log_lik {AIUQ}R Documentation

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
)

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

Value

The numerical value of natural logarithm of the likelihood.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

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.


[Package AIUQ version 0.5.3 Index]