损失函数 L ( θ , a ) L(\theta, a) L(θ,a) ：表示用 a 去估计 θ \theta θ 时所造成的的损失。（平方差损失函数、平方相对差损失函数、加权平方差损失函数、绝对差损失函数）

决策函数 d ( ξ 1 , ξ 2 , ⋅ ⋅ ⋅ , ξ n ) d(\xi_1, \xi_2, ··· , \xi_n) d(ξ1​,ξ2​,⋅⋅⋅,ξn​) ：决策 a，它是一个随机变量，所对应的损失为 L [ θ , d ( ξ 1 , ξ 2 , ⋅ ⋅ ⋅ , ξ n ) ] L[\theta, d(\xi_1, \xi_2, ··· , \xi_n)] L[θ,d(ξ1​,ξ2​,⋅⋅⋅,ξn​)]

风险函数 R ( θ , d ) R(\theta, d) R(θ,d)：是损失函数在参数为 θ \theta θ 时的数学期望，代表了使用 d d d 估计 θ \theta θ 时所造成的平均损失 R ( θ , d ) = E θ { L [ θ , d ( ξ 1 , ξ 2 , ⋅ ⋅ ⋅ , ξ n ) ] } R(\theta, d) = E_\theta \{ L[\theta, d(\xi_1, \xi_2, ··· , \xi_n)] \} R(θ,d)=Eθ​{L[θ,d(ξ1​,ξ2​,⋅⋅⋅,ξn​)]}

最大风险最小化估计量、极小极大估计量 ：P66页，例2.5.1

贝叶斯风险函数 B ( d ) B(d) B(d)： B ( d ) B(d) B(d) 为决策函数 d ( ξ 1 , ξ 2 , ⋅ ⋅ ⋅ , ξ n ) d(\xi_1, \xi_2, ··· , \xi_n) d(ξ1​,ξ2​,⋅⋅⋅,ξn​) 的贝叶斯风险函数 B ( d ) = E { L [ θ , d ( ξ 1 , ξ 2 , ⋅ ⋅ ⋅ , ξ n ) ] } = E { E ( L [ θ , d ( ξ 1 , ξ 2 , ⋅ ⋅ ⋅ , ξ n ) ] ∣ θ ) } B(d) = E \{ L[\theta, d(\xi_1, \xi_2, ··· , \xi_n)] \} = E \{ E(L[\theta, d(\xi_1, \xi_2, ··· , \xi_n)]| \theta) \} B(d)=E{L[θ,d(ξ1​,ξ2​,⋅⋅⋅,ξn​)]}=E{E(L[θ,d(ξ1​,ξ2​,⋅⋅⋅,ξn​)]∣θ)} = E { E ( L [ θ , d ( ξ 1 , ξ 2 , ⋅ ⋅ ⋅ , ξ n ) ] ∣ ξ 1 , ξ 2 , ⋅ ⋅ ⋅ , ξ n ) } = E \{ E(L[\theta, d(\xi_1, \xi_2, ··· , \xi_n)]| \xi_1, \xi_2, ··· , \xi_n) \} =E{E(L[θ,d(ξ1​,ξ2​,⋅⋅⋅,ξn​)]∣ξ1​,ξ2​,⋅⋅⋅,ξn​)}

贝叶斯估计量、贝叶斯解 d ~ ( ξ 1 , ξ 2 , ⋅ ⋅ ⋅ , ξ n ) \tilde{d}(\xi_1, \xi_2, ··· , \xi_n) d~(ξ1​,ξ2​,⋅⋅⋅,ξn​)： B ( d ~ ) = m i n d ∈ G { B ( d ) } B(\tilde{d}) = min_{d \in G} \{B(d)\} B(d~)=mind∈G​{B(d)}

核：如果函数 φ ( x ) \varphi(x) φ(x) 与函数 f ( x ) f(x) f(x) 只相差一个常熟因子，则称 φ ( x ) \varphi(x) φ(x) 为 f ( x ) f(x) f(x) 的核，记为 f ( x ) ∝ φ ( x ) f (x) \propto \varphi(x) f(x)∝φ(x)