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AIUQ (version 0.5.3)

Ab Initio Uncertainty Quantification

Description

Uncertainty quantification and inverse estimation by probabilistic generative models from the beginning of the data analysis. An example is a Fourier basis method for inverse estimation in scattering analysis of microscopy videos. It does not require specifying a certain range of Fourier bases and it substantially reduces computational cost via the generalized Schur algorithm. See the reference: Mengyang Gu, Yue He, Xubo Liu and Yimin Luo (2023), .

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Version

Install

install.packages('AIUQ')

Monthly Downloads

206

Version

0.5.3

License

GPL (>= 3)

Maintainer

Mengyang Gu

Last Published

July 2nd, 2024

Functions in AIUQ (0.5.3)

corr_fBM

Construct correlation matrix for FBM
fbm_ou_particle_intensity

Simulate 2D particle trajectory follows fBM plus OU
fill_intensity

Construct intensity profile for a given particle trajectory
fbm_particle_intensity

Simulate 2D particle trajectory follows fBM
get_dqt

Compute observed dynamic image structure function
get_MSD_with_grad

Construct MSD and MSD gradient with transformed parameters
fftshift

fftshift
l2_estAB

Compute l2 loss for Dqt
get_est_param

Transform parameters estimated in SAM class to parameters structure in MSD function
get_est_parameters_MSD_SAM_interval

Construct 95% confidence interval
intensity_format_transform

Transform intensity profile into SS_T matrix
l2_fixedAB

Compute l2 loss for Dqt with fixed A(q) and B
log_lik

Log likelihood of the model
modeled_dqt

Compute modeled dynamic image structure function
plot_intensity

Plot 2D intensity
get_isf

Compute empirical intermediate scattering function
plot_traj

Plot 2D particle trajectory
modeled_isf

Compute modeled intermediate scattering function
ou_particle_intensity

Simulate 2D particle trajectory follows OU process
log_lik_grad

Gradient of log likelihood
get_initial_param

Construct initial values for the parameters to be optimized over
get_MSD

Construct MSD
get_grad_trans

Construct parameter transformation for optimization using exact gradient
get_true_param_aniso_sim

Transform parameters in anisotropic simulation class to parameters structure in MSD function
get_est_parameters_MSD_SAM_interval_anisotropic

Construct 95% confidence interval for anisotropic processes
show.aniso_sam

Show scattering analysis of microscopy for anisotropic processes (aniso_SAM) object
param_uncertainty_anisotropic

Compute 95% confidence interval for anisotropic processes
numerical_msd

Compute numerical MSD
get_true_param_sim

Transform parameters in simulation class to parameters structure in MSD function
plot_MSD

Plot estimated MSD with uncertainty from SAM class
show.aniso_simulation

Show anisotropic simulation object
show.simulation

Show simulation object
show.sam

Show scattering analysis of microscopy (SAM) object
theta_est_l2_dqt_estAB

Minimize l2 loss for Dqt
simulation

Simulate 2D particle movement
simulation-class

Simulation class
theta_est_l2_dqt_fixedAB

Minimize l2 loss for Dqt with fixed A(q) and B
param_uncertainty

Compute 95% confidence interval
aniso_SAM

Scattering analysis of microscopy for anisotropic processes
aniso_simulation-class

Anisotropic simulation class
SAM

Scattering analysis of microscopy
SAM_Dqt

Compute dynamic image structure function
FFT2D

2D Fourier transformation and calculate wave number
aniso_SAM-class

Anisotropic SAM class
AIUQ-package

AIUQ: Ab Initio Uncertainty Quantification
bm_particle_intensity

Simulate 2D particle trajectory follows Brownian Motion
cart2polar

Transform Cartesian coordinates to polar coordinates
anisotropic_numerical_msd

Compute anisotropic numerical MSD
SAM-class

SAM class
aniso_simulation

Simulate anisotropic 2D particle movement
anisotropic_ou_particle_intensity

Simulate 2D particle trajectory follows anisotropic OU process
anisotropic_fbm_particle_intensity

Simulate 2D particle trajectory follows anisotropic fBM
anisotropic_fbm_ou_particle_intensity

Simulate 2D particle trajectory follows anisotropic fBM plus OU
anisotropic_bm_particle_intensity

Simulate 2D particle trajectory follows anisotropic Brownian Motion
anisotropic_log_lik

Log likelihood for anisotropic processes
anisotropic_log_lik_grad

Gradient of log likelihood for anisotropic processes