天文数据分析PPT课件

-,1,天文数据分析,国家天文台赵永恒2015年4月,-,2,数据分析方法,-,3,累积概率分布,-,4,任意分布的随机数,-,5,常用概率分布,-,6,数据插值,-,7,内插和外推,-,8,插值(erpolate),线性1d插值(interp1d)1d样条插值(interpolate.splXXX)2d样条插值(bisplrep)RBF（radialbasisfunction）插值/平滑,-,9,erpolateimportRbfimportmatplotlib.pyplotaspltfrommatplotlibimportcm#2-dtests-setupscattereddatax=np.random.rand(100)*4.0-2.0y=np.random.rand(100)*4.0-2.0z=x*np.exp(-x*2-y*2)ti=np.linspace(-2.0,2.0,100)XI,YI=np.meshgrid(ti,ti)#useRBFrbf=Rbf(x,y,z,epsilon=2)ZI=rbf(XI,YI)#plottheresultn=plt.Normalize(-2.,2.)plt.subplot(1,1,1)plt.pcolor(XI,YI,ZI,cmap=cm.jet)plt.scatter(x,y,100,z,cmap=cm.jet)plt.title(RBFinterpolation-multiquadrics)plt.xlim(-2,2)plt.ylim(-2,2)plt.colorbar()plt.show(),-,10,数据拟合,-,11,拟合模型,O=T+e,-,12,最小二乘法,-,13,importnumpyasnpimportscipy.linalgassplinimportmatplotlib.pyplotaspltc1,c2=5.0,2.0i=np.r_1:11xi=0.1*iyi=c1*np.exp(-xi)+c2*xizi=yi+0.05*np.max(yi)*np.random.randn(len(yi)A=np.c_np.exp(-xi):,np.newaxis,xi:,np.newaxisc,resid,rank,sigma=splin.lstsq(A,zi)printc,resid,rank,sigmaxi2=np.r_0.1:1.0:100jyi2=c0*np.exp(-xi2)+c1*xi2plt.plot(xi,zi,x,xi2,yi2)plt.axis(0,1.1,3.0,5.5)plt.xlabel($x_i$)plt.title(Datafittingwithlinalg.lstsq)plt.show(),-,14,非线性拟合,拟合系数有非线性函数关系,-,15,fromnumpyimportx=arange(0,6e-2,6e-2/30)A,k,theta=10,1.0/3e-2,pi/6y_true=A*sin(2*pi*k*x+theta)y_meas=y_true+2*random.randn(len(x)defresiduals(p,y,x):A,k,theta=perr=y-A*sin(2*pi*k*x+theta)returnerrdefpeval(x,p):returnp0*sin(2*pi*p1*x+p2)p0=8,1/2.3e-2,pi/3printarray(p0)#8.43.47831.0472fromscipy.optimizeimportleastsqplsq=leastsq(residuals,p0,args=(y_meas,x)printplsq0#10.943733.36050.5834printarray(A,k,theta)#10.33.33330.5236importmatplotlib.pyplotaspltplt.plot(x,peval(x,plsq0),x,y_meas,o,x,y_true)plt.title(Least-squaresfittonoisydata)plt.legend(Fit,Noisy,True)plt.show(),-,16,MaximumLikelihoodEstimation(MLE),-,17,最大似然估计,一致收敛渐近于正态分布：有极值,-,18,等精度高斯分布,-,19,非等精度高斯分布,-,20,上下限分布,-,21,求极值scipy.optimize,Acollectionofgeneral-purposeoptimizationroutines.fmin-Nelder-MeadSimplexalgorithm(usesonlyfunctioncalls)fmin_powell-Powells(modified)levelsetmethod(usesonlyfunctioncalls)fmin_cg-Non-linear(Polak-Ribiere)conjugategradientalgorithm(canusefunctionandgradient).fmin_bfgs-Quasi-Newtonmethod(Broydon-Fletcher-Goldfarb-Shanno);(canusefunctionandgradient)fmin_ncg-Line-searchNewtonConjugateGradient(canusefunction,gradientandHessian).leastsq-MinimizethesumofsquaresofMequationsinNunknownsgivenastartingestimate.ConstrainedOptimizers(multivariate)fmin_l_bfgs_b-Zhu,Byrd,andNocedalsL-BFGS-Bconstrainedoptimizer(ifyouusethispleasequotetheirpapers-seehelp)fmin_tnc-TruncatedNewtonCodeoriginallywrittenbyStephenNashandadaptedtoCbyJean-SebastienRoy.fmin_cobyla-ConstrainedOptimizationBYLinearApproximation,-,22,EM算法,Expect-Maximum算法EM算法的目标是找出有隐性变量的概率模型的最大可能性解分为2个步骤，E-step和M-stepE-step根据最初假设的模型参数值或者上一步的模型参数计算出隐性变量的后验概率，其实就是隐性变量的期望M-step根据这个E-step的后验概率重新计算出模型参数，然后再重复这两个步骤，直至目标函数收敛。,-,23,拟合度,-,24,好模型,-,25,精度估计,Bootstrap方法“杰克刀”方法,-,26,Bootstrap方法,用已知数据建立分布可有N!组新数据,-,27,SN1987A中微子事件,9个中微子,-,28,“杰克刀”方法,每次丢掉1或多个数据,-,29,KolmogorovSmirnov(K-S)检验,-,30,高斯分布？,AndersonDarling检验ShapiroWilk检验,-,31,Bayes统计推断,-,32,高斯分布,问题：,-,33,问题：,-,34,-,35,-,36,直方图,-,37,MarkovchainMonteCarlo(MCMC),-,38,时间序列分析,-,39,Fourier变换scipy.fftpack,-,40,卷积定理,-,41,离散Fourier变换,-,42,窗效应,-,43,GX5-1,-,44,LombScargle周期图,不等间隔,-,45,相位图,注意：倍频、差频,-,46,相关分析,-,47,小波变换,-,48,-,49,-,50,课后作业II