective Therapy for Bleeding Peptic Ulcers," Journal of the American Medical Association, 264, 494-499.
van Houwelingen, H. C., and Zwinderman, K. H. (1993), "A Bivariate Approach to Meta-analysis," Statistics in Medicine, 12, 2273-2284.
Wilk, M. B., and Gnanadesikan, R. (1968), "Probability Plotting Methods for the Analysis of Data," Biometrika, 55, 1-17.