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Under such an assumption, this work builds upon a recently introduced multi-index sequential Monte Carlo (SMC) ratio estimator, which provably enjoys the complexity improvements of multi-index Monte Carlo (MIMC) and the efficiency of SMC for inference. The present work leverages a randomization strategy to remove bias entirely, which simplifies estimation substantially, particularly in the MIMC context, where the choice of index set is otherwise important. Under reasonable assumptions, the proposed method provably achieves the same canonical complexity of MSE\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$^{-1}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msup>\n                            <mml:mrow\/>\n                            <mml:mrow>\n                              <mml:mo>-<\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    as the original method (where MSE is mean squared error), but without discretization bias. It is illustrated on examples of Bayesian inverse and spatial statistics problems.\n                  <\/jats:p>","DOI":"10.1007\/s11222-023-10249-9","type":"journal-article","created":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T09:05:00Z","timestamp":1688979900000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A randomized multi-index sequential Monte Carlo method"],"prefix":"10.1007","volume":"33","author":[{"given":"Xinzhu","family":"Liang","sequence":"first","affiliation":[]},{"given":"Shangda","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Simon L.","family":"Cotter","sequence":"additional","affiliation":[]},{"given":"Kody J. 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