## Bayesian inference: suggested readings for ecologists

#### Last revised/updated: 13 March 2001

Bibliography Quicklinks:

I. Philosophical Background

II. Ecological Examples

III. Statistical Papers

A. Hypothesis testing and estimation

B. Theory and mathematical methodology

IV. Teaching Tools

A. Useful Textbooks

B. How to Teach Bayes

C. Software and Application Programs

*BERGER, J. O. and D. A. BERRY. 1988. Statistical analysis and the illusion of objectivity. *American Scientist* 76: 159-165.

DAWID, A. P. 1982. The well-calibrated Bayesian. *Journal of the American Statistical Association* 77: 605-613.

*De GROOT, M. H. 1973. Doing what comes naturally: interpreting a tail area as a posterior probability or as a likelihood ratio. *Journal of the American Statistical Association* 68: 966-969.

*DENNIS, B. 1996. Discussion: should ecologists become Bayesians? *Ecological Applications* 6: 1095-1103.

*EDWARDS, D. 1996. Comment: the first data analysis should be journalistic. *Ecological Applications* 6: 1090-1094.

EFRON, B. 1978. Controversies in the foundations of statistics. *American Mathematical Monthly* 85: 231-246.

*EFRON, B. 1986. Why isn't everyone a Bayesian? *The American Statistician* 40: 1-11.

EL-GAMAL, M. A. and D. M. GRETHER. 1995. Are people Bayesian? Uncovering behavioral stragegies. *Journal of the American Statistical Association* 90: 1137-1145.

LINDLEY, D. V. 1957. A statistical paradox. *Biometrika* 44: 187-192.

*MOORE, D. S. 1997. Bayes for beginners? some reasons to hesitate. *The American Statistician* 51: 254-261.

ORESKES, N., K. SHRADER-FRECHETTE, and K. BELITZ. 1994. Verification, validation, and confirmation of numerical models in the earth sciences. *Science* 263: 641-646.

PIERCE, D. A. 1973. On some difficulties in a frequency theory of inference. *The Annals of Statistics* 1: 241-250.

PRATT, J. W. 1965. Bayesian interpretation of standard inference statements. *Journal of the Royal Statistical Society* 27: 169-203.

*PRATT, J. W., H. RAIFFA, and R. SCHLAIFER. 1964. The foundations of decision under uncertainty: an elementary exposition. *Journal of the American Statistical Association* 59: 353-375.

ROBINSON, G. K. 1975. Some counterexamples to the theory of confidence intervals. *Biometrika* 62: 155-161.

SHAFER, G. 1982. Lindley's paradox. *Journal of the American Statistical Association* 77: 325-351.

*SHRADER-FRECHETTE, K. S. 1994. Science, environmental risk assessment, and the frame problem. *BioScience* 44: 548-552.

SMITH, A. F. M. 1984. Present position and potential developments: some personal views: Bayesian statistics. *Journal of the Royal Statistical Society* A 147: 245-259.

ALTMAN, N. S. and G. CASELLA. 1995. Nonparametric empirical Bayes growth curve analysis. *Journal of the American Statistical Association* 90: 508-517.

BURNHAM, K. P. and D. R. ANDERSON.. 1998. *Model selection and inference: a practical information-theoretic approach*. Springer-Verlag, Berlin.

CROME, F. H. J., M. R. THOMAS, and L. A. MOORE. 1996. A novel Bayesian approach to assessing impacts of rain forest logging. *Ecological Applications* 6: 1104-1123.

ELLISON, A. M. 1996. An introduction to Bayesian inference for ecological research and environmental decision-making. *Ecological Applications* 6: 1036-1046.

FORBES, F. and A. E. RAFTERY. 1999. Bayesian morphology: fast unsupervised Bayesian image analysis. *Journal of the American Statistical Association* 94: 555-568.

GIVENS, G. H. 2000. Multicriterion decision merging: competitive development of an aboriginal whaling management procedure. *Journal of the American Statistical Association* 94: 1003-1014.

GUSTAFSON, L. and W. FRANKLIN 1995. Predictors of neonatal mortality in the guanacos (Lama guanaco) of Torres del Paine, Chile: a pilot study in adaptive modeling of wildlife population health. In T. B. Herman, S. Bondrup-Nielson, J. H. M. Willison, and N. P. Munro [eds.], *Ecosystem monitoring and protected areas*, pages 285-289. Science and Management of Protected Areas Association, Wolfville, Nova Scotia, Canada.

LUDWIG, D. 1996. Uncertainty and the assessment of extinction probabilities. *Ecological Application*s 6: 1067-1076.

MURTAUGH, P. A. and D. L. PHILLIPS. 1998. Temporal correlation of classifications in remote sensing. *Journal of Agricultural, Biological, and Environmental Statistics* 3: 99-110.

NICHOLSON, M. and J. BARRY. 1995. Inferences from spatial surveys about the presence of an unobserved species. *Oikos* 72: 74-78.

OLSSON, O. and N. M. A. HOLMGREN. 1999. Gaining ecological information about Bayesian foragers through their behaviour. I. Models with predictions. *Oikos* 87: 251-263.

OLSSON, O., U. WIKTANDER, N. M. A. HOLMGREN, and S. G. NILSSON. 1999. Gaining ecological information about Bayesian foragers through their behaviour. II. A field test with woodpeckers. *Oikos* 87: 264-276.

PASCUAL, M. A. and R. HILBORN. 1995. Conservation of harvested populations in fluctuating environments: the case of the Serengeti wildebeest. *Journal of Applied Ecolog*y 32: 468-480.

PASCUAL, M. A. and P. KAREIVA. 1996. Predicting the outcome of competition using experimental data: maximum likelihood and Bayesian approaches. *Ecology* 77: 337-349.

RAFTERY, A. E. and J. E. ZEH. 1998. Estimating bowhead whale population size and rate of increase from the 1993 census. *Journal of the American Statistical Association* 93: 451-463.

RAFTERY, A. E., G. H. GIVENS, and J. E. ZEH. 1995. Inference from a deterministic population dynamics model for bowhead whales (with comments and rejoinder). *Journal of the American Statistical Association* 90: 402-430.

RECKHOW, K. H. 1990. Bayesian inference in non-replicated ecological studies. *Ecology* 71: 253-259.

SOLOW, A. R. 1994. On the Bayesian estimation of the number of species in a community. *Ecology* 75: 2139-2142.

STOW, C. A., S. R. CARPENTER, and K. L. COTTINGHAM. 1995. Resource vs. ratio-dependent consumer-resource models: a Bayesian perspective. *Ecology* 76: 1986-1990.

TAYLOR, B. L., P. R. WADE, R. A. STEHN, and J. F. COCHRANE. 1996. A Bayesian approach to classification criteria for Spectacled Eiders. *Ecological Applications* 6: 1077-1089.

TUFTO, J., B. E. SAETHER, S. ENGEN, P. ARCESE, K. JERSTAD, O. W. ROSTAD, and J. N. M. SMITH. 2000. Bayesian meta-analysis of demographic parameters in three small, temperate passerines. *Oikos* 88: 273-281.

VER HOEF, J. M. 1996. Parametric empirical Bayes methods for ecological applications. *Ecological Applications* 6: 1047-1055.

WADE, P.R. 2000. Bayesian methods in conservation biology. *Conservation Biology* 14: 1308-1316.

WOLFSON, L. J., J. B. KADANE, and M. J. SMALL. 1996. Bayesian environmental policy decisions: two case studies. *Ecological Applications* 6: 1056-1066.

*A. Hypothesis testing and estimation*

ALBERT, J. H. 1997. Bayesian testing and estimation of association in a two-way contingency table. *Journal of the American Statistical Association* 92: 685-693.

*BERGER, J. O. and M. DELAMPADY. 1987. Testing precise hypotheses. *Journal of the American Statistical Association* 82: 106-111. *Journal of the American Statistical Association* 94: 542-554.

*BERGER, J. O. and T. SELLKE. 1987. Testing a point null hypothesis: the irreconcilability of P values and evidence. *Journal of the American Statistical Association* 82: 112-139.

*BERTOLINO, F., L. PICCINATO, and W. RACUGNO. 1995. Multiple Bayes factors for testing hypotheses. *Journal of the American Statistical Association* 90: 213-219.

*CASELLA, G. and R. L. BERGER. 1987. Reconciling Bayesian and frequentist evidence in the one-sided testing problem. *Journal of the American Statistical Association* 82: 106-111.

CHRISTENSEN, R. and M. D. HUFFMAN. 1985. Bayesian point estimation using the predictive distribution. *The American Statistician* 39: 319-321.

COPAS, J. B. 1969. Compound decisions and empirical Bayes. *Journal of the Royal Statistical Society* B 31: 397-425.

DAYANANDA, R. A. and I. G. EVANS. 1973. Bayesian acceptance-sampling schemes for two-sided tests of the mean of a normal distribution of known variance. *Journal of the American Statistical Association* 68: 131-136.

*De GROOT, M. H. 1973. Doing what comes naturally: interpreting a tail area as a posterior probability or as a likelihood ratio. *Journal of the American Statistical Association* 68: 966-969.

DEELY, J. J. and W. J. ZIMMER. 1969. Shorter confidence intervals using prior observations. *Journal of the American Statistical Association* 64: 378-386.

DIACONIS, P. and D. FREEDMAN.. 1986. On the consistency of Bayes estimates. *The Annals of Statistics* 14: 1-67.

DIACONIS, P. and D. FREEDMAN. 1986. On inconsistent Bayes estimates of location. *The Annals of Statistics* 14: 68-87.

EFRON, B. 1982. Maximum likelihood and decision theory. *The Annals of Statistics* 10: 340-356.

EFRON, B. and C. MORRIS.. 1972. Limiting the risk of Bayes and empirical Bayes estimators-Part II: the empirical Bayes case. *Journal of the American Statistical Association* 67: 130-139.

EFRON, B. and C. MORRIS. 1973. Stein's estimation rule and its competitors - an empirical Bayes approach. *Journal of the American Statistical Association* 68: 117-130.

EFRON, B. and C. MORRIS. 1975. Data analysis using Stein's estimator and its generalization. *Journal of the American Statistical Association* 70: 311-319.

EFRON, B. and C. MORRIS.. 1977. Stein's paradox in statistics. *Scientific American* 236 (5): 119-127.

ESCOBAR, M. D. and M. WEST. 1995. Bayesian density estimation and inference using mixtures. *Journal of the American Statistical Association* 90: 577-588.

*GOUTIS, C., G. CASELLA, and M. T. WELLS. 1996. Assessing evidence in multiple hypotheses. *Journal of the American Statistical Association* 91: 1268-1277.

DEMPSTER, A. P., M. SCHATZOFF, and N. WERMUTH. 1977. A simulation study of alternatives to ordinary least squares. *Journal of the American Statistical Association* 72: 77-106.

DOMINICI, F., G. PARMIGIANI, K. H. RECKHOW, and R. L. WOLPERT. 1997. Combining information from related regressions. *Journal of Agricultural, Biological, and Environmental Statistics* 2: 313-332.

HALPERN, E. F. 1973. Polynomial regression from a Bayesian approach. *Journal of the American Statistical Association* 68: 137-143.

HARTIGAN, J. A. 1969. Linear Bayesian methods. *Journal of the Royal Statistical Society* B 34: 446-454.

HOADLEY, B. 1970. A Bayesian look at inverse linear regression. *Journal of the American Statistical Association* 65: 356-369.

*KASS, R. E. and A. E. RAFTERY. 1995. Bayes factors. *Journal of the American Statistical Association* 90: 773-795.

KASS, R. E. and L. WASSERMAN. 1995. A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. *Journal of the American Statistical Association* 90: 928-934.

LEONARD, T. 1977. A Bayesian approach to some multinomial estimation and pretesting problems. *Journal of the American Statistical Association* 72: 869-874.

LEONARD, T.. 1978. Density estimation, stochastic processes and prior information. *Journal of the Royal Statistical Society* B 40: 113-146.

LINDLEY, D. V. and A. F. M. SMITH. 1972. Bayes estimates for the linear model. *Journal of the Royal Statistical Society* B 34: 1-41.

LINDLEY, D. V. and L. D. PHILLIPS. 1976. Inference for a Bernoulli process (a Bayesian view). *The American Statistician* 30: 112-119.

PAULER, D. K., J. C. WAKEFIELD, and R. E. KASS. 2000. Bayes factors and approximations for variance component models. *Journal of the American Statistical Association* 94: 1242-1253.

PENNELLO, G. 1997. The k-ratio multiple comparisons Bayes rule for the balanced two-way design. *Journal of the American Statistical Association* 92: 675-684.

RAFTERY, A. E., D. MADIGAN, and J. A. HOETING. 1997. Bayesian model averaging for linear regression models. *Journal of the American Statistical Association* 92: 179-191.

ROBBINS, H. 1995. The empirical Bayes approach to statistical decision problems. *Annals of Mathematical Statistics* 35: 1-20.

RUBIN, D. B. 1984. Bayesianly justifiable and relevant frequency calculations for the applied statistician. *The Annals of Statistics* 12: 1151-1172.

*SAMANIEGO, F. J. and D. M. RENEAU. 1994. Toward a reconciliation of the Bayesian and frequentist approaches to point estimation. *Journal of the American Statistical Association* 89: 947-957.

*SCHERVISH, M. J. 1996. P values: what they are and what they are not. *The American Statistician* 50: 203-206.

STEIN, C. M. 1981. Estimation of the mean of a multivariate normal distribution. *The Annals of Statistics* 9: 1135-1151.

WALLER, R. A. and D. B. DUNCAN. 1969. A Bayes rule for the symmetric multiple comparisons problem. *Journal of the American Statistical Association* 64: 1484-1503.

WOOD, S. and R. KOHN. 1998. A Bayesian approach to robust binary nonparametric regression. *Journal of the American Statistical Association* 93: 203-213.

**B. Theory and mathematical methodology**

BEDRICK, E. J., R. CHRISTENSEN, and W. JOHNSON. 1996. A new perspective on priors for generalized linear models. *Journal of the American Statistical Association* 91: 1450-1460.

BERGER, J. 1982. Bayesian robustness and the Stein effect. *Journal of the American Statistical Association* 77: 358-368.

BOX, G. E. P. 1980. Sampling and Bayes' inference in scientific modelling and robustness. *Journal of the Royal Statistical Society* A 143: 383-430.

BROWN, L. D., G. CASELLA, and J. T. G. HWANT. 1995. Optimal confidence sets, bioequivalence, and the limacon of Pascal. *Journal of the American Statistical Association* 90: 880-889.

BROWN, P. J., T. FEARN, and M. S. HAQUE. 2000. Discrimination with many variables. *Journal of the American Statistical Association* 94: 1320-1329.

BUCKLE, D. J. 1995. Bayesian inference for stable distributions. *Journal of the American Statistical Association* 90: 605-613.

*CASELLA, G. 1985. An introduction to empirical Bayes data analysis. *The American Statistician* 39: 83-87.

DEELY, J. J. and D. V. LINDLEY. 1981. Bayes empirical Bayes. *Journal of the American Statistical Association* 76: 833-841.

DEMPSTER, A. P., M. SCHATZOFF, and N. WERMUTH. 1977. A simulation study of alternatives to ordinary least squares. *Journal of the American Statistical Association* 72: 77-106.

EFRON, B. and D. V. HINKLEY. 1978. Assessing the accuracy of the maximum likelihood estimator: observed versus expected Fisher information. *Biometrika* 65: 457-487.

FERGUSON, T. S. 1973. A Bayesian analysis of some nonparametric problems. *The Annals of Statistics* 1: 209-230.

FERNÁNDEZ, C. and M. F. J. STEEL. 1998. On Bayesian modeling of fat tails and skewness. *Journal of the American Statistical Association* 93: 359-371.

GELFAND, A. E., B. K. MALLICK, and D. K. DEY. 1995. Modeling expert opinion arising as a partial probabilistic specification. *Journal of the American Statistical Association* 90: 598-604.

HAMADA, M. and C. F. J. WU. 1995. Analysis of censored data from fractionated experiments: a Bayesian approach. *Journal of the American Statistical Association* 90: 467-477.

HEAGERTY, P. J. and S. R. LELE. 1998. A composite likelihood approach to binary spatial data. *Journal of the American Statistical Association* 93: 1099-1111.

HILL, B. M. 1995. Posterior distribution of percentiles: Bayes' theorem for sampling from a population. *Journal of the American Statistical Association* 677-691

*HOBERT, J. P. and G. CASELLA. 1996. The effect of improper priors on Gibbs sampling in hierarchical linear mixed models. *Journal of the American Statistical Association* 91: 1461-1473..

*KASS, R. E. and L. WASSERMAN. 1996. The selection of prior distributions by formal rules. *Journal of the American Statistical Association* 91: 1343-1370.

LEWIS, S. M. and A. E. RAFTERY. 1997. Estimating Bayes factors via posterior simulation with the Laplace-Metropolis estimator. *Journal of the American Statistical Associatio*n 92: 648-655.

*MADIGAN, D. and A. E. RAFTERY. 1994. Model selection and accounting for model uncertainty in graphical models using Occam's window. *Journal of the American Statistical Association* 89: 1535-1546.

MORRIS, C. N. 1983. Parametric empirical Bayes inference: theory and applications. *Journal of the American Statistical Association* 78: 47-65.

MONAHAN, J. and A. GENZ. 1997. Spherical-radial integration rules for a Bayesian computation. *Journal of the American Statistical Association* 92: 664-674.

PHILLIPS, D. B. and A. F. M. SMITH. 1994. Bayesian faces via hierarchical template modeling. *Journal of the American Statistical Association* 89: 1151-1163.

SUN, D. and K. YE. 1995. Reference prior Bayesian analysis for normal mean products. *Journal of the American Statistical Association* 90: 589-597.

VERDINELLI, I. and L. WASSERMAN. 1995. Computing Bayes factors using a generalization of the Savage-Dickey density ratio. *Journal of the American Statistical Association* 90: 614-618.

WEISS, R. E. 1995. The influence of variable selection: a Bayesian diagnostic perspective. *Journal of the American Statistical Association* 90: 619-625.

BERGER, J. O. 1985. *Statistical Decision Theory and Bayesian Analysis*. Springer-Verlag.

BERNARDO, J. M. and A. F. M. SMITH. 1994. *Bayesian Theory*. John Wiley & Sons.

BOX, G. E. P. and G. C. TIAO. 1973. *Bayesian Inference in Statistical Analysis*. John Wiley & Sons

*GELMAN, A., J. B. CARLIN, H. S. STERN, and D. B. RUBIN. 1995. *Bayesian Data Analysis*. Chapman & Hall.

HILBORN, R. and M. MANGEL. 1997. *The Ecological Detective*. Princeton University Press.

HOFFMAN-JØRGENSEN, J. 1994. *Probability with a View Toward Statistics (2 volumes)*. Chapman & Hall.

*LEE, P. M. 1997. *Bayesian statistics: an introduction, 2nd editio*n. Arnold, London.

WEST, M. and J. HARRISON. 1989. *Bayesian Forecasting and Dynamic Models*. Springer-Verlag

*ALBERT, J. 1997. Teaching Bayes' rule: a data-oriented approach. *The American Statistician* 51: 247-253.

*BERRY, D. A. 1997. Teaching elementary Bayesian statistics with real applications in science. *The American Statistician* 51: 241-246.

**C. Software and application programs**

ALBERT, J. H. 1996. *Bayesian computation using Minitab*. Duxbury Press, Belmont, California

This is a set of macros for Minitab 8. I have not had any success converting it to the Windows 95/98/NT version of Minitab, but that doesn't mean it can't be done!

COOK, P. and L. D. BROEMELING. 1995. *Bayesian statistics using Mathematica*. The American Statistician 49: 70-76.

O'HAGEN, T. 1996. *FirstBayes* 1.3.

This is essentially a teaching package; it is used for the examples in Wade (2000) [see Ecological examples]. A new version is promised for late 2000/early 2001.

POLE, A., M. WEST and J. HARRISON. 1994. *Applied Bayesian forecasting and time-series analysis*. Chapman & Hall, New York.

This is a DOS and Windows 3.1 version; Current version (Windows 95, 98, NT) is the bts library of functions for S-Plus, available from the STALIB archive.

SPIEGELHALTER, D. THOMAS, A, and BEST, N. 2000. WinBUGS 1.3 (Bayesian inference Using the Gibbs Sampler, for Windows). Click here.

This is a serious research package, that is not especially user-friendly. There is an active list-server/user's group for this package. It is used by Tufto et al. (2000) [see Ecological examples]

STATLIB archive (Bayesian macros for various software packages, including S-Plus). Click here.

This is an archive of software routines, datasets etc. for the professional statistical community. I make use the S-archive extensively to get new functions for S-Plus. Much more software is available for Linux/Unix than for Windows