{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T13:29:55Z","timestamp":1762954195367,"version":"3.45.0"},"reference-count":46,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T00:00:00Z","timestamp":1762905600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Comput. Neurosci."],"abstract":"<jats:p>Brain activities often follow an exponential family of distributions. The exponential distribution is the maximum entropy distribution of continuous random variables in the presence of a mean. The memoryless and peakless properties of an exponential distribution impose difficulties for data analysis methods. To estimate the rate parameter of multivariate exponential distribution from a time series of sensory inputs (i.e., observations), we constructed a hierarchical Bayesian inference model based on a variant of general hierarchical Brownian filter (GHBF). To account for the complex interactions among multivariate exponential random variables, the model estimates the second-order interaction of the rate intensity parameter in logarithmic space. Using variational Bayesian scheme, a family of closed-form and analytical update equations are introduced. These update equations also constitute a complete predictive coding framework. The simulation study shows that our model has the ability to evaluate the time-varying rate parameters and the underlying correlation structure of volatile multivariate exponentially distributed signals. The proposed hierarchical Bayesian inference model is of practical utility in analyzing high-dimensional neural activities.<\/jats:p>","DOI":"10.3389\/fncom.2025.1408836","type":"journal-article","created":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T13:23:51Z","timestamp":1762953831000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A hierarchical Bayesian inference model for volatile multivariate exponentially distributed signals"],"prefix":"10.3389","volume":"19","author":[{"given":"Changbo","family":"Zhu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ke","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fengzhen","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yandong","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoli","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bailu","family":"Si","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1965","published-online":{"date-parts":[[2025,11,12]]},"reference":[{"key":"B1","author":"Beal","year":"2003","journal-title":"Variational Algorithms for Approximate Bayesian Inference"},{"key":"B2","author":"Berger","year":"2013","journal-title":"Statistical Decision Theory and Bayesian Analysis"},{"key":"B3","unstructured":"Probability distributions and maximum entropy\n          \n          10\n          \n            \n              Conrad\n              K.\n            \n          \n          Entropy\n          6\n          2004"},{"key":"B4","doi-asserted-by":"publisher","first-page":"3038","DOI":"10.1103\/PhysRevLett.81.3038","article-title":"Exponential distribution of locomotion activity in cell cultures","volume":"81","author":"Czir\u00f3k","year":"1998","journal-title":"Phys. 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