如何配置`scipy.stats`中的函数与`scipy.optimize.curve_fit`一起使用？

Question

我正在创建一个统一的概率向量，为区域增加权重，再次转换为概率。我希望通过在曲线上拟合beta分布来平滑曲线。我不能使用stats.beta.fit，因为我没有任何来自这些概率的绘制只是曲线的支架。

如何配置scipy.stats的功能以使用scipy.optimize.curve_fit？如果可能，我不想将其限制为beta个版本。是否有一般方法将这些转换为可以最小化以优化参数集的形式？

基本上，我正在寻找最适合特定分布曲线的参数集（在本例中为beta）。

有什么想法吗？

# Uniform probabilities
n = 10
x = np.linspace(0,1,n)
probs_num = np.ones(n)/n # y-values

# Update the mass around an area
idx_update = 2
probs_num[idx_update] += 0.382

# Convert fo probs
probs_num = probs_num/probs_num.sum()

# Plot
with plt.style.context("ggplot"):
    fig, ax = plt.subplots()
    ax.plot(x,probs_num)
    ax.set_ylabel("Density")
    ax.set_xlabel("$x$")


probs_num

from scipy.optimize import curve_fit
from scipy import stats
popt, pcov = curve_fit(stats.beta, x, probs_num) # NOTE: I know this is the wrong way to use it but I'm leaving it as a placeholder

回应下面的答案：

import lmfit
def beta_fcn(x, alpha, beta, loc):
    return stats.beta.pdf(x, alpha, beta, loc)
bmodel = lmfit.Model(beta_fcn)
params = bmodel.make_params(alpha=1, beta=1., loc=0.5)
result = bmodel.fit(probs_num, params, x=x)

# ---------------------------------------------------------------------------
# ValueError                                Traceback (most recent call last)
# <ipython-input-34-61ec32095934> in <module>()
#       4 bmodel = lmfit.Model(beta_fcn)
#       5 params = bmodel.make_params(alpha=1, beta=1., loc=0.5)
# ----> 6 result = bmodel.fit(probs_num, params, x=x)

# ~/anaconda/envs/python3/lib/python3.6/site-packages/lmfit/model.py in fit(self, data, params, weights, method, iter_cb, scale_covar, verbose, fit_kws, nan_policy, **kwargs)
#     871                              scale_covar=scale_covar, fcn_kws=kwargs,
#     872                              nan_policy=self.nan_policy, **fit_kws)
# --> 873         output.fit(data=data, weights=weights)
#     874         output.components = self.components
#     875         return output

# ~/anaconda/envs/python3/lib/python3.6/site-packages/lmfit/model.py in fit(self, data, params, weights, method, nan_policy, **kwargs)
#    1215         self.userkws.update(kwargs)
#    1216         self.init_fit = self.model.eval(params=self.params, **self.userkws)
# -> 1217         _ret = self.minimize(method=self.method)
#    1218 
#    1219         for attr in dir(_ret):

# ~/anaconda/envs/python3/lib/python3.6/site-packages/lmfit/minimizer.py in minimize(self, method, params, **kws)
#    1636                         val.lower().startswith(user_method)):
#    1637                     kwargs['method'] = val
# -> 1638         return function(**kwargs)
#    1639 
#    1640 

# ~/anaconda/envs/python3/lib/python3.6/site-packages/lmfit/minimizer.py in leastsq(self, params, **kws)
#    1288         np.seterr(all='ignore')
#    1289 
# -> 1290         lsout = scipy_leastsq(self.__residual, variables, **lskws)
#    1291         _best, _cov, infodict, errmsg, ier = lsout
#    1292         result.aborted = self._abort

# ~/anaconda/envs/python3/lib/python3.6/site-packages/scipy/optimize/minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
#     385             maxfev = 200*(n + 1)
#     386         retval = _minpack._lmdif(func, x0, args, full_output, ftol, xtol,
# --> 387                                  gtol, maxfev, epsfcn, factor, diag)
#     388     else:
#     389         if col_deriv:

# ~/anaconda/envs/python3/lib/python3.6/site-packages/lmfit/minimizer.py in __residual(self, fvars, apply_bounds_transformation)
#     489         if not self._abort:
#     490             return _nan_policy(np.asarray(out).ravel(),
# --> 491                                nan_policy=self.nan_policy)
#     492 
#     493     def __jacobian(self, fvars):

# ~/anaconda/envs/python3/lib/python3.6/site-packages/lmfit/minimizer.py in _nan_policy(arr, nan_policy, handle_inf)
#    1846 
#    1847         if contains_nan:
# -> 1848             raise ValueError("The input contains nan values")
#    1849     return arr
#    1850 

# ValueError: The input contains nan values

Answer 1

您可能希望使用Row({'points': '30', 'name': 'John', 'Played': '7'}) ，例如：

beta.pdf

您可能还会发现lmfit（https://lmfit.github.io/lmfit-py/）很有用。为此，您必须包装import numpy as np from scipy import stats from scipy.optimize import curve_fit import matplotlib.pyplot as plt n = 21 x = np.linspace(0, 1, n) y = stats.beta.pdf(x, 2.5, 15, 0.3) + np.random.normal(scale=0.1, size=n) p0 = [2.0, 10.0, 0.5] popt, pcov = curve_fit(stats.beta.pdf, x, y, p0) print(popt) ，但这样可以更灵活地在参数上设置边界或修复它们：

stats.beta.pdf

这将打印出来

from lmfit import Model
def beta_fcn(x, alpha, beta, loc):
    return stats.beta.pdf(x, alpha, beta, loc)

bmodel = Model(beta_fcn)

params = bmodel.make_params(alpha=2, beta=10., loc=0.5)
params['alpha'].min = 1.0

result = bmodel.fit(y, params, x=x)

print(result.fit_report())

with plt.style.context("ggplot"):
    fig, ax = plt.subplots()
    ax.plot(x, y, 'o')
    ax.plot(x, result.best_fit)
    ax.set_ylabel("Density")
    ax.set_xlabel("$x$")
plt.show()

（并且，很明显，最合适的值和不确定性将与上面的[[Model]] Model(beta_fcn) [[Fit Statistics]] # fitting method = leastsq # function evals = 75 # data points = 21 # variables = 3 chi-square = 0.06244742 reduced chi-square = 0.00346930 Akaike info crit = -116.177008 Bayesian info crit = -113.043441 [[Variables]] alpha: 2.50445306 +/- 0.06843391 (2.73%) (init = 2) beta: 14.9105872 +/- 0.31198655 (2.09%) (init = 10) loc: 0.29906057 +/- 0.00190835 (0.64%) (init = 0.5) [[Correlations]] (unreported correlations are < 0.100) C(alpha, beta) = 0.894 C(alpha, loc) = -0.834 C(beta, loc) = -0.564 示例相同）和

的图表