log_lik: Log likelihood of the model

Description

This function computes the natural logarithm of the likelihood of the latent factor model for selected range of wave vectors. See 'References'.

Usage

log_lik(
  param,
  I_q_cur,
  B_cur,
  index_q,
  I_o_q_2_ori,
  d_input,
  q_ori_ring_loc_unique_index,
  sz,
  len_t,
  q,
  model_name,
  A_neg,
  msd_fn = NA,
  msd_grad_fn = NA
)

Value

The numerical value of natural logarithm of the likelihood.

Arguments

param: a vector of natural logarithm of parameters
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
d_input: sequence of lag times
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
q: wave vector in unit of um^-1
model_name: model for constructing MSD, options from ('BM','OU', 'FBM','OU+FBM', 'user_defined')
msd_fn: user defined mean squared displacement structure (MSD), a function of param parameters and d_input lag times
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.