Ước lượng Jeffreys cho phân phối nhị thức âm và phân phối nhị thức âm có gia tăng số 0

Anders, S. and Huber, W. (2010). Differential expression analysis for sequence count data. Nature Precedings 1–1. Anscombe, F.J. (1949). The statistical analysis of insect counts based on the negative binomial distribution. Biometrics 5, 165–173. Bayarri, M., Berger, J.O., Datta, G.S. et al. (2008). Objective Bayes testing of Poisson versus inflated Poisson models. Institute of Mathematical Statistics, p. 105–121. Bliss, C.I. and Fisher, R.A. (1953). Fitting the negative binomial distribution to biological data. Biometrics 9, 176–200. Bowden, D.C., Anderson, A.E. and Medin, E. (1969). Frequency distributions of mule deer fecal group counts. J. Wildl. Manag. 33, 895–905. Bradlow, E.T., Hardie, B.G.S. and Fader, P.S. (2002). Bayesian inference for the negative binomial distribution via polynomial expansions. J. Comput. Graph. Stat. 11, 189–201. Burrell, Q.L. (1990). Using the Gamma-Poisson model to predict library circulations. J. Am. Soc. Inf. Sci. 41, 164–170. Chen, J., King, E., Deek, R., Wei, Z., Yu, Y., Grill, D. and Ballman, K. (2017). An omnibus test for differential distribution analysis of microbiome sequencing data. Bioinformatics 34, 643–651. Douglas, J.B., Leroux, B. and Puterman, M.L. (1994). Empirical fitting of discrete distributions. Biometrics 576–579. Fisher, R.A. (1941). The negative binomial distribution. Ann. Eugen.11, 182–187. Guo, X., Fu, Q., Wang, Y. and Land, K.C. (2020). A numerical method to compute fisher information for a special case of heterogeneous negative binomial regression. Commun. Pure Appl. Anal. 19, 4179. Gupta, P.L., Gupta, R.C. and Tripathi, R.C. (1996). Analysis of zero-adjusted count data. Computat. Stat. Data Anal. 23, 207–218. Kass, R.E. and Raftery, A.E. (1995). Bayes factors. J. Am. Stat. Assoc. 90, 773–795. Kass, R.E. and Vaidyanathan, S.K. (1992). Approximate bayes factors and orthogonal parameters, with application to testing equality of two binomial proportions. J. R. Stat. Soc.: Ser. B (Methodol.) 54, 129–144. Lüdecke, D, Ben-Shachar, M.S., Patil, I., Waggoner, P. and Makowski, D. (2021). Performance: an R package for assessment, comparison and testing of statistical models. J. Open Source Softw. 6, 60, 3139. https://doi.org/10.21105/joss.03139. Leroux, B.G. and Puterman, M.L. (1992). Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models. Biometrics 545–558. Minami, M., Lennert-Cody, C.E., Gao, W. and Roman-Verdesoto, M. (2007). Modeling shark bycatch: the zero-inflated negative binomial regression model with smoothing. Fish. Res. 84, 210–221. Nedelman, J. (1983). A negative binomial model for sampling mosquitoes in a malaria survey. Biometrics 39, 1009–1020. Pritchard, N.A. and Tebbs, J.M. (2011). Bayesian inference for disease prevalence using negative binomial group testing. Biom. J. 53, 40–56. R. Core Team (2021). R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. https://www.R-project.org/. Ridout, M., Hinde, J. and DeméAtrio, C.G. (2001). A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives. Biometrics 57, 219–223. Robinson, M.D. and Smyth, G.K. (2007). Moderated statistical tests for assessing differences in tag abundance. Bioinformatics 23, 2881–2887. White, G.C. and Bennetts, R.E. (1996). Analysis of frequency count data using the negative binomial distribution. Ecology 77, 2549–2557. Yau, K.K., Wang, K. and Lee, A.H. (2003). Zero-inflated negative binomial mixed regression modeling of over-dispersed count data with extra zeros. Biom. J.: J. Math. Methods Biosci. 45, 437–452.