PRML-公式推导 1.25

\(p_{y}(y)=p_{x}(x)\left|\frac{\mathrm{d} x}{\mathrm{d} y}\right|=p_{x}(g(y))\left|g^{\prime}(y)\right| \tag{1.27}\)

\(令x=g(y)\)
\(f(x)=f(g(y))\)
\(观测区间(x,x+\delta x)\to (y,y+\delta y)\)
\(当\delta x很小\)
\(P_x(x)\delta x = P_y(y)\delta y\)
\(P_y(y)=P_x(x)|\frac{dx}{dy}|\)
\(代入x=g(y)\)
\(P_y(y)=Px(g(y))|g'(y)|\)