log_lik_grad {AIUQ} | R Documentation |
This function computes the gradient for natural logarithm of the likelihood for selected range of wave vectors. See 'References'.
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
)
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 |
msd_grad_fn |
user defined MSD gradient structure, a function of
|
The numerical value of gradient for natural logarithm of the likelihood.
Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]
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.