The semi-Markov beta-Stacy process: a Bayesian non-parametric prior for semi-Markov processes.

Arfè A (2020) Bayesian methods for the design and analysis of complex follow-up studies. Ph.D. thesis, Bocconi University, Milan, Italy Arfè A, Peluso P, Muliere P (2018) Reinforced urns and the subdistribution beta-stacy process prior for competing risks analysis. Scand J Statist 46:706–734 Barbu V, Boussemart M, Limnios N (2004) Discrete-time semi-Markov model for reliability and survival analysis. Commun Statist Theory Methods 33:2833–2868 Barbu V, Limnios N (2009) Semi-Markov chains and hidden semi-Markov models toward applications : their use in reliability and DNA analysis. Lecture notes in statistics. Springer, New York Blackwell D, MacQueen JB (1973) Ferguson distributions via polya urn schemes. Ann Statist 1:353–355 Bulla J, Bulla I (2006) Stylized facts of financial time series and hidden semi-Markov models. Comput Statist Data Anal 51:2192–2209 Bulla P, Muliere P (2007) Bayesian nonparametric estimation for reinforced markov renewal processes. Statist Inference Stoch Process 10:283–303 Caron F, Neiswanger W, Wood F, Doucet A, Davy M (2017) Generalized pólya urn for time-varying pitman-yor processes. J Mach Learn Res 18:1–32 Çinlar E (2011) Probability and stochastics. Springer, New York Çinlar E (1969) Markov renewal theory. Adv Appl Probab 1:123–187 Coppersmith D, Diaconis P (1986) Random walk with reinforcement. unpublished manuscript Diaconis P (1988) Recent progress on de Finetti’s notions of exchangeability. In: Bernardo JM, DeGroot MH, Lindley DV, Smith AFM (eds) Bayesian statistics, vol 3. Oxford University Press, pp 111–125 Doksum K (1974) Tailfree and neutral random probabilities and their posterior distributions. Ann Probab 2(2):183–201 Ferguson TS (1973) A Bayesian analysis of some nonparametric problems. Ann Statist 1:209–230 Fortini S, Petrone S (2012) Predictive construction of priors in Bayesian nonparametrics. Braz J Probab Statist 26:423–449 Heitjan DF, Rubin DB (1991) Ignorability and coarse data. Ann Statist 19:2244–2253 Hjort NL, Holmes C, Müller P, Walker SG (2010) Bayesian nonparametrics. Cambridge University Press, Cambridge Janssen J, Manca R (2007) Semi-Markov risk models for finance. Insurance and reliability. Springer, Berlin Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley, Hoboken Kallenberg O (2006) Foundations of modern probability. probability and its applications. Springer, New York Ko SI, Chong TT, Ghosh P et al (2015) Dirichlet process hidden Markov multiple change-point model. Bayesian Anal 10:275–296 Masala G (2013) Hurricane lifespan modeling through a semi-Markov parametric approach. J Forecast 32:369–384 Mauldin RD, Sudderth WD, Williams S (1992) Polya trees and random distributions. Ann Statist 20:1203–1221 Mitchell C, Hudgens M, King C, Cu-Uvin S, Lo Y, Rompalo A, Sobel J, Smith J (2011) Discrete-time semi-Markov modeling of human papillomavirus persistence. Statist Med 30:2160–2170 Muliere P, Paganoni AM, Secchi P (2006) A randomly reinforced urn. J Statist Plan Inference 136:1853–1874 Muliere P, Scarsini M (1985) Change-point problems: A and Bayesian nonparametric approach. Aplikace Matematiky 30:397–402 Muliere P, Secchi P, Walker S (2000) Urn schemes and reinforced random walks. Stoch Process Appl 88:59–78 Muliere P, Secchi P, Walker S (2005) Partially exchangeable processes indexed by the vertices of a k-tree constructed via reinforcement. Stoch Process Appl 115:661–677 Muliere P, Secchi P, Walker SG (2003) Reinforced random processes in continuous time. Stoch Process Appl 104:117–130 Nakagawa T, Osaki S (1975) The discrete weibull distribution. IEEE Trans Reliab 24:300–301 Paganoni AM, Secchi P (2004) Interacting reinforced-urn systems. Adv Appl Probab 36:791–804 Patwardhan AS, Kulkarni RB, Tocher D (1980) A semi-Markov model for characterizing recurrence of great earthquakes. Bull Seismol Soc Am 70:323–347 Peluso S, Mira A, Muliere P (2015) Reinforced urn processes for credit risk models. J Econ 184:1–12 Peluso S, Chib S, Mira A (2019) Semiparametric multivariate and multiple change-point modeling. Bayesian Anal 14(3):727–751 Pemantle R (1988) Random processes with reinforcement. Ph.D. thesis, Massachussets Institute of Technology Pemantle R (2007) A survey of random processes with reinforcement. Probab Surv 4:1–79 Phelan MJ (1990) Bayes estimation from a Markov renewal process. Ann Statist 18:603–616 Satten GA, Sternberg MR (1999) Fitting semi-Markov models to interval-censored data with unknown initiation times. Biometrics 55:507–513 Schiffman M, Castle PE, Maucort-Boulch D, Plummer M, Wheeler CM of Undetermined Significance/Low-Grade Squamous Intraepithelial Lesions Triage Study) Group, A. A. S. C. (2007) A 2-year prospective study of human papillomavirus persistence among women with a cytological diagnosis of atypical squamous cells of undetermined significance or low-grade squamous intraepithelial lesion. J Infect Dis 195:1582–1589 Singpurwalla ND (2006) Reliability and risk: a Bayesian perspective. Wiley, Chichester Smith A (1975) A Bayesian approach to inference about a change-point in a sequence of random variables. Biometrika 62:407–416 Walker S, Muliere P (1997) Beta-Stacy processes and a generalization of the Pólya-urn scheme. Ann Statist 25:1762–1780 Zhao L, Hu XJ (2013) Estimation with right-censored observations under a semi-Markov model. Can J Statist 41:237–256