vec_math
Class Bootstrap

java.lang.Object
  vec_math.Bootstrap

public class Bootstrap
extends Object

A class to work together with GeneralLinearRegression. If you have a data set and do not know or not care about underlying model, this class helps you to establish confidence limits on your solution. It supports similar constructors as the GeneralLinearRegression class, with the difference that the measurements are set after construct with #setMeasurements. The bootstrapping works in the following way: From the original data set, the basic solution is derived by using GeneralLinearRegression. Then, depending on the simualtion count, a number of simulated data sets are produced by replacing a certain fraction of the original data with duplicates from the origina data set. Each simulated data set is then solved for its linear model parameters. The standard deviation of the linear parameters from all simulated sets acts as the confidence estimate of the original solution. Literature: Numerical Recipes in C, p 691ff.

Nested Class Summary

private static class	Bootstrap.ExchangedData Helper class containing an exchanged data set.
static class	Bootstrap.StraightLine We fit data to a straight line.

Field Summary

private NVector	average The parameter averages on the solution to the simulated data.
private NVector	confidence The confidence estimations on the solution to the original data.
private NVector	data The original data.
private NVector[]	depend Where/how we measured the data.
private double	duplicate The fraction of data duplication, defaults to DUPLICATE.
static double	DUPLICATE The amount of duplicated data in the simulated sets.
private NVector	error The errors of the original data.
private Object[]	fit The fittings, either an array of functions or multidimensionals.
private int	freedom The number of simulated data sets per degree of freedom.
static int	FREEDOM The number of simulated data sets.
private NVector	maxima The parameter maxima on the solution to the simulated data.
private NVector	minima The parameter minima on the solution to the simulated data.
private static Random	random We use a random number generator, constructed at class load.
private double	rmsav The measures dropped at bootstrapping are used for a RMS average.
private double	rmsmax The measures dropped at bootstrapping are used for a RMS average.
private double	rmsmin The measures dropped at bootstrapping are used for a RMS average.
private boolean	usecovariance If true, we weigh the simulated parameters with their covariance sigma
static boolean	USECOVARIANCE The default usage of the covariance parameter estimates.

Constructor Summary

	Bootstrap(Function[] fitting, NVector x, NVector y, NVector sigma) Constructs a new bootstrap object from the supplied basic functions and the measurement with their errors.
	Bootstrap(Multidimensional[] fitting, NVector[] x, NVector y, NVector sigma) Constructs a new bootstrap object from the supplied basic functions and the measurement with their errors.
private	Bootstrap(NVector y, NVector sigma) Common constructor.

Method Summary

private void	doBootstrap() The time consuming part of the bootstrap class.
private static double	fitDropped(Object[] fitting, NVector solution, NVector[] x, NVector y) Fits a data set in y contained in the dependant variables x to the linear model parameters in solution.
NVector	getConfidenceEstimates() Returns a confidence estimate on the linear model parameter by bootstrapping the data.
private static Bootstrap.ExchangedData	getExchangedData(NVector[] depend, NVector data, NVector err, double duplicate) From our measurements and theier errors we derive a simulated data set.
double	getOriginalChiSquare() Returns the chi-square value of the original data set.
QuadMatrix	getOriginalCovariance() Returns the covariance matrix of the original fit.
double	getOriginalQuality() Returns the quality estimate of the original data set.
NVector	getOriginalSigma() Returns the standard diviation to the original solution.
NVector	getOriginalSolution() Returns the orignal solution to the linear model.
double	getResidualOfDroppedData() Returns the average RMS to the bootstrapped data sets remnant.
double	getResidualOfDroppedMaxima() Returns the maximum RMS to the bootstrapped data sets remnant.
double	getResidualOfDroppedMinima() Returns the minimum RMS to the bootstrapped data sets remnant.
NVector	getSimulatedMaxima() Returns the maximas on the linear model parameter from bootstrapping the data.
NVector	getSimulatedMinima() Returns the minimas on the linear model parameter from bootstrapping the data.
NVector	getSimulatedSolution() Returns the averages on the linear model parameter from bootstrapping the data.
private static GeneralLinearRegression	prepareRegression(Object[] fitting, NVector[] x, NVector y, NVector err) Prepares a GeneralLinearRegression from the funtions, dependables and measurements passed over.
void	setDuplication(double frac) Changes the fraction of duplication to the stated value.
void	setSimulationCount(int simcount) Changes the number of simulated data sets per degree of freedom.
void	setUseCovariance(boolean use) Sets the useage of the covariance sigma estimate on the fitted parameters on the simulated data sets as the weights in the statistical calculation of the confidence estimates.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

DUPLICATE

public static final double DUPLICATE

The amount of duplicated data in the simulated sets.

See Also:

Constant Field Values

FREEDOM

public static final int FREEDOM

The number of simulated data sets.

See Also:

Constant Field Values

USECOVARIANCE

public static final boolean USECOVARIANCE

The default usage of the covariance parameter estimates.

See Also:

Constant Field Values

random

private static final Random random

We use a random number generator, constructed at class load.

depend

private NVector[] depend

Where/how we measured the data. For t-dependencie, lenght=1; Omega=2.

fit

private Object[] fit

The fittings, either an array of functions or multidimensionals.

data

private NVector data

The original data.

error

private NVector error

The errors of the original data. May be null.

usecovariance

private boolean usecovariance

If true, we weigh the simulated parameters with their covariance sigma

average

private NVector average

The parameter averages on the solution to the simulated data.

confidence

private NVector confidence

The confidence estimations on the solution to the original data.

minima

private NVector minima

The parameter minima on the solution to the simulated data.

maxima

private NVector maxima

The parameter maxima on the solution to the simulated data.

rmsav

private double rmsav

The measures dropped at bootstrapping are used for a RMS average.

rmsmin

private double rmsmin

The measures dropped at bootstrapping are used for a RMS average.

rmsmax

private double rmsmax

The measures dropped at bootstrapping are used for a RMS average.

duplicate

private double duplicate

The fraction of data duplication, defaults to DUPLICATE.

freedom

private int freedom

The number of simulated data sets per degree of freedom.

Constructor Detail

Bootstrap

private Bootstrap(NVector y,
                  NVector sigma)

Common constructor. Stores the measurement and its errors. The dependend varaibales depend are set later. The dependencies specifies the measurement in your parameter space, i.e. if you have measurements dependant on time only, your depend array will have a single index, linked to the Vector stating the time of the measurement. If you have data that are linked to pointings on a sphere, depend will have two dimensions, the azimuthal and polar angle of your measurement, etc.

Bootstrap

public Bootstrap(Function[] fitting,
                 NVector x,
                 NVector y,
                 NVector sigma)

Constructs a new bootstrap object from the supplied basic functions and the measurement with their errors.

Bootstrap

public Bootstrap(Multidimensional[] fitting,
                 NVector[] x,
                 NVector y,
                 NVector sigma)

Constructs a new bootstrap object from the supplied basic functions and the measurement with their errors.

Method Detail

setUseCovariance

public void setUseCovariance(boolean use)

Sets the useage of the covariance sigma estimate on the fitted parameters on the simulated data sets as the weights in the statistical calculation of the confidence estimates.

setDuplication

public void setDuplication(double frac)

Changes the fraction of duplication to the stated value. Rejects values outside ]0,1[.

setSimulationCount

public void setSimulationCount(int simcount)

Changes the number of simulated data sets per degree of freedom.

getOriginalSolution

public NVector getOriginalSolution()

Returns the orignal solution to the linear model. Pipes to the underlying general linear regression.

getOriginalSigma

public NVector getOriginalSigma()

Returns the standard diviation to the original solution. These are the diagonal elements of the covariance matrix. Pipes to the underlying general linear regression.

getOriginalCovariance

public QuadMatrix getOriginalCovariance()

Returns the covariance matrix of the original fit.

getOriginalChiSquare

public double getOriginalChiSquare()

Returns the chi-square value of the original data set. Pipes to the underlying general linear regression.

getOriginalQuality

public double getOriginalQuality()

Returns the quality estimate of the original data set. Pipes to the underlying general linear regression.

getConfidenceEstimates

public NVector getConfidenceEstimates()

Returns a confidence estimate on the linear model parameter by bootstrapping the data.

See Also:

doBootstrap()

getSimulatedSolution

public NVector getSimulatedSolution()

Returns the averages on the linear model parameter from bootstrapping the data. Use to compare it to the original solution.

See Also:

doBootstrap()

getSimulatedMinima

public NVector getSimulatedMinima()

Returns the minimas on the linear model parameter from bootstrapping the data. Use to compare it to the original solution.

See Also:

doBootstrap()

getSimulatedMaxima

public NVector getSimulatedMaxima()

Returns the maximas on the linear model parameter from bootstrapping the data. Use to compare it to the original solution.

See Also:

doBootstrap()

getResidualOfDroppedData

public double getResidualOfDroppedData()

Returns the average RMS to the bootstrapped data sets remnant. For each bootstrapping data set, the data points that have been dropped are then fitted to the resulting model. They provide an RMS per bootstrapping model, whose average is returned here.

getResidualOfDroppedMinima

public double getResidualOfDroppedMinima()

Returns the minimum RMS to the bootstrapped data sets remnant. For each bootstrapping data set, the data points that have been dropped are then fitted to the resulting model. They provide an RMS per bootstrapping model, whose minima is returned here.

getResidualOfDroppedMaxima

public double getResidualOfDroppedMaxima()

Returns the maximum RMS to the bootstrapped data sets remnant. For each bootstrapping data set, the data points that have been dropped are then fitted to the resulting model. They provide an RMS per bootstrapping model, whose maxima is returned here.

doBootstrap

private void doBootstrap()

The time consuming part of the bootstrap class. We calculate confidence estimates on the linear model by duplicating measurements of the original data set. The simulation count defines the number of simulated data sets generated. From all data sets returned, we derive confidence estimations by calculating the standard deviation of all simulated set solutions. Additionally, we record the minima and maxima of the simulated data set parameter estimations, as well as their averages. Implementation note: This is a time and memory intense operation.

prepareRegression

private static GeneralLinearRegression prepareRegression(Object[] fitting,
                                                         NVector[] x,
                                                         NVector y,
                                                         NVector err)

Prepares a GeneralLinearRegression from the funtions, dependables and measurements passed over.

fitDropped

private static double fitDropped(Object[] fitting,
                                 NVector solution,
                                 NVector[] x,
                                 NVector y)

Fits a data set in y contained in the dependant variables x to the linear model parameters in solution.

Parameters:

fitting - The regression model as an array of function or multidimensionals.

solution - Vector of linear regression coefficients.

x - The array of dependant variabels.

y - The measurements.

Returns:

A RMS of the measures.

getExchangedData

private static Bootstrap.ExchangedData getExchangedData(NVector[] depend,
                                                        NVector data,
                                                        NVector err,
                                                        double duplicate)

From our measurements and theier errors we derive a simulated data set. This is done as follows: From the original data set, we remain the fraction of 1-duplicate data points. The missing data points are filled in with data from the reduced remaining set, allowing for (arbitrary) multiple duplication of any data point.

Returns:

The simulated data on index zero, the error or null on index 1.