LTPDA Toolbox™

Method ao/mhsample

  MHSAMPLE The Metropolis - Hastings algorithm
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  The Metropolis - Hastings algorithm: Samples a given likelihood function.
                   
               Warning: The function mhsample does not performs sanity
                        checks on the inputs. It assumes that the given
                        data-sets are in frequency domain and correctly
                        defined.
 
  CALL:        b = mhsample(out, pl)
 
  INPUTS:      out     - analysis objects with measured outputs
 
               pl      - parameter list
 
  OUTPUTS:     b       - pest object contatining estimated information
 
  Parameters Description
        
 
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Method Details
Access	public
Defining Class	ao
Sealed	0
Static	0

Parameter Description

Sets for this method …
Default

Default
no description
Key	Default Value	Options	Description
mhsample
INNAMES	''	none	Input names. Used for ssm models
OUTNAMES	''	none	Output names. Used for ssm models
MODEL	''	none	Model to fit.
FITPARAMS	[]	none	A cell array of evaluated parameters.
INPUT	''	none	A matrix array of input signals.
NSAMPLES	1000	none	number of samples of the chain.
COV	[]	none	covariance of the gaussian jumping distribution.
SCALE MATRIX	''	none	A matrix array of noise spectrum (PSD) used to compute the likelihood. It is possible to input just a scale matrix, containing the desirable weights.
LOG-LIKELIHOOD	''	none	The log-likelihood to sample with the MH or Simplex algorithm. If left empty, then the standard Gaussian approximation will be employed.
RANGE	[]	none	Range where the parameteters are sampled.
SEARCH	1	1 0	Set to true to use bigger jumps in parameter space during annealing and cool down.
PROPOSAL SAMPLER	[]	none	Set the proposal PDF to sample from. If left empty the multivariate Gaussian is used.
PROPOSAL PDF	[]	none	Input the proposal PDF. This is needed when the proposal PDF is not symmetric.If this field is empty, a symmetric PDF is assumed. Check help for details.
HEAT	1	none	The heat index flattening likelihood surface during annealing.
TC	[0 1]	none	An array of two values [i j], setting the i-th and j-th sample for the cooling down.
X0	[]	none	The proposed initial values.
UPDATE FIM FREQ	[]	none	Provide with the desired frequency where the FIM should be updated.
JUMPS	[]	none	An array of four numbers setting the rescaling of the covariance matrix during the search phase.
PLOT TRACES	[]	none	Select indexes of the parameters to be plotted.
PLOT DIAGNOSTICS	0	0 1	Set to true to plot diagnostigs at the end of the sampling.
DEBUG	0	0 1	Set to true to get debug information of the MCMC process.
INMODEL	''	none	Input model. Still under test
OUTMODEL	''	none	Output model. Still under test
FPRINT	100	none	Print progress on screen every specified numeber of samples.
TXT	0	0 1	Set to true to print the acceptance ratio to a txt file during the MH sampling.
PRIOR	''	none	blah
LOG PARAMETERS	''	none	Select the parameters to be treated in log scale.
ANNEAL	'simul'	'simul' 'thermo'	Choose type of annealing during sampling. Default value is simulated annealing. Choose "thermo" for annealing with a thermostat. SNR is computed and if it is larger than a fixed value SNR0 (provided also in the plist), then the chains are heated by a factor of (SNR(1)/SNR0)^2.
MODELFREQDEPENDENT	1	1 0	Set to true to use frequency dependent s models, set to false when using constant models
LOGSPACE	1	1 0	False-True key to choose the way of sampling.
SNR0	200	none	Fixed value for thermostated annealing.
FREQUENCIES VECTOR	200	none	A vector of frequencies. Used for the update of the Fisher Matrix during the MH sampling.
crb
PINV	0	0 1	Use the Penrose-Moore pseudoinverse
TOL	[]	none	Tolerance for the Penrose-Moore pseudoinverse
DIFFSTEP	[]	none	Numerical differentiation step for ssm models
NGRID	[]	none	Number of points in the grid to compute the optimal differentiation step for ssm models
STEPRANGES	[]	none	An array with upper and lower values for the parameters ranges. To be used to compute the optimal differentiation step for ssm models.
FREQUENCIES	[]	none	The frequencies to perform the analysis.
FSOUT	[]	none	Resampling.
F1	[]	none	Initial frequency for the analysis.
F2	[]	none	Final frequency for the analysis.
NOISE SCALE	'PSD'	'PSD' 'LPSD'	Select the way to handle the noise/weight data. Can use the PSD/CPSD or the LPSD/CLPSD functions.
YUNITS	'm s^-2'	none	The Y units of the noise time series, in case the MFH object is a 'core' type.
TRIM	[100 -100]	none	A 2x1 vector that denotes the samples to split from the star and end of the time-series (split in offsets).
REGULARIZE	0	0 1	If the resulting fisher matrix is not positive definite, try a numerical trick to continue sampling.
NEARESTSPD	0	0 1	Try to find the nearest symmetric and positive definite covariance matrix, with the 'nearestSPD' method from MATLAB file exchange.
VERSION	'core'	'core' 'ao'	Choose between 'AO' and 'CORE' types. Applies to MFH models.
NFFT	-1	none	The number of samples in each fft [default: length of input data]. A string value containing the variable 'fs' can also be used, e.g., `plist('Nfft', '2*fs')`
WIN	'BH92'	'Rectangular' 'Welch' 'Bartlett' 'Hanning' 'Hamming' 'Nuttall3' 'Nuttall4' 'Nuttall3a' 'Nuttall3b' 'Nuttall4a' 'Nuttall4b' 'Nuttall4c' 'BH92' 'SFT3F' 'SFT3M' 'FTNI' 'SFT4F' 'SFT5F' 'SFT4M' 'FTHP' 'HFT70' 'FTSRS' 'SFT5M' 'HFT90D' 'HFT95' 'HFT116D' 'HFT144D' 'HFT169D' 'HFT196D' 'HFT223D' 'HFT248D' 'Kaiser' 'levelledHanning'	The window to be applied to the data to remove the discontinuities at edges of segments. [default: taken from user prefs] Only the design parameters of the window object are used. Enter a string value containing the window name e.g. `plist('Win', 'Kaiser', 'psll', 200)` `plist('Win', 'BH92')`
PSLL	200	none	The peak sidelobe level for Kaiser windows. Note: it is ignored for all other windows
OLAP	-1	none	The segment percent overlap [-1 == take from window function]
ORDER, N	0	-1 0 1 2 3 4 5 6 7 8 9	The order of segment detrending: -1 - no detrending 0 - subtract mean 1 - subtract linear fit N - subtract fit of polynomial, order N
NAVS	-1	none	Force number of averages. If set, and if Nfft was set to 0 or -1, the number of points for each window will be calculated to match the request.
DROP WINDOW SAMPLES	1	1 0	Drop the recommended (by the window) number of samples of the final computed spectral series.
TIMES, SPLIT	[]	none	The time range to analyze. If not empty, sets the time interval to operate on. As in ao/split, the interval can be specified by: a vector of doubles a timespan object a cell array of time strings a vector of time objects
computeICSMatrix
NOUT	''	none	The number of outputs.
INVERSE	1	1 0	Set to false to return the spectrum matrix, but not inverted.
ISDIAG	0	0 1	For the case of systems where the cross-spectrum matrix is diagonal it can be set to true to skip estimating the non-diagonal elements. Useful for multiple inputs/outputs.
FS	1	none	The sampling frequency of the data.
INTERPOLATION METHOD, INTERP METHOD	'LINEAR'	'LINEAR' 'SPLINE' 'PCHIP' 'CUBIC'	The interpolation method.
FREQS	[]	none	Array of frequencies where the analysis is performed.
BIN DATA	0	0 1	Set to true to re-bin the measured noise data.
FIT NOISE MODEL	0	0 1	Set to true to attempt a fit on the noise spectra using the 'polyfitSpectrum' function.
POLYNOMIAL ORDER	[-4 -3 -2 -1 0 1 2 3 4]	none	The order of the polynomial to be used in the 'polyfitSpectrum' function.
PLOT FITS	0	0 1	Set to true to produce plots of the fits in case of 'fit noise model' is set to true.
lpsd
KDES	100	none	The desired number of averages.
JDES	1000	none	The desired number of spectral frequencies to compute.
LMIN	0	none	The minimum segment length.
SCALE	'PSD'	'PSD' 'ASD' 'PS' 'AS'	The scaling of output. Choose from: PSD - Power Spectral Density ASD - Amplitude (linear) Spectral Density PS - Power Spectrum AS - Amplitude (linear) Spectrum

Example
plist('INNAMES', '', 'OUTNAMES', '', 'MODEL', '', 'FITPARAMS', [[]], 'INPUT', '', 'NSAMPLES', [1000], 'COV', [[]], 'SCALE MATRIX', '', 'LOG-LIKELIHOOD', '', 'RANGE', [[]], 'SEARCH', [true], 'PROPOSAL SAMPLER', [[]], 'PROPOSAL PDF', [[]], 'HEAT', [1], 'TC', [[0 1]], 'X0', [[]], 'UPDATE FIM FREQ', [[]], 'JUMPS', [[]], 'PLOT TRACES', [[]], 'PLOT DIAGNOSTICS', [false], 'DEBUG', [false], 'INMODEL', '', 'OUTMODEL', '', 'FPRINT', [100], 'TXT', [false], 'PRIOR', '', 'LOG PARAMETERS', '', 'ANNEAL', 'simul', 'MODELFREQDEPENDENT', [true], 'LOGSPACE', [true], 'SNR0', [200], 'FREQUENCIES VECTOR', [200], 'PINV', [false], 'TOL', [[]], 'DIFFSTEP', [[]], 'NGRID', [[]], 'STEPRANGES', [[]], 'FREQUENCIES', [[]], 'FSOUT', [[]], 'F1', [[]], 'F2', [[]], 'NOISE SCALE', 'PSD', 'YUNITS', 'm s^-2', 'TRIM', [[100 -100]], 'REGULARIZE', [false], 'NEARESTSPD', [false], 'VERSION', 'core', 'NFFT', [-1], 'WIN', 'BH92', 'PSLL', [200], 'OLAP', [-1], 'ORDER', [0], 'NAVS', [-1], 'DROP WINDOW SAMPLES', [true], 'TIMES', [[]], 'NOUT', '', 'INVERSE', [true], 'ISDIAG', [false], 'FS', [1], 'INTERPOLATION METHOD', 'LINEAR', 'FREQS', [[]], 'BIN DATA', [false], 'FIT NOISE MODEL', [false], 'POLYNOMIAL ORDER', [[-4 -3 -2 -1 0 1 2 3 4]], 'PLOT FITS', [false], 'KDES', [100], 'JDES', [1000], 'LMIN', [0], 'SCALE', 'PSD')

Example

plist('INNAMES', '', 'OUTNAMES', '', 'MODEL', '', 'FITPARAMS', [[]], 'INPUT', '', 'NSAMPLES', [1000], 'COV', [[]], 'SCALE MATRIX', '', 'LOG-LIKELIHOOD', '', 'RANGE', [[]], 'SEARCH', [true], 'PROPOSAL SAMPLER', [[]], 'PROPOSAL PDF', [[]], 'HEAT', [1], 'TC', [[0 1]], 'X0', [[]], 'UPDATE FIM FREQ', [[]], 'JUMPS', [[]], 'PLOT TRACES', [[]], 'PLOT DIAGNOSTICS', [false], 'DEBUG', [false], 'INMODEL', '', 'OUTMODEL', '', 'FPRINT', [100], 'TXT', [false], 'PRIOR', '', 'LOG PARAMETERS', '', 'ANNEAL', 'simul', 'MODELFREQDEPENDENT', [true], 'LOGSPACE', [true], 'SNR0', [200], 'FREQUENCIES VECTOR', [200], 'PINV', [false], 'TOL', [[]], 'DIFFSTEP', [[]], 'NGRID', [[]], 'STEPRANGES', [[]], 'FREQUENCIES', [[]], 'FSOUT', [[]], 'F1', [[]], 'F2', [[]], 'NOISE SCALE', 'PSD', 'YUNITS', 'm s^-2', 'TRIM', [[100 -100]], 'REGULARIZE', [false], 'NEARESTSPD', [false], 'VERSION', 'core', 'NFFT', [-1], 'WIN', 'BH92', 'PSLL', [200], 'OLAP', [-1], 'ORDER', [0], 'NAVS', [-1], 'DROP WINDOW SAMPLES', [true], 'TIMES', [[]], 'NOUT', '', 'INVERSE', [true], 'ISDIAG', [false], 'FS', [1], 'INTERPOLATION METHOD', 'LINEAR', 'FREQS', [[]], 'BIN DATA', [false], 'FIT NOISE MODEL', [false], 'POLYNOMIAL ORDER', [[-4 -3 -2 -1 0 1 2 3 4]], 'PLOT FITS', [false], 'KDES', [100], 'JDES', [1000], 'LMIN', [0], 'SCALE', 'PSD')

Some information of the method ao/mhsample are listed below:
Class name	ao
Method name	mhsample
Category	Signal Processing
Package name	ltpda
VCS Version	967b0eec0dece803a81af8ef54ad2f8c784b20b2
Min input args	1
Max input args	-1
Min output args	1
Max output args	-1
Can be used as modifier	1
Supported numeric types	{'double'}

Method: ao/map3D

Method: ao/modelSelect

Method ao/mhsample

Parameter Description

Default

Example