예제 #1
0
def bootstrap(data,
              start=None,
              nsamples=2000,
              nafc=2,
              sigmoid="logistic",
              core="ab",
              priors=None,
              cuts=None,
              parametric=True,
              gammaislambda=False):
    """ Parametric bootstrap of a psychometric function.

    Parameters
    ----------

    data : A list of lists or an array of data.
        The first column should be stimulus intensity, the second column should
        be number of correct responses (in 2AFC) or number of yes- responses (in
        Yes/No), the third column should be number of trials. See also: the examples
        section below.

    start : sequence of floats of length number of model parameters
        Generating values for the bootstrap samples. If this is None, the
        generating value will be the MAP estimate. Length should be 4 for Yes/No
        and 3 for nAFC.

    nsamples : number
        Number of bootstrap samples to be drawn.

    nafc : int
        Number of alternatives for nAFC tasks. If nafc==1 a Yes/No task is
        assumed.

    sigmoid : string
        Name of the sigmoid to be fitted. Valid sigmoids include:
                logistic
                gauss
                gumbel_l
                gumbel_r
        See `swignifit.utility.available_sigmoids()` for all available sigmoids.

    core : string
        \"core\"-type of the psychometric function. Valid choices include:
                ab       (x-a)/b
                mw%g     midpoint and width
                linear   a+bx
                log      a+b log(x)
        See `swignifit.utility.available_cores()` for all available sigmoids.

    priors : sequence of strings length number of parameters
        Constraints on the likelihood estimation. These are expressed in the form of a list of
        prior names. Valid prior choices include:
                Uniform(%g,%g)
                Gauss(%g,%g)
                Beta(%g,%g)
                Gamma(%g,%g)
                nGamma(%g,%g)
                if an invalid prior or `None` is selected, no constraints are imposed at all.
        See `swignifit.utility.available_priors()` for all available sigmoids.

    cuts : a single number or a sequence of numbers.
        Cuts indicating the performances that should be considered 'threshold'
        performances. This means that in a 2AFC task, cuts==0.5 the 'threshold'
        is somewhere around 75%% correct performance, depending on the lapse
        rate parametric boolean to indicate whether or not the bootstrap
        procedure should be parametric or not.

    parametric : boolean
        If `True` do parametric, otherwise do a non-parametric bootstrap.

    gammaislambda : boolean
        Set the gamma == lambda prior.

    Returns
    -------

    (samples,estimates,deviance,
    threshold, th_bias, th_acceleration,
    slope, slope_bias, slope_accelerateion
    Rkd,Rpd,outliers,influential)

    samples : numpy array, shape: (nsamples, nblocks)
        the bootstrap sampled data

    estimates : numpy array, shape: (nsamples, nblocks)
        estimated parameters associated with the data sets

    deviance : numpy array, length: nsamples
        deviances for the bootstraped datasets

    threshold : numpy array, shape: (nsamples, ncuts)
        thresholds/cuts for each bootstraped datasets

    th_bias : numpy array, shape: (ncuts)
        the bias term associated with the threshold

    th_acc : numpy array, shape: (ncuts)
        the acceleration constant associated with the threshold

    slope : numpy array, shape: (nsamples, ncuts)
        slope at each cuts for each bootstraped datasets

    sl_bias : numpy array, shape: (ncuts)
        bias term associated with the slope

    sl_acc : numpy array, shape: (ncuts)
        acceleration term associated with the slope

    Rkd : numpy array, length: nsamples
        correlations between block index and deviance residuals

    Rpd : numpy array, length: nsamples
        correlations between model prediction and deviance residuals

    outliers : numpy array of booleans, length nblocks
        points that are outliers

    influential : numpy array of booleans, length nblocks
        points that are influential observations

    Example
    -------
    >>> x = [float(2*k) for k in xrange(6)]
    >>> k = [34,32,40,48,50,48]
    >>> n = [50]*6
    >>> d = [[xx,kk,nn] for xx,kk,nn in zip(x,k,n)]
    >>> priors = ('flat','flat','Uniform(0,0.1)')
    >>> samples,est,D,thres,thbias,thacc,slope,slbias,slacc,Rkd,Rpd,out,influ \
            = bootstrap(d,nsamples=2000,priors=priors)
    >>> np.mean(est[:,0])
    2.7547034408466811
    >>> mean(est[:,1])
    1.4057297989923003

    """
    dataset, pmf, nparams = sfu.make_dataset_and_pmf(
        data, nafc, sigmoid, core, priors, gammaislambda=gammaislambda)

    cuts = sfu.get_cuts(cuts)
    ncuts = len(cuts)
    if start is not None:
        start = sfu.get_start(start, nparams)

    bs_list = sfr.bootstrap(nsamples, dataset, pmf, cuts, start, True,
                            parametric)
    jk_list = sfr.jackknifedata(dataset, pmf)

    nblocks = dataset.getNblocks()

    # construct the massive tuple of return values
    samples = np.zeros((nsamples, nblocks), dtype=np.int32)
    estimates = np.zeros((nsamples, nparams))
    deviance = np.zeros((nsamples))
    thres = np.zeros((nsamples, ncuts))
    slope = np.zeros((nsamples, ncuts))
    Rpd = np.zeros((nsamples))
    Rkd = np.zeros((nsamples))
    for row_index in xrange(nsamples):
        samples[row_index] = bs_list.getData(row_index)
        estimates[row_index] = bs_list.getEst(row_index)
        deviance[row_index] = bs_list.getdeviance(row_index)
        thres[row_index] = [
            bs_list.getThres_byPos(row_index, j) for j in xrange(ncuts)
        ]
        slope[row_index] = [
            bs_list.getSlope_byPos(row_index, j) for j in xrange(ncuts)
        ]
        Rpd[row_index] = bs_list.getRpd(row_index)
        Rkd[row_index] = bs_list.getRkd(row_index)

    thacc = np.zeros((ncuts))
    thbias = np.zeros((ncuts))
    slacc = np.zeros((ncuts))
    slbias = np.zeros((ncuts))
    for cut in xrange(ncuts):
        thacc[cut] = bs_list.getAcc_t(cut)
        thbias[cut] = bs_list.getBias_t(cut)
        slacc[cut] = bs_list.getAcc_s(cut)
        slbias[cut] = bs_list.getBias_s(cut)

    ci_lower = sfr.vector_double(nparams)
    ci_upper = sfr.vector_double(nparams)

    for param in xrange(nparams):
        ci_lower[param] = bs_list.getPercentile(0.025, param)
        ci_upper[param] = bs_list.getPercentile(0.975, param)

    outliers = np.zeros((nblocks), dtype=np.bool)
    influential = np.zeros((nblocks))

    for block in xrange(nblocks):
        outliers[block] = jk_list.outlier(block)
        influential[block] = jk_list.influential(block, ci_lower, ci_upper)

    return samples, estimates, deviance, thres, thbias, thacc, slope, slbias, slacc, Rpd, Rkd, outliers, influential
예제 #2
0
 def generate_test_bootstrap_list():
     data = TestData.generate_test_dataset()
     psi = TestPsychometric.generate_test_model()
     cuts = sfr.vector_double([1, 0.5])
     return sfr.bootstrap(999, data, psi, cuts)
예제 #3
0
 def generate_test_bootstrap_list():
     data = TestData.generate_test_dataset()
     psi = TestPsychometric.generate_test_model()
     cuts = sfr.vector_double([1, 0.5])
     return sfr.bootstrap(999, data, psi, cuts)
예제 #4
0
def bootstrap(data, start=None, nsamples=2000, nafc=2, sigmoid="logistic",
        core="ab", priors=None, cuts=None, parametric=True, gammaislambda=False ):
    """ Parametric bootstrap of a psychometric function.

    Parameters
    ----------

    data : A list of lists or an array of data.
        The first column should be stimulus intensity, the second column should
        be number of correct responses (in 2AFC) or number of yes- responses (in
        Yes/No), the third column should be number of trials. See also: the examples
        section below.

    start : sequence of floats of length number of model parameters
        Generating values for the bootstrap samples. If this is None, the
        generating value will be the MAP estimate. Length should be 4 for Yes/No
        and 3 for nAFC.

    nsamples : number
        Number of bootstrap samples to be drawn.

    nafc : int
        Number of alternatives for nAFC tasks. If nafc==1 a Yes/No task is
        assumed.

    sigmoid : string
        Name of the sigmoid to be fitted. Valid sigmoids include:
                logistic    (1+exp(-x))**-1 [Default]
                gauss       Phi(x)
                gumbel_l    1 - exp(-exp(x))
                gumbel_r    exp(-exp(-x))
                exponential x>0: 1 - exp(-x); else: 0
                cauchy      atan(x)/pi + 0.5
                id          x; only useful in conjunction with NakaRushton core
        See `swignifit.utility.available_sigmoids()` for all available sigmoids.

    core : string
        \"core\"-type of the psychometric function. Valid choices include:
                ab          (x-a)/b [Default]
                mw%g        midpoint and width, with "%g" a number larger than 0 and less than 0.5. 
                            mw%g corresponds to a parameterization in terms of midpoint and width of
                            the rising part of the sigmoid. This width is defined as the length of the
                            interval on which the sigmoidal part reaches from "%g" to 1-"%g".
                linear      a+b*x
                log         a+b*log(x)
                weibull     2*s*m*(log(x)-log(m))/log(2) + log(log(2)) 
                            This will give you a weibull if combined with the gumbel_l sigmoid and a
                            reverse weibull if combined with the gumbel_r sigmoid.
                poly        (x/a)**b   Will give you a weibull if combined with an exp sigmoid
                NakaRushton The Naka-Rushton nonlinearity; should only be used with an id core
        See `swignifit.utility.available_cores()` for all available cores.

    priors : sequence of strings length number of parameters
        Constraints on the likelihood estimation. These are expressed in the form of a list of
        prior names. Valid prior choices include:
                Uniform(%g,%g)   Uniform distribution on an interval
                Gauss(%g,%g)     Gaussian distribution with mean and standard deviation
                Beta(%g,%g)      Beta distribution
                Gamma(%g,%g)     Gamma distribution
                nGamma(%g,%g)    Gamma distribution on the negative axis
                invGamma(%g,%g)  inverse Gamma distribution
                ninvGamma(%g,%g) inverse Gamma distribution on the negative axis
                if an invalid prior or `None` is selected, no constraints are imposed at all.
        See `swignifit.utility.available_priors()` for all available sigmoids.

    cuts : a single number or a sequence of numbers.
        Cuts indicating the performances that should be considered 'threshold'
        performances. This means that in a 2AFC task, cuts==0.5 the 'threshold'
        is somewhere around 75%% correct performance, depending on the lapse
        rate parametric boolean to indicate whether or not the bootstrap
        procedure should be parametric or not.

    parametric : boolean
        If `True` do parametric, otherwise do a non-parametric bootstrap.

    gammaislambda : boolean
        Set the gamma == lambda prior.

    Returns
    -------

    (samples,estimates,deviance,
    threshold, th_bias, th_acceleration,
    slope, slope_bias, slope_accelerateion
    Rkd,Rpd,outliers,influential)

    samples : numpy array, shape: (nsamples, nblocks)
        the bootstrap sampled data

    estimates : numpy array, shape: (nsamples, nblocks)
        estimated parameters associated with the data sets

    deviance : numpy array, length: nsamples
        deviances for the bootstraped datasets

    threshold : numpy array, shape: (nsamples, ncuts)
        thresholds/cuts for each bootstraped datasets

    th_bias : numpy array, shape: (ncuts)
        the bias term associated with the threshold

    th_acc : numpy array, shape: (ncuts)
        the acceleration constant associated with the threshold

    slope : numpy array, shape: (nsamples, ncuts)
        slope at each cuts for each bootstraped datasets

    sl_bias : numpy array, shape: (ncuts)
        bias term associated with the slope

    sl_acc : numpy array, shape: (ncuts)
        acceleration term associated with the slope

    Rkd : numpy array, length: nsamples
        correlations between block index and deviance residuals

    Rpd : numpy array, length: nsamples
        correlations between model prediction and deviance residuals

    outliers : numpy array of booleans, length nblocks
        points that are outliers

    influential : numpy array of booleans, length nblocks
        points that are influential observations

    Example
    -------
    >>> x = [float(2*k) for k in xrange(6)]
    >>> k = [34,32,40,48,50,48]
    >>> n = [50]*6
    >>> d = [[xx,kk,nn] for xx,kk,nn in zip(x,k,n)]
    >>> priors = ('flat','flat','Uniform(0,0.1)')
    >>> samples,est,D,thres,thbias,thacc,slope,slbias,slacc,Rkd,Rpd,out,influ \
            = bootstrap(d,nsamples=2000,priors=priors)
    >>> np.mean(est[:,0])
    2.7547034408466811
    >>> mean(est[:,1])
    1.4057297989923003

    """
    dataset, pmf, nparams = sfu.make_dataset_and_pmf(data, nafc, sigmoid, core, priors, gammaislambda=gammaislambda)

    cuts = sfu.get_cuts(cuts)
    ncuts = len(cuts)
    if start is not None:
        start = sfu.get_start(start, nparams)

    bs_list = sfr.bootstrap(nsamples, dataset, pmf, cuts, start, True, parametric)
    jk_list = sfr.jackknifedata(dataset, pmf)

    nblocks = dataset.getNblocks()

    # construct the massive tuple of return values
    samples = np.zeros((nsamples, nblocks), dtype=np.int32)
    estimates = np.zeros((nsamples, nparams))
    deviance = np.zeros((nsamples))
    thres = np.zeros((nsamples, ncuts))
    slope = np.zeros((nsamples, ncuts))
    Rpd = np.zeros((nsamples))
    Rkd = np.zeros((nsamples))
    for row_index in xrange(nsamples):
        samples[row_index] = bs_list.getData(row_index)
        estimates[row_index] = bs_list.getEst(row_index)
        deviance[row_index] = bs_list.getdeviance(row_index)
        thres[row_index] = [bs_list.getThres_byPos(row_index, j) for j in xrange(ncuts)]
        slope[row_index] = [bs_list.getSlope_byPos(row_index, j) for j in xrange(ncuts)]
        Rpd[row_index] = bs_list.getRpd(row_index)
        Rkd[row_index] = bs_list.getRkd(row_index)

    thacc = np.zeros((ncuts))
    thbias = np.zeros((ncuts))
    slacc = np.zeros((ncuts))
    slbias = np.zeros((ncuts))
    for cut in xrange(ncuts):
        thacc[cut] = bs_list.getAcc_t(cut)
        thbias[cut] = bs_list.getBias_t(cut)
        slacc[cut] = bs_list.getAcc_s(cut)
        slbias[cut] = bs_list.getBias_s(cut)

    ci_lower = sfr.vector_double(nparams)
    ci_upper = sfr.vector_double(nparams)

    for param in xrange(nparams):
        ci_lower[param] = bs_list.getPercentile(0.025, param)
        ci_upper[param] = bs_list.getPercentile(0.975, param)

    outliers = np.zeros((nblocks), dtype=np.bool)
    influential = np.zeros((nblocks))

    for block in xrange(nblocks):
        outliers[block] = jk_list.outlier(block)
        influential[block] = jk_list.influential(block, ci_lower, ci_upper)

    return samples, estimates, deviance, thres, thbias, thacc, slope, slbias, slacc, Rpd, Rkd, outliers, influential