{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:02:43Z","timestamp":1760238163543,"version":"build-2065373602"},"reference-count":62,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,17]],"date-time":"2020-07-17T00:00:00Z","timestamp":1594944000000},"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>Information dynamics and computational mechanics provide a suite of measures for assessing the information- and computation-theoretic properties of complex systems in the absence of mechanistic models. However, both approaches lack a core set of inferential tools needed to make them more broadly useful for analyzing real-world systems, namely reliable methods for constructing confidence sets and hypothesis tests for their underlying measures. We develop the computational mechanics bootstrap, a bootstrap method for constructing confidence sets and significance tests for information-dynamic measures via confidence distributions using estimates of    \u03f5   -machines inferred via the Causal State Splitting Reconstruction (CSSR) algorithm. Via Monte Carlo simulation, we compare the inferential properties of the computational mechanics bootstrap to a Markov model bootstrap. The computational mechanics bootstrap is shown to have desirable inferential properties for a collection of model systems and generally outperforms the Markov model bootstrap. Finally, we perform an in silico experiment to assess the computational mechanics bootstrap\u2019s performance on a corpus of    \u03f5   -machines derived from the activity patterns of fifteen-thousand Twitter users.<\/jats:p>","DOI":"10.3390\/e22070782","type":"journal-article","created":{"date-parts":[[2020,7,17]],"date-time":"2020-07-17T10:22:02Z","timestamp":1594981322000},"page":"782","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Discrete Information Dynamics with Confidence via the Computational Mechanics Bootstrap: Confidence Sets and Significance Tests for Information-Dynamic Measures"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4624-3951","authenticated-orcid":false,"given":"David","family":"Darmon","sequence":"first","affiliation":[{"name":"Department of Mathematics, Monmouth University, West Long Branch, NJ 07764, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2056","DOI":"10.1109\/36.851786","article-title":"Complexity in the atmosphere","volume":"38","author":"Palmer","year":"2000","journal-title":"IEEE Trans. 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