log_lik_grad {AIUQ}R Documentation

Gradient of log likelihood

Description

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

Usage

log_lik_grad(
  param,
  I_q_cur,
  B_cur,
  A_neg,
  index_q,
  I_o_q_2_ori,
  d_input,
  q_ori_ring_loc_unique_index,
  sz,
  len_t,
  q,
  model_name,
  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

stochastic process 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 gradient for 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 0.5.2 Index]