anisotropic_log_lik_grad {AIUQ} | R Documentation |
Gradient of log likelihood for anisotropic processes
Description
This function computes the gradient for natural logarithm of the likelihood for selected range of wave vectors of anisotropic processes. See 'References'.
Usage
anisotropic_log_lik_grad(
param,
I_q_cur,
B_cur,
index_q,
I_o_q_2_ori,
d_input,
q_ori_ring_loc_unique_index,
sz,
len_t,
model_name,
q1,
q2,
q1_unique_index,
q2_unique_index,
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 |
model_name |
stochastic process for constructing MSD, options from ('BM', 'OU','FBM','OU+FBM', 'user_defined') |
q1 |
wave vector in unit of um^-1 in x direction |
q2 |
wave vector in unit of um^-1 in y direction |
q1_unique_index |
index for wave vector that give unique frequency in x direction |
q2_unique_index |
index for wave vector that give unique frequency in y direction |
msd_fn |
user defined mean squared displacement structure (MSD), a
function of |
msd_grad_fn |
user defined MSD gradient structure, a function of
|
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.