param_uncertainty: Compute 95% confidence interval

Description

This function construct the lower and upper bound for 95% confidence interval of estimated parameters for the given model, including parameters contained in the intermediate scattering function and background noise. See 'References'.

Usage

param_uncertainty(
  param_est,
  I_q_cur,
  B_cur = NA,
  A_neg,
  index_q,
  I_o_q_2_ori,
  q_ori_ring_loc_unique_index,
  sz,
  len_t,
  d_input,
  q,
  model_name,
  estimation_method = "asymptotic",
  M,
  num_iteration_max,
  lower_bound,
  msd_fn = NA,
  msd_grad_fn = NA
)

Value

A matrix of lower and upper bound for natural logarithm of parameters in the fitted model using AIUQ method in SAM class

Arguments

param_est: a vector of natural logarithm of estimated parameters from maximize the log likelihood. This vector will serve as initial values in the optim function.
I_q_cur: Fourier transformed intensity profile
B_cur: current value of B. This parameter is determined by the noise in the system. See 'References'.
index_q: selected index of wave number
I_o_q_2_ori: absolute square of Fourier transformed intensity profile, ensemble over time
q_ori_ring_loc_unique_index: index for wave vector that give unique frequency
sz: frame size of the intensity profile
len_t: number of time steps
d_input: sequence of lag times
q: wave vector in unit of um^-1
model_name: model name for the fitted model, options from ('BM','OU', 'FBM',OU+FBM','user_defined')
estimation_method: method for constructing 95% confidence interval, default is asymptotic
M: number of particles
num_iteration_max: the maximum number of iterations in optim
lower_bound: lower bound for the "L-BFGS-B" method in optim
msd_grad_fn: user defined MSD gradient structure, a function of param and d_input

Author

tools:::Rd_package_author("AIUQ")

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.