{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T17:31:45Z","timestamp":1772213505088,"version":"3.50.1"},"reference-count":78,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T00:00:00Z","timestamp":1694131200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"UK Engineering and Physical Sciences Research Council","award":["EP\/V055380\/1"],"award-info":[{"award-number":["EP\/V055380\/1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Developing an efficient computational scheme for high-dimensional Bayesian variable selection in generalised linear models and survival models has always been a challenging problem due to the absence of closed-form solutions to the marginal likelihood. The Reversible Jump Markov Chain Monte Carlo (RJMCMC) approach can be employed to jointly sample models and coefficients, but the effective design of the trans-dimensional jumps of RJMCMC can be challenging, making it hard to implement. Alternatively, the marginal likelihood can be derived conditional on latent variables using a data-augmentation scheme (e.g., P\u00f3lya-gamma data augmentation for logistic regression) or using other estimation methods. However, suitable data-augmentation schemes are not available for every generalised linear model and survival model, and estimating the marginal likelihood using a Laplace approximation or a correlated pseudo-marginal method can be computationally expensive. In this paper, three main contributions are presented. Firstly, we present an extended Point-wise implementation of Adaptive Random Neighbourhood Informed proposal (PARNI) to efficiently sample models directly from the marginal posterior distributions of generalised linear models and survival models. Secondly, in light of the recently proposed approximate Laplace approximation, we describe an efficient and accurate estimation method for marginal likelihood that involves adaptive parameters. Additionally, we describe a new method to adapt the algorithmic tuning parameters of the PARNI proposal by replacing Rao-Blackwellised estimates with the combination of a warm-start estimate and the ergodic average. We present numerous numerical results from simulated data and eight high-dimensional genetic mapping data-sets to showcase the efficiency of the novel PARNI proposal compared with the baseline add\u2013delete\u2013swap proposal.<\/jats:p>","DOI":"10.3390\/e25091310","type":"journal-article","created":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T07:52:11Z","timestamp":1694159531000},"page":"1310","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2434-1841","authenticated-orcid":false,"given":"Xitong","family":"Liang","sequence":"first","affiliation":[{"name":"Department of Statistical Science, University College London, London WC1E 6BT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7277-086X","authenticated-orcid":false,"given":"Samuel","family":"Livingstone","sequence":"additional","affiliation":[{"name":"Department of Statistical Science, University College London, London WC1E 6BT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4828-7368","authenticated-orcid":false,"given":"Jim","family":"Griffin","sequence":"additional","affiliation":[{"name":"Department of Statistical Science, University College London, London WC1E 6BT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hastie, T., Tibshirani, R., and Wainwright, M. (2015). Statistical Learning with Sparsity: The Lasso and Generalizations, CRC Press.","DOI":"10.1201\/b18401"},{"key":"ref_2","unstructured":"Akaike, H. (1998). Selected Papers of Hirotugu Akaike, Springer."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1214\/aos\/1176344136","article-title":"Estimating the dimension of a model","volume":"6","author":"Schwarz","year":"1978","journal-title":"Ann. Stat."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1111\/1467-9868.00353","article-title":"Bayesian measures of model complexity and fit","volume":"64","author":"Spiegelhalter","year":"2002","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"ref_5","first-page":"3571","article-title":"Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory","volume":"11","author":"Watanabe","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1080\/01621459.1988.10478694","article-title":"Bayesian variable selection in linear regression","volume":"83","author":"Mitchell","year":"1988","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1214\/lnms\/1215540964","article-title":"The practical implementation of Bayesian model selection","volume":"38","author":"Chipman","year":"2001","journal-title":"Lect. Notes Monogr. Ser."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1002\/sam.11428","article-title":"Bayesian variable selection for logistic regression","volume":"12","author":"Tian","year":"2019","journal-title":"Stat. Anal. Data Min. ASA Data Sci. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1214\/08-BA323","article-title":"Bayesian variable selection and computation for generalized linear models with conjugate priors","volume":"3","author":"Chen","year":"2008","journal-title":"Bayesian Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1093\/biomet\/62.2.269","article-title":"Partial likelihood","volume":"62","author":"Cox","year":"1975","journal-title":"Biometrika"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"701","DOI":"10.2307\/3316126","article-title":"Bayesian variable selection for proportional hazards models","volume":"27","author":"Ibrahim","year":"1999","journal-title":"Can. J. Stat."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1007\/s10985-008-9101-5","article-title":"Bayesian variable selection for the Cox regression model with missing covariates","volume":"14","author":"Ibrahim","year":"2008","journal-title":"Lifetime Data Anal."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5376","DOI":"10.1002\/sim.7089","article-title":"Objective Bayesian model selection for Cox regression","volume":"35","author":"Held","year":"2016","journal-title":"Stat. Med."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1214\/21-STS846","article-title":"Additive Bayesian variable selection under censoring and misspecification","volume":"38","author":"Rossell","year":"2023","journal-title":"Stat. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1177\/0962280214548748","article-title":"Weibull regression with Bayesian variable selection to identify prognostic tumour markers of breast cancer survival","volume":"26","author":"Newcombe","year":"2017","journal-title":"Stat. Methods Med. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1111\/rssb.12466","article-title":"Approximate Laplace approximations for scalable model selection","volume":"83","author":"Rossell","year":"2021","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Green, P.J. (2003). Highly Structured Stochastic Systems, Oxford University Press.","DOI":"10.1093\/oso\/9780198510550.001.0001"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1093\/biomet\/asm069","article-title":"Population-based reversible jump Markov chain Monte Carlo","volume":"94","author":"Jasra","year":"2007","journal-title":"Biometrika"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1080\/01621459.1987.10478458","article-title":"The calculation of posterior distributions by data augmentation","volume":"82","author":"Tanner","year":"1987","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1080\/01621459.2013.829001","article-title":"Bayesian inference for logistic models using P\u00f3lya\u2013Gamma latent variables","volume":"108","author":"Polson","year":"2013","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1111\/rssb.12280","article-title":"The correlated pseudomarginal method","volume":"80","author":"Deligiannidis","year":"2018","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"ref_22","first-page":"173","article-title":"Bayesian wavelength selection in multicomponent analysis","volume":"12","author":"Brown","year":"1998","journal-title":"J. Chemom. J. Chemom. Soc."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2497","DOI":"10.1214\/15-AOS1417","article-title":"On the computataional complexity of high-dimensional Bayesian variable selection","volume":"44","author":"Yang","year":"2016","journal-title":"Ann. Stat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s11222-008-9110-y","article-title":"A tutorial on adaptive MCMC","volume":"18","author":"Andrieu","year":"2008","journal-title":"Stat. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1198\/jcgs.2009.08027","article-title":"Transdimensional sampling algorithms for Bayesian variable selection in classification problems with many more variables than observations","volume":"18","author":"Lamnisos","year":"2009","journal-title":"J. Comput. Graph. Stat."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1093\/biomet\/asaa055","article-title":"In search of lost mixing time: Adaptive Markov chain Monte Carlo schemes for Bayesian variable selection with very large p","volume":"108","author":"Griffin","year":"2021","journal-title":"Biometrika"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1007\/s11222-020-09974-2","article-title":"An adaptive MCMC method for Bayesian variable selection in logistic and accelerated failure time regression models","volume":"31","author":"Wan","year":"2021","journal-title":"Stat. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1598","DOI":"10.1080\/01621459.2016.1222288","article-title":"The Hamming ball sampler","volume":"112","author":"Titsias","year":"2017","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1111\/rssb.12316","article-title":"Scalable importance tempering and Bayesian variable selection","volume":"81","author":"Zanella","year":"2019","journal-title":"J. R. Stat. Soc. Ser. Stat. Methodol."},{"key":"ref_30","unstructured":"Jankowiak, M. (2021). Fast Bayesian Variable Selection in Binomial and Negative Binomial Regression. arXiv."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"852","DOI":"10.1080\/01621459.2019.1585255","article-title":"Informed proposals for local MCMC in discrete spaces","volume":"115","author":"Zanella","year":"2020","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1751","DOI":"10.1111\/rssb.12546","article-title":"Dimension-free mixing for high-dimensional Bayesian variable selection","volume":"84","author":"Zhou","year":"2022","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1007\/s11222-022-10137-8","article-title":"Adaptive random neighbourhood informed Markov chain Monte Carlo for high-dimensional Bayesian variable selection","volume":"32","author":"Liang","year":"2022","journal-title":"Stat. Comput."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1198\/016214507000000121","article-title":"Shotgun stochastic search for \u201clarge p\u201d regression","volume":"102","author":"Hans","year":"2007","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1111\/j.1467-9868.2008.00700.x","article-title":"Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations","volume":"71","author":"Rue","year":"2009","journal-title":"J. R. Stat. Soc. Ser. Stat. Methodol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"104255","DOI":"10.1016\/j.chemolab.2021.104255","article-title":"Bayesian global-local shrinkage methods for regularisation in the high dimension linear model","volume":"210","author":"Griffin","year":"2021","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1111\/j.1467-9469.2010.00715.x","article-title":"Approximate Bayesian inference for survival models","volume":"38","author":"Martino","year":"2011","journal-title":"Scand. J. Stat."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","article-title":"Variational inference: A review for statisticians","volume":"112","author":"Blei","year":"2017","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_39","first-page":"14423","article-title":"Spike and slab variational Bayes for high dimensional logistic regression","volume":"33","author":"Ray","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1080\/01621459.2020.1847121","article-title":"Variational Bayes for high-dimensional linear regression with sparse priors","volume":"117","author":"Ray","year":"2022","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3918","DOI":"10.1093\/bioinformatics\/btac416","article-title":"Variational Bayes for high-dimensional proportional hazards models with applications within gene expression","volume":"38","author":"Komodromos","year":"2022","journal-title":"Bioinformatics"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1007\/s11222-022-10180-5","article-title":"Sticky PDMP samplers for sparse and local inference problems","volume":"33","author":"Bierkens","year":"2023","journal-title":"Stat. Comput."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Chevallier, A., Fearnhead, P., and Sutton, M. (2022). Reversible jump PDMP samplers for variable selection. J. Am. Stat. Assoc., 1\u201313.","DOI":"10.1080\/01621459.2022.2099402"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1093\/biomet\/asq017","article-title":"The horseshoe estimator for sparse signals","volume":"97","author":"Carvalho","year":"2010","journal-title":"Biometrika"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1214\/12-BA730","article-title":"On the half-Cauchy prior for a global scale parameter","volume":"7","author":"Polson","year":"2012","journal-title":"Bayesian Anal."},{"key":"ref_46","first-page":"79","article-title":"Hierarchical Bayesian Survival Analysis and Projective Covariate Selection in Cardiovascular Event Risk Prediction","volume":"27","author":"Peltola","year":"2014","journal-title":"BMA@UAI"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1198\/016214507000001337","article-title":"Mixtures of g priors for Bayesian variable selection","volume":"103","author":"Liang","year":"2008","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1828","DOI":"10.1080\/01621459.2018.1469992","article-title":"Mixtures of g-priors in generalized linear models","volume":"113","author":"Li","year":"2018","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1002\/jae.1057","article-title":"On the effect of prior assumptions in Bayesian model averaging with applications to growth regression","volume":"24","author":"Ley","year":"2009","journal-title":"J. Appl. Econom."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1023\/A:1011916902934","article-title":"Nonparametric regression using linear combinations of basis functions","volume":"11","author":"Kohn","year":"2001","journal-title":"Stat. Comput."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1214\/20-AOAS1325","article-title":"Bayesian variable selection for survival data using inverse moment priors","volume":"14","author":"Nikooienejad","year":"2020","journal-title":"Ann. Appl. Stat."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1111\/j.2517-6161.1978.tb01666.x","article-title":"Non-parametric Bayesian analysis of survival time data","volume":"40","author":"Kalbfleisch","year":"1978","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1093\/biomet\/90.3.629","article-title":"A Bayesian justification of Cox\u2019s partial likelihood","volume":"90","author":"Sinha","year":"2003","journal-title":"Biometrika"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1063\/1.1699114","article-title":"Equation of state calculations by fast computing machines","volume":"21","author":"Metropolis","year":"1953","journal-title":"J. Chem. Phys."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1093\/biomet\/57.1.97","article-title":"Monte Carlo sampling methods using Markov chains and their applications","volume":"57","author":"Hastings","year":"1970","journal-title":"Biometrika"},{"key":"ref_56","unstructured":"Makalic, E., and Schmidt, D. (2016). High-Dimensional Bayesian Regularised Regression with the BayesReg Package. arXiv."},{"key":"ref_57","unstructured":"Zens, G., Fr\u00fchwirth-Schnatter, S., and Wagner, H. (2020). Ultimate P\u00f3lya Gamma Samplers\u2014Efficient MCMC for possibly imbalanced binary and categorical data. arXiv."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1394","DOI":"10.1080\/01621459.2018.1505626","article-title":"MCMC for imbalanced categorical data","volume":"114","author":"Johndrow","year":"2018","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_59","unstructured":"Geissner, S., Hodges, J.S., Press, S.J., and Zellner, A. (1990). Bayesian and Likelihood Methods in Statistics and Econometrics, University of Minnesota."},{"key":"ref_60","unstructured":"Barber, R.F., Drton, M., and Tan, K.M. (2014, January 5\u20139). Laplace approximation in high-dimensional Bayesian regression. Proceedings of the Statistical Analysis for High-Dimensional Data: The Abel Symposium 2014, Lofoten, Norway."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1093\/genetics\/164.3.1139","article-title":"Estimation of population growth or decline in genetically monitored populations","volume":"164","author":"Beaumont","year":"2003","journal-title":"Genetics"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1214\/07-AOS574","article-title":"The pseudo-marginal approach for efficient Monte Carlo computations","volume":"37","author":"Andrieu","year":"2009","journal-title":"Ann. Stat."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1023\/A:1018509429360","article-title":"Sampling from the posterior distribution in generalized linear mixed models","volume":"7","author":"Gamerman","year":"1997","journal-title":"Stat. Comput."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1038\/ng.3603","article-title":"Genome-wide association meta-analysis in Chinese and European individuals identifies ten new loci associated with systemic lupus erythematosus","volume":"48","author":"Morris","year":"2016","journal-title":"Nat. Genet."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Tadesse, M.G., and Vannucci, M. (2021). Handbook of Bayesian Variable Selection, CRC Press.","DOI":"10.1201\/9781003089018"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v040.i08","article-title":"Rcpp: Seamless R and C++ Integration","volume":"40","author":"Eddelbuettel","year":"2011","journal-title":"J. Stat. Softw."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"1236","DOI":"10.1038\/srep01236","article-title":"Extracting insights from the shape of complex data using topology","volume":"3","author":"Lum","year":"2013","journal-title":"Sci. Rep."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"7265","DOI":"10.1073\/pnas.1102826108","article-title":"Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival","volume":"108","author":"Nicolau","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"11479","DOI":"10.1038\/ncomms11479","article-title":"The somatic mutation profiles of 2433 breast cancers refine their genomic and transcriptomic landscapes","volume":"7","author":"Pereira","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1038\/s41523-018-0056-8","article-title":"Associations between genomic stratification of breast cancer and centrally reviewed tumour pathology in the METABRIC cohort","volume":"4","author":"Mukherjee","year":"2018","journal-title":"NPJ Breast Cancer"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1158\/2159-8290.CD-12-0095","article-title":"The cBio cancer genomics portal: An open platform for exploring multidimensional cancer genomics data","volume":"2","author":"Cerami","year":"2012","journal-title":"Cancer Discov."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1080\/00949655.2014.929131","article-title":"Automatic model selection for high-dimensional survival analysis","volume":"85","author":"Lang","year":"2015","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Math\u00e9, E., and Davis, S. (2016). Statistical Genomics: Methods and Protocols, Humana.","DOI":"10.1007\/978-1-4939-3578-9"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/s12144-015-9404-0","article-title":"Using the gamma generalized linear model for modeling continuous, skewed and heteroscedastic outcomes in psychology","volume":"36","author":"Ng","year":"2017","journal-title":"Curr. Psychol."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"1530","DOI":"10.1080\/01621459.2020.1864381","article-title":"Survival regression models with dependent Bayesian nonparametric priors","volume":"117","author":"Leisen","year":"2022","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_76","unstructured":"Johndrow, J.E., Pillai, N.S., and Smith, A. (2020). No free lunch for approximate MCMC. arXiv."},{"key":"ref_77","unstructured":"R Core Team (2013). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"4352","DOI":"10.1002\/sim.2836","article-title":"Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution","volume":"26","author":"Cox","year":"2007","journal-title":"Stat. Med."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/9\/1310\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:47:18Z","timestamp":1760129238000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/9\/1310"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,8]]},"references-count":78,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["e25091310"],"URL":"https:\/\/doi.org\/10.3390\/e25091310","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,8]]}}}