{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:23:21Z","timestamp":1760243001759,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,3,20]],"date-time":"2015-03-20T00:00:00Z","timestamp":1426809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In models with nuisance parameters, Bayesian procedures based on Markov Chain Monte Carlo (MCMC) methods have been developed to approximate the posterior distribution of the parameter of interest. Because these procedures require burdensome computations related to the use of MCMC, approximation and convergence in these procedures are important issues. In this paper, we explore Gibbs sensitivity by using an alternative to the full conditional distribution of the nuisance parameter. The approximate sensitivity of the posterior distribution of interest is studied in terms of an information measure, including Kullback\u2013Leibler divergence. As an illustration, we then apply these results to simple spatial model settings.<\/jats:p>","DOI":"10.3390\/e17031441","type":"journal-article","created":{"date-parts":[[2015,3,20]],"date-time":"2015-03-20T11:31:36Z","timestamp":1426851096000},"page":"1441-1451","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Approximated Information Analysis in Bayesian Inference"],"prefix":"10.3390","volume":"17","author":[{"given":"Jung","family":"Seo","sequence":"first","affiliation":[{"name":"Department of Statistics, Yeungnam University, Gyeongsan 712-749, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongku","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Statistics, Kyungpook National University, Daegu 702-701, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1080\/01621459.1986.10478240","article-title":"Accurate approximations for posterior moments and marginal densities","volume":"81","author":"Tierney","year":"1986","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1198\/jcgs.2011.203main","article-title":"To center or not to center: That is not the question\u2014An Ancillarity-Sufficiency Interweaving Strategy (ASIS) for boosting MCMC efficiency","volume":"20","author":"Yu","year":"2011","journal-title":"J. Comput. Graph. Stat"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Filippone, M., and Girolami, M. (2014). Pseudo-marginal Bayesian inference for Gaussian Processes. IEEE Trans. Pattern. Anal. Mach. Intell., doi:TPAMI.2014.2316530.","DOI":"10.1109\/TPAMI.2014.2316530"},{"key":"ref_4","unstructured":"Attias, H. (August, January 30). Inferring parameters and structure of latent variable models by variational Bayes. Stockholm, Sweden."},{"key":"ref_5","unstructured":"Minka, T.P. (2001, January 2\u20135). Expectation propagation for approximate Bayesian inference. Seattle, WA, USA."},{"key":"ref_6","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. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s11222-008-9075-x","article-title":"Spatial model fitting for large datasets with applications to climate and microarray problems","volume":"19","author":"Furrer","year":"2008","journal-title":"Stat. Comput"},{"key":"ref_8","unstructured":"Kim, Y., and Kim, D.H. (2015). An approximate likelihood function of spatial correlation parameters, submitted."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Cressie, N. (1993). Statistics for Spatial Data, Wiley. Revised ed.","DOI":"10.1002\/9781119115151"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1080\/01621459.1976.10481547","article-title":"Approximate posterior distributions","volume":"71","author":"Dickey","year":"1976","journal-title":"J. Am. Stat. Assoc"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1002\/j.1538-7305.1948.tb00917.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J"},{"key":"ref_13","unstructured":"Schneier, B. (1996). Applied Cryptography, John Wiley and Sons. [2nd]."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/3\/1441\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:43:46Z","timestamp":1760215426000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/3\/1441"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,20]]},"references-count":13,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,3]]}},"alternative-id":["e17031441"],"URL":"https:\/\/doi.org\/10.3390\/e17031441","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,3,20]]}}}