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  "Title": "Multivariate Normal Probabilities using Vecchia Approximation",
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  "Date": "2026-01-26",
  "Authors@R": "c(person(\"Jian Cao\", role = c(\"aut\", \"cre\"), email = \"jcao2416@gmail.com\"),\nperson(\"Matthias Katzfuss\", role = \"aut\"))",
  "Author": "Jian Cao [aut, cre], Matthias Katzfuss [aut]",
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  "Description": "Under a different representation of the multivariate\nnormal (MVN) probability, we can use the Vecchia approximation\nto sample the integrand at a linear complexity with respect to\nn. Additionally, both the SOV algorithm from Genz (92) and the\nexponential-tilting method from Botev (2017) can be adapted to\nlinear complexity. The reference for the method implemented in\nthis package is Jian Cao and Matthias Katzfuss (2024)\n\"Linear-Cost Vecchia Approximation of Multivariate Normal\nProbabilities\" <doi:10.48550/arXiv.2311.09426>. Two major\nreferences for the development of our method are Alan Genz\n(1992) \"Numerical Computation of Multivariate Normal\nProbabilities\" <doi:10.1080/10618600.1992.10477010> and Z. I.\nBotev (2017) \"The Normal Law Under Linear Restrictions:\nSimulation and Estimation via Minimax Tilting\"\n<doi:10.48550/arXiv.1603.04166>.",
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      "title": "Univariate ordering under FIC approximation, first m chosen by m iter of dense univariate reordering",
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        "FIC_reorder_univar"
      ]
    },
    {
      "page": "find_nn_corr",
      "title": "Find ordered nearest neighbors based on a correlation Matrix. Assuming the absolute value of the correlation is monotonically decreasing with distance. Returns an n X (m + 1) matrix similar to `GpGp::find_ordered_nn`.",
      "topics": [
        "find_nn_corr"
      ]
    },
    {
      "page": "get_sp_inv_chol",
      "title": "Get the inverse upper Cholesky factor under the Vecchia approximation",
      "topics": [
        "get_sp_inv_chol"
      ]
    },
    {
      "page": "loglk_censor_MVN",
      "title": "Compute censored multivariate normal (MVN) log-probabilities that have spatial covariance matrices using Vecchia approximation",
      "topics": [
        "loglk_censor_MVN"
      ]
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    {
      "page": "mvrandn",
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      "topics": [
        "mvrandn"
      ]
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    {
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      "title": "Simulate truncated multivariate normal (TMVT) using the Vecchia approximation",
      "topics": [
        "mvrandt"
      ]
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      "page": "pmvn",
      "title": "Compute multivariate normal (MVN) probabilities that have spatial covariance matrices using Vecchia approximation",
      "topics": [
        "pmvn"
      ]
    },
    {
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      "title": "Applying the multi-level Monte Carlo (MLMC) technique to the pmvn function The function uses 'NLevel1 = 1' for 'm = m2' and the same exponential tilting parameter as 'm = m1' to compute one MC estimate. This MC estimate is used to correct the bias from the Vecchia approximation",
      "topics": [
        "pmvn_MLMC"
      ]
    },
    {
      "page": "pmvt",
      "title": "Compute multivariate Student-t (MVT) probabilities that have spatial covariance matrices using Vecchia approximation",
      "topics": [
        "pmvt"
      ]
    },
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      "page": "pmvt_MLMC",
      "title": "Applying the multi-level Monte Carlo (MLMC) technique to the pmvt function The function uses 'NLevel1 = 1' for 'm = m2' and the same exponential tilting parameter as 'm = m1' to compute one MC estimate. This MC estimate is used to correct the bias from the Vecchia approximation",
      "topics": [
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      "page": "ptmvrandn",
      "title": "Simulate partially censored multivariate normal (MVN) at censored locations using the Vecchia approximation",
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