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  "Title": "Ab Initio Uncertainty Quantification",
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  "Author": "Yue He [aut], Xubo Liu [aut], Tong Lin [aut], Mengyang Gu [aut,\ncre]",
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  "Description": "Uncertainty quantification and inverse estimation by\nprobabilistic generative models from the beginning of the data\nanalysis. An example is a Fourier basis method for inverse\nestimation in scattering analysis of microscopy videos. It does\nnot require specifying a certain range of Fourier bases and it\nsubstantially reduces computational cost via the generalized\nSchur algorithm. See the reference: Mengyang Gu, Yue He, Xubo\nLiu and Yimin Luo (2023), <doi:10.48550/arXiv.2309.02468>.",
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    "aniso_simulation",
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    "anisotropic_fbm_ou_particle_intensity",
    "anisotropic_fbm_particle_intensity",
    "anisotropic_log_lik",
    "anisotropic_log_lik_grad",
    "anisotropic_numerical_msd",
    "anisotropic_ou_particle_intensity",
    "bm_particle_intensity",
    "cart2polar",
    "corr_fBM",
    "fbm_ou_particle_intensity",
    "fbm_particle_intensity",
    "FFT2D",
    "fftshift",
    "fill_intensity",
    "get_dqt",
    "get_est_param",
    "get_est_parameters_MSD_SAM_interval",
    "get_est_parameters_MSD_SAM_interval_anisotropic",
    "Get_Gp_Gpp_GSER",
    "get_grad_trans",
    "get_initial_param",
    "get_isf",
    "get_MSD",
    "get_MSD_with_grad",
    "get_true_param_aniso_sim",
    "get_true_param_sim",
    "intensity_format_transform",
    "l2_estAB",
    "l2_fixedAB",
    "log_lik",
    "log_lik_grad",
    "modeled_dqt",
    "modeled_isf",
    "numerical_msd",
    "ou_particle_intensity",
    "param_uncertainty",
    "param_uncertainty_anisotropic",
    "plot_intensity",
    "plot_MSD",
    "plot_traj",
    "SAM",
    "SAM_Dqt",
    "show.aniso_sam",
    "show.aniso_simulation",
    "show.sam",
    "show.simulation",
    "simulation",
    "theta_est_l2_dqt_estAB",
    "theta_est_l2_dqt_fixedAB"
  ],
  "_help": [
    {
      "page": "aniso_SAM",
      "title": "Scattering analysis of microscopy for anisotropic processes",
      "topics": [
        "aniso_SAM"
      ]
    },
    {
      "page": "aniso_SAM-class",
      "title": "Anisotropic SAM class",
      "topics": [
        "aniso_SAM-class"
      ]
    },
    {
      "page": "aniso_simulation",
      "title": "Simulate anisotropic 2D particle movement",
      "topics": [
        "aniso_simulation"
      ]
    },
    {
      "page": "aniso_simulation-class",
      "title": "Anisotropic simulation class",
      "topics": [
        "aniso_simulation-class"
      ]
    },
    {
      "page": "get_dqt",
      "title": "Compute observed dynamic image structure function",
      "topics": [
        "get_dqt"
      ]
    },
    {
      "page": "Get_Gp_Gpp_GSER",
      "title": "Estimate Viscoelastic Moduli by GSER",
      "topics": [
        "Get_Gp_Gpp_GSER"
      ]
    },
    {
      "page": "get_isf",
      "title": "Compute empirical intermediate scattering function",
      "topics": [
        "get_isf"
      ]
    },
    {
      "page": "modeled_dqt",
      "title": "Compute modeled dynamic image structure function",
      "topics": [
        "modeled_dqt"
      ]
    },
    {
      "page": "modeled_isf",
      "title": "Compute modeled intermediate scattering function",
      "topics": [
        "modeled_isf"
      ]
    },
    {
      "page": "plot_intensity",
      "title": "Plot 2D intensity",
      "topics": [
        "plot_intensity"
      ]
    },
    {
      "page": "plot_MSD",
      "title": "Plot estimated MSD with uncertainty from SAM class",
      "topics": [
        "plot_MSD"
      ]
    },
    {
      "page": "plot_traj",
      "title": "Plot 2D particle trajectory",
      "topics": [
        "plot_traj"
      ]
    },
    {
      "page": "SAM",
      "title": "Scattering analysis of microscopy",
      "topics": [
        "SAM"
      ]
    },
    {
      "page": "SAM-class",
      "title": "SAM class",
      "topics": [
        "SAM-class"
      ]
    },
    {
      "page": "show.aniso_sam",
      "title": "Show scattering analysis of microscopy for anisotropic processes (aniso_SAM) object",
      "topics": [
        "show.aniso_sam"
      ]
    },
    {
      "page": "show.aniso_simulation",
      "title": "Show anisotropic simulation object",
      "topics": [
        "show.aniso_simulation"
      ]
    },
    {
      "page": "show.sam",
      "title": "Show scattering analysis of microscopy (SAM) object",
      "topics": [
        "show.sam"
      ]
    },
    {
      "page": "show.simulation",
      "title": "Show simulation object",
      "topics": [
        "show.simulation"
      ]
    },
    {
      "page": "simulation",
      "title": "Simulate 2D particle movement",
      "topics": [
        "simulation"
      ]
    },
    {
      "page": "simulation-class",
      "title": "Simulation class",
      "topics": [
        "simulation-class"
      ]
    }
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    "fftw",
    "fftwtools",
    "geometry",
    "linprog",
    "lpSolve",
    "magic",
    "misc3d",
    "nloptr",
    "plot3D",
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    "Rcpp",
    "RcppEigen",
    "RcppProgress",
    "RobustGaSP",
    "SuperGauss"
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      "source": "AIUQ.Rmd",
      "filename": "AIUQ.html",
      "title": "AIUQ tutorial",
      "author": "Yue He, Xubo Liu, Mengyang Gu, Tong Lin",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Example 1: Simulate BM and get estimated parameters using BM model",
        "Example 2: Simulate BM with user defined parameters and get estimated MSD with uncertainty",
        "Example 3: Simulate OU process and get estimated parameters using OU model",
        "Example 4: User defined MSD structure",
        "Example 5: Simulate BM and get model-free MSD estimation",
        "Example 6: Real data and get model-free MSD estimation",
        "Example 7: Real data and get storage and loss moduli estimation"
      ],
      "created": "2024-07-03 02:41:34",
      "modified": "2026-05-25 19:20:02",
      "commits": 2
    }
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