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As we know for multivariate Normal distribution as: wN,习=V尼丽pa-y-网 Let∑=Iandμ=0,we get: o)=即() Let x =(y-xo)/h,and keep(v1,...,yp)as a distribution, we get: 6w-wm--] 2h2 where,h comes from the Jacobian determinant calculated by transforming integrals between the two coordinate systems. 15/27▶ As we know for multivariate Normal distribution as: fx(x1,. . . ,xD)∼N(µ, Σ)= 1 √ (2π) D|Σ| exp [ − 1 2 (x−µ) TΣ −1 (x−µ) ] ▶ Let Σ = I and µ = 0, we get: fx(x1, . . . , xD) = 1 √ (2π) D exp ( − x Tx 2 ) ▶ Let x = (y − x0)/h, and keep fy(y1, . . . , yD) as a distribution, we get: fy(y1, . . . , yD) = 1 √ (2π) Dh D exp [ − (y − x0) T (y − x0) 2h 2 ] , where, h D comes from the Jacobian determinant calculated by transforming integrals between the two coordinate systems. 15 / 27
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