I am creating a uniform vector of probabilities, adding weight to a region, converting to probabilities once again. I want to smooth the curve by fitting a beta distribution to the curve. I can't use stats.beta.fit because I don't have any draws from these probabilities only a scaffold for the curve.
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。我想通过在曲线上拟合β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。
How can I configure a function from scipy.stats to work with scipy.optimize.curve_fit? I don't want to limit it to just beta distributions if possible. Is there a general way to convert these into a form that can be minimized to optimize the parameter set?
如何从scipy.stats配置函数以使用scipy.optimize.curve_fit?如果可能的话,我不想将其限制为beta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?
Essentially, I'm looking for the parameter set that best fits the curve to a particular distribution (in this case a beta).
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)。
Any ideas?
# 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
In response to the lm answer below:
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
1 个解决方案
#1
0
You probably want to use beta.pdf, as with:
您可能希望使用beta.pdf,如下所示:
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)
You may also find lmfit (https://lmfit.github.io/lmfit-py/) useful. For this, you would have to wrap stats.beta.pdf, but this gives you a lot more flexibility in putting bounds on parameters or fixing them:
您可能还会发现lmfit(https://lmfit.github.io/lmfit-py/)很有用。为此,您必须包装stats.beta.pdf,但这使您可以更灵活地在参数上设置边界或修复它们:
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()
This will print out
这将打印出来
[[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
(and, to be clear, the best fit values and uncertainties will be the same from the curve_fit example above) and a plot of
(并且,要明确的是,最佳拟合值和不确定性将与上面的curve_fit示例相同)和
#1
0
You probably want to use beta.pdf, as with:
您可能希望使用beta.pdf,如下所示:
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)
You may also find lmfit (https://lmfit.github.io/lmfit-py/) useful. For this, you would have to wrap stats.beta.pdf, but this gives you a lot more flexibility in putting bounds on parameters or fixing them:
您可能还会发现lmfit(https://lmfit.github.io/lmfit-py/)很有用。为此,您必须包装stats.beta.pdf,但这使您可以更灵活地在参数上设置边界或修复它们:
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()
This will print out
这将打印出来
[[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
(and, to be clear, the best fit values and uncertainties will be the same from the curve_fit example above) and a plot of
(并且,要明确的是,最佳拟合值和不确定性将与上面的curve_fit示例相同)和