[result, options] = replicate_regression(t, y, sigma, r, flag_fix_parameters, varargin)
Bayesian replicate regression for multiple time series measured in replicate.
Data are directly provided as vectors; they can be transformed to logarithmic scale if desired
FUNCTION ARGUMENTS
t, y, sigma, r:
input data (times, values, standard errors, replicate labels)
given as row vectors (see replicate_regression_core.m)
flag_fix_parameters (Boolean, optional):
If set to 1, the options given in the following argument(s) will be accepted
without changes (otherwise they will be checked and updated)
varagin (optional)
Either a list of property/value pairs for algorithm options (list see below).
or a structure containing the property/value pairs (this is mandatory if flag_fix_parameters is set to 1)
FUNCTION OUTPUT
result
matlab struct with results from replicate regression
options
matlab struct with options values that were used in the calculation
The options list is supposed to be ordered by priority; earlier options override later options
The function is a wrapper for the function 'replicate_regression_core'
In converting the data to logarithms, y and sigma are either taken to be
*medians* and *geometric standard deviations*, or *means* and *standard deviations*
of the data values. The choice is defined by the argument 'options.transformation'
LIST OF OPTIONS ('X' marks options also appearing in function 'replicate_regression_core')
OPTION TYPE DEFAULT MEANING
options.verbose Boolean 1 Output information during regression
options.is_logarithmic Boolean 0 Declare that data are logarithmic
options.convert_to_logarithm Boolean 1 Convert data to logarithms for regression
options.log_transformation string 'arithmetic' 'arithmetic', 'geometric'
options.run_crossvalidation Boolean 0 Run crossvalidation
options.set_std float nan Value to replace all data standard deviations
options.insert_std float 1 Value to replace missing data standard deviations
options.start_at_t float 0 Start regression curves at starting time 'start_at_t' (instead of t=0)
options.start_value float nan Fixed start value for regression curves
options.shift_data string 'mean' Policy for shifting data before regression
{'none', 'fixed_start_value', 'mean', 'initial', 'fixed_1'}
options.shift_value float nan Shift used when shifting the data
options.basis X string 'cos+sin' Type of basis functions
options.n_comp X int nan Fixed number of basis functions
options.n_comp_min int 1 Minimal number of basis functions
options.n_comp_max int 20 Maximal number of basis functions
options.use_offset X Boolean 1 Use constant function as one of the basis functions
options.constant_before_start X Boolean 0 Set all basis functions constant for t<0
options.deviation_same_start Boolean 0 Enforce identical start values for all replicates
options.remove_offset X Boolean 0 Omit offset when creating the regression curves
options.t_smooth float nan Time constant for setting decreasing prior widths
options.t_jump X float nan Time constant for initial jump basis function
options.t_interp float t Time points for interpolated regression curves
options.average_std X string 'std_dev_mean' Type of uncertainty to be reported for average curve
options.central_offset_mean X float 0 Prior mean sigma_alpha_0 (for alpha_0 )
options.central_offset_width X float 1 Prior width sigma_alpha_0 (for alpha_0 )
options.central_first_mode_mean X float 0 Prior mean sigma_alpha_1 (for alpha_1 )
options.central_first_mode_width X float 1 Prior width sigma_alpha_1 (for alpha_1 )
options.central_mode_mean X vector [] Prior means sigma_alpha_m (for alpha_m )
options.central_mode_width X vector [] Prior widths sigma_alpha_m (for alpha_m )
options.central_jump_mean X float nan Prior means sigma_alpha_jump (for alpha_jump)
options.central_jump_width X float nan Prior widths sigma_alpha_jump (for alpha_jump)
options.deviation_offset_mean X float 0 Prior mean sigma_beta_0 (for beta_0 )
options.deviation_offset_width X float 1 Prior width sigma_beta_0 (for beta_0 )
options.deviation_first_mode_mean X float 0 Prior mean sigma_beta_1 (for beta_1 )
options.deviation_first_mode_width X float 1 Prior width sigma_beta_1 (for beta_1 )
options.deviation_mode_mean X float [] Prior means sigma_beta_m (for beta_m )
options.deviation_mode_width X float [] Prior widths sigma_beta_m (for beta_m )
options.deviation_jump_mean X float 0 Prior means sigma_beta_jump (for beta_jump )
options.deviation_jump_width X float 1 Prior widths sigma_beta_jump (for beta_jump )
options.flag_draw_sample X Boolean 1 Draw sample curve parameters and curve from the posterior
options.flag_time_derivative X Boolean 0 Compute time derivative curves
The basis functions are adjusted to the final time interval [ta,tb](from tt)
'cos' : cosine function, zero slope at t=ta and t=tb
'sin' : sine function, zero value at t=ta and t=tb
'sin_half' : sine function, zero value at t=ta
'sin_horizontal' : sine function, zero value at t=ta, zero slope at t=tb
'cos+sin' : cosine and sine functions, no restriction
'polynomial' : polynomial function, zero value at t=ta
'exp' : exponentially relaxing functions (t<0 => f=0; t>0 => f = 1-exp(t/tau);
The entire curves are shifted by a constant basis function
This can be suppressed by setting options.use_offset = 1
Wolfram Liebermeister (2013)
wolfram.liebermeister@gmail.com