{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T15:24:46Z","timestamp":1787239486637,"version":"build-2736575974"},"reference-count":0,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:p>Marginal likelihood and Bayes factors are key components of the Bayesian analysis used in hypothesis testing and model selection. In many applications in statistics, applied mathematics, signal processing, and machine learning, the computation of normalizing constants of probability models or ratios of these constants plays a fundamental role. The first Survey and Review paper in this issue, \u201cMarginal Likelihood Computation for Model Selection and Hypothesis Testing: An Extensive Review,\u201d by F. Llorente, L. Martino, D. Delgado, and J. L\u00f3pez-Santiago, provides a comprehensive study of the state of the art of this topic.<\/jats:p>\n                  <jats:p>The authors highlight respective benefits and limitations of many computational schemes for approximating the marginal likelihood of different models or the ratio of two marginal likelihoods. Connections and differences among these techniques are worked out. Some of the most relevant methodologies are compared through theoretical comparisons and numerical experiments. The chief accomplishment is the presentation of various methods introduced independently in the literature in a unified framework.<\/jats:p>\n                  <jats:p>The second Survey and Review paper, \u201cFlow-Based Algorithms for Improving Clusters: A Unifying Framework, Software, and Performance,\u201d by Kimon Fountoulakis, Meng Liu, David F. Gleich, and Michael W. Mahoney, addresses the improvement of clusters of points in a vector space or nodes in a graph, which is a primary problem in statistical data analysis.<\/jats:p>\n                  <jats:p>Clustering means grouping of objects in a set such that objects in the same cluster are more similar to each other than to those in other groups. It is a main task of exploratory data analysis and a common technique for statistical data analysis, used in pattern recognition, image analysis, data compression, machine learning, and many other fields.<\/jats:p>\n                  <jats:p>A frequent practice is improving a given cluster such that conductance is minimized. Cluster analysis can be achieved by various algorithms. While the literature is rich on global spectral methods, flow-based methods have attracted less attention so far, since they lack the simplicity of related spectral methods and seeded graph diffusion methods like PageRank. These spectral methods are often easy to explain in terms of random walks, Markov chains, linear systems, and intuitive notions of diffusion. On the other hand, at the expense of complex graph constructions, the flow-based methods often yield impressive theoretical results.<\/jats:p>\n                  <jats:p>The goal of this review is to provide a unified framework for flow-based methods, based on a class of optimization methods known as fractional programming. The fractional programming optimization perspective unifies all existing flow-based cluster improvement methods, showing that these methods are attractive alternatives to global spectral methods.<\/jats:p>","DOI":"10.1137\/23n975612","type":"journal-article","created":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T12:38:38Z","timestamp":1675946318000},"page":"1-1","source":"Crossref","is-referenced-by-count":0,"title":["Survey and Review"],"prefix":"10.1137","volume":"65","author":[{"given":"Marlis","family":"Hochbruck","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,2,9]]},"container-title":["SIAM Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/23N975612","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:33:39Z","timestamp":1787236419000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23N975612"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["10.1137\/23N975612"],"URL":"https:\/\/doi.org\/10.1137\/23n975612","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2]]}}}