Question

我正在使用lmfit来拟合拉曼数据。我正在使用7个高斯峰和一个线性背景（这些峰中有5个已知，其中两个未知）我已经包含了一个权重数组（stdev的反平方）。当我包括权重时 - 视觉上的拟合看起来好得多，并且绘制的残差也具有较少的结构，然而，卡方和减小的卡方值被报告为0.我不确定我是否使用加权值正确，或者可能无法正确解释结果。我在下面复制了我的代码。非常感谢你的帮助

[[Model]]
    (((((((Model(gaussian, prefix='one_') + Model(gaussian, prefix='two_')) + Model(gaussian, prefix='three_')) + Model(gaussian, prefix='unknown_')) + Model(gaussian, prefix='unknown2_')) + Model(gaussian, prefix='six_')) + Model(gaussian, prefix='seven_')) + Model(linear, prefix='lin1_'))
[[Fit Statistics]]
    # function evals   = 366
    # data points      = 172
    # variables        = 23
    chi-square         = 0.000
    reduced chi-square = 0.000
    Akaike info crit   = -2481.840
    Bayesian info crit = -2409.448
[[Variables]]
    lin1_intercept:       7.87347446 +/- 0.202758 (2.58%) (init= 16.00284)
    lin1_slope:          -0.00399367 +/- 0.000115 (2.88%) (init=-0.006952215)
    one_sigma:            21.2666157 +/- 1.423474 (6.69%) (init= 2)
    one_center:           1204.02129 +/- 1.132164 (0.09%) (init= 1200)
    one_amplitude:        102.715569 +/- 9.153523 (8.91%) (init= 10)
    one_fwhm:             50.0790521 +/- 3.352026 (6.69%)  == '2.3548200*one_sigma'
    one_height:           1.92685033 +/- 0.073258 (3.80%)  == '0.3989423*one_amplitude/max(1.e-15, one_sigma)'
    two_sigma:            25.7977895 +/- 0.871817 (3.38%) (init= 2)
    two_center:           1287.20816 +/- 1.068676 (0.08%) (init= 1275)
    two_amplitude:        527.208091 +/- 24.04663 (4.56%) (init= 10)
    two_fwhm:             60.7491508 +/- 2.052973 (3.38%)  == '2.3548200*two_sigma'
    two_height:           8.15285388 +/- 0.212054 (2.60%)  == '0.3989423*two_amplitude/max(1.e-15, two_sigma)'
    three_sigma:          19.5097449 +/- 0.798387 (4.09%) (init= 2)
    three_center:         1444.94305 +/- 0.757566 (0.05%) (init= 1450)
    three_amplitude:      518.683054 +/- 24.82361 (4.79%) (init= 10)
    three_fwhm:           45.9419376 +/- 1.880058 (4.09%)  == '2.3548200*three_sigma'
    three_height:         10.6062181 +/- 0.249698 (2.35%)  == '0.3989423*three_amplitude/max(1.e-15, three_sigma)'
    unknown_sigma:        33.8695907 +/- 4.913019 (14.51%) (init= 2)
    unknown_center:       1365.89866 +/- 2.572737 (0.19%) (init= 1355)
    unknown_amplitude:    224.557732 +/- 33.37427 (14.86%) (init= 10)
    unknown_fwhm:         79.7567896 +/- 11.56927 (14.51%)  == '2.3548200*unknown_sigma'
    unknown_height:       2.64501508 +/- 0.077333 (2.92%)  == '0.3989423*unknown_amplitude/max(1.e-15, unknown_sigma)'
    unknown2_sigma:       16.8566531 +/- 1.909319 (11.33%) (init= 2)
    unknown2_center:      1497.93496 +/- 1.297153 (0.09%) (init= 1510)
    unknown2_amplitude:   189.598971 +/- 27.39291 (14.45%) (init= 10)
    unknown2_fwhm:        39.6943839 +/- 4.496103 (11.33%)  == '2.3548200*unknown2_sigma'
    unknown2_height:      4.48719263 +/- 0.196189 (4.37%)  == '0.3989423*unknown2_amplitude/max(1.e-15, unknown2_sigma)'
    six_sigma:            22.0949199 +/- 2.010271 (9.10%) (init= 2)
    six_center:           1552.18018 +/- 1.324973 (0.09%) (init= 1550)
    six_amplitude:        333.936881 +/- 54.65493 (16.37%) (init= 10)
    six_fwhm:             52.0295593 +/- 4.733827 (9.10%)  == '2.3548200*six_sigma'
    six_height:           6.02951031 +/- 0.537614 (8.92%)  == '0.3989423*six_amplitude/max(1.e-15, six_sigma)'
    seven_sigma:          41.8944271 +/- 1.648292 (3.93%) (init= 2)
    seven_center:         1603.04249 +/- 4.014783 (0.25%) (init= 1600)
    seven_amplitude:      547.973799 +/- 48.61137 (8.87%) (init= 10)
    seven_fwhm:           98.6538348 +/- 3.881433 (3.93%)  == '2.3548200*seven_sigma'
    seven_height:         5.21811474 +/- 0.274354 (5.26%)  == '0.3989423*seven_amplitude/max(1.e-15, seven_sigma)'
[[Correlations]] (unreported correlations are <  0.100)
    C(lin1_intercept, lin1_slope)  = -0.999 
    C(seven_center, seven_amplitude)  = -0.987 
    C(unknown_sigma, unknown_amplitude)  =  0.980 
    C(unknown2_sigma, unknown2_amplitude)  =  0.971 
    C(seven_sigma, seven_center)  = -0.966 
    C(seven_sigma, seven_amplitude)  =  0.953 
    C(six_amplitude, seven_amplitude)  = -0.946 
    C(six_amplitude, seven_center)  =  0.935 
    C(one_sigma, one_amplitude)  =  0.920 
    C(six_sigma, six_amplitude)  =  0.910 
    C(two_amplitude, unknown_sigma)  = -0.900 
    C(two_amplitude, unknown_amplitude)  = -0.896 
    C(two_center, unknown_amplitude)  = -0.886 
    C(two_center, unknown_sigma)  = -0.880 
    C(six_amplitude, seven_sigma)  = -0.877 
    C(three_sigma, three_amplitude)  =  0.871 
    C(two_center, two_amplitude)  =  0.858 
    C(lin1_intercept, one_amplitude)  = -0.844 
    C(lin1_slope, one_amplitude)  =  0.839 
    C(two_sigma, two_amplitude)  =  0.826 
    C(two_sigma, unknown_center)  =  0.820 
    C(two_sigma, unknown_amplitude)  = -0.813 
    C(two_amplitude, unknown_center)  =  0.805 
    C(two_center, unknown_center)  =  0.799 
    C(six_sigma, seven_amplitude)  = -0.784 
    C(two_sigma, unknown_sigma)  = -0.764 
    C(lin1_intercept, one_sigma)  = -0.758 
    C(six_sigma, seven_center)   =  0.754 
    C(lin1_slope, one_sigma)     =  0.754 
    C(three_amplitude, unknown2_amplitude)  = -0.748 
    C(two_sigma, two_center)     =  0.737 
    C(unknown_center, unknown_amplitude)  = -0.731 
    C(three_amplitude, unknown2_sigma)  = -0.717 
    C(three_center, unknown2_amplitude)  = -0.713 
    C(three_center, unknown2_sigma)  = -0.705 
    C(three_sigma, unknown2_amplitude)  = -0.696 
    C(unknown_sigma, unknown_center)  = -0.688 
    C(unknown2_amplitude, six_sigma)  = -0.682 
    C(unknown2_amplitude, six_center)  =  0.681 
    C(unknown2_sigma, six_center)  =  0.675 
    C(six_sigma, seven_sigma)    = -0.671 
    C(three_sigma, unknown_sigma)  = -0.662 
    C(three_amplitude, unknown_sigma)  = -0.660 
    C(unknown2_sigma, six_sigma)  = -0.653 
    C(three_sigma, unknown2_sigma)  = -0.643 
    C(three_sigma, unknown_amplitude)  = -0.640 
    C(three_amplitude, unknown_amplitude)  = -0.631 
    C(three_center, three_amplitude)  =  0.621 
    C(one_center, two_sigma)     = -0.620 
    C(three_sigma, three_center)  =  0.548 
    C(two_amplitude, three_amplitude)  =  0.542 
    C(unknown2_sigma, six_amplitude)  = -0.539 
    C(unknown2_amplitude, six_amplitude)  = -0.533 
    C(two_amplitude, three_sigma)  =  0.518 
    C(two_center, three_amplitude)  =  0.517 
    C(one_amplitude, two_sigma)  = -0.497 
    C(two_center, three_sigma)   =  0.494 
    C(one_sigma, two_sigma)      = -0.484 
    C(unknown2_center, six_sigma)  = -0.483 
    C(one_center, two_amplitude)  = -0.468 
    C(one_amplitude, unknown_amplitude)  =  0.442 
    C(one_sigma, one_center)     =  0.431 
    C(one_center, one_amplitude)  =  0.422 
    C(three_sigma, unknown2_center)  =  0.416 
    C(one_center, unknown_center)  = -0.414 
    C(one_sigma, unknown_amplitude)  =  0.408 
    C(two_sigma, three_amplitude)  =  0.406 
    C(three_center, six_center)  = -0.404 
    C(three_amplitude, six_center)  = -0.398 
    C(two_sigma, three_sigma)    =  0.383 
    C(unknown2_center, six_amplitude)  = -0.374 
    C(one_center, unknown_amplitude)  =  0.364 
    C(three_amplitude, unknown2_center)  =  0.358 
    C(three_center, six_sigma)   =  0.356 
    C(one_amplitude, unknown_center)  = -0.349 
    C(three_amplitude, six_sigma)  =  0.348 
    C(three_sigma, six_center)   = -0.340 
    C(one_center, unknown_sigma)  =  0.337 
    C(unknown_sigma, unknown2_amplitude)  =  0.333 
    C(unknown_amplitude, unknown2_amplitude)  =  0.332 
    C(one_sigma, unknown_center)  = -0.329 
    C(one_amplitude, unknown_sigma)  =  0.324 
    C(unknown2_sigma, seven_amplitude)  =  0.321 
    C(unknown2_amplitude, seven_amplitude)  =  0.309 
    C(three_center, six_amplitude)  =  0.301 
    C(one_sigma, unknown_sigma)  =  0.300 
    C(unknown2_sigma, seven_center)  = -0.297 
    C(three_amplitude, six_amplitude)  =  0.296 
    C(three_sigma, six_sigma)    =  0.294 
    C(unknown_sigma, unknown2_sigma)  =  0.291 
    C(unknown_amplitude, unknown2_sigma)  =  0.288 
    C(lin1_intercept, unknown_amplitude)  = -0.286 
    C(lin1_slope, unknown_amplitude)  =  0.284 
    C(unknown2_amplitude, seven_center)  = -0.278 
    C(three_center, unknown2_center)  =  0.277 
    C(one_sigma, two_amplitude)  = -0.276 
    C(one_amplitude, two_amplitude)  = -0.275 
    C(unknown2_center, seven_amplitude)  =  0.272 
    C(unknown2_center, six_center)  =  0.265 
    C(unknown2_center, seven_center)  = -0.254 
    C(three_sigma, six_amplitude)  =  0.252 
    C(unknown2_sigma, seven_sigma)  =  0.249 
    C(two_amplitude, unknown2_amplitude)  = -0.245 
    C(two_center, unknown2_amplitude)  = -0.238 
    C(unknown_sigma, unknown2_center)  = -0.237 
    C(three_amplitude, unknown_center)  =  0.237 
    C(unknown_amplitude, unknown2_center)  = -0.228 
    C(unknown2_amplitude, seven_sigma)  =  0.225 
    C(six_sigma, six_center)     = -0.220 
    C(two_amplitude, unknown2_sigma)  = -0.215 
    C(six_center, seven_center)  =  0.212 
    C(one_amplitude, seven_sigma)  =  0.211 
    C(one_center, two_center)    = -0.208 
    C(two_center, unknown2_sigma)  = -0.207 
    C(unknown2_center, seven_sigma)  =  0.207 
    C(lin1_intercept, seven_sigma)  = -0.205 
    C(six_center, seven_sigma)   = -0.205 
    C(six_center, seven_amplitude)  = -0.205 
    C(one_amplitude, two_center)  = -0.201 
    C(one_amplitude, seven_amplitude)  =  0.190 
    C(lin1_intercept, two_sigma)  =  0.189 
    C(one_sigma, seven_sigma)    =  0.188 
    C(lin1_slope, two_sigma)     = -0.188 
    C(two_sigma, unknown2_amplitude)  = -0.187 
    C(lin1_slope, seven_sigma)   =  0.186 
    C(lin1_intercept, seven_amplitude)  = -0.185 
    C(two_amplitude, unknown2_center)  =  0.183 
    C(two_center, unknown2_center)  =  0.173 
    C(one_center, three_amplitude)  = -0.173 
    C(one_sigma, seven_amplitude)  =  0.170 
    C(three_center, seven_amplitude)  = -0.170 
    C(lin1_slope, seven_amplitude)  =  0.169 
    C(one_sigma, two_center)     = -0.166 
    C(three_amplitude, seven_amplitude)  = -0.166 
    C(lin1_intercept, unknown_sigma)  = -0.164 
    C(lin1_slope, unknown_sigma)  =  0.163 
    C(three_sigma, unknown_center)  =  0.162 
    C(two_sigma, unknown2_sigma)  = -0.161 
    C(three_center, seven_center)  =  0.160 
    C(one_center, three_sigma)   = -0.157 
    C(three_amplitude, seven_center)  =  0.156 
    C(lin1_intercept, unknown_center)  =  0.146 
    C(lin1_slope, unknown_center)  = -0.146 
    C(one_amplitude, seven_center)  = -0.145 
    C(three_sigma, seven_amplitude)  = -0.145 
    C(unknown_amplitude, six_sigma)  = -0.141 
    C(unknown_amplitude, six_amplitude)  = -0.137 
    C(unknown_sigma, six_center)  =  0.136 
    C(lin1_intercept, seven_center)  =  0.135 
    C(three_center, unknown_center)  = -0.135 
    C(three_sigma, seven_center)  =  0.134 
    C(unknown_sigma, six_sigma)  = -0.133 
    C(three_center, seven_sigma)  = -0.132 
    C(two_sigma, unknown2_center)  =  0.132 
    C(three_amplitude, seven_sigma)  = -0.130 
    C(one_sigma, seven_center)   = -0.130 
    C(unknown_amplitude, six_center)  =  0.126 
    C(one_amplitude, three_sigma)  = -0.123 
    C(one_amplitude, six_amplitude)  = -0.122 
    C(unknown_sigma, six_amplitude)  = -0.122 
    C(lin1_slope, seven_center)  = -0.121 
    C(unknown_amplitude, seven_amplitude)  =  0.118 
    C(three_sigma, seven_sigma)  = -0.116 
    C(unknown_amplitude, seven_sigma)  =  0.114 
    C(one_sigma, three_sigma)    = -0.113 
    C(unknown2_center, unknown2_amplitude)  =  0.111 
    C(one_sigma, six_amplitude)  = -0.109 
    C(unknown2_sigma, unknown2_center)  =  0.109 
    C(one_amplitude, unknown2_amplitude)  =  0.107 
    C(two_amplitude, six_center)  = -0.107 
    C(lin1_intercept, six_amplitude)  =  0.105 
    C(lin1_intercept, two_center)  =  0.101

输出包括权重：

{{1}}

Answer 1

卡方统计的报告在您使用的版本中限制为3位数。我相信这是在最新版本（0.9.9）中修复的，并且在最新的开发版本中肯定是固定的。您也可以自己更精确地打印出值：

print("chi-square = %14.8g, reduced chi-square = %14.8g" % (out.chisqr, out.redchi))

但是：我认为使用“stdev的反平方”的权重可能不是你想要的。为清楚起见，权重是应用于（数据模型）的乘法因子，然后卡方将是“Sum [（数据模型）*权重] ** 2”。因此，我认为使用“权重= 1./（数据的stddev）”（即，不是平方）是预期正态分布的数据的最常用方法，并且您的拉曼数据可能至少在通过计算小数字来控制没有信号的感觉（优先选择Poission统计数据）。

希望有所帮助。

Chi Squared并使用lmfit减少Chi Squared = 0

1 个答案: