Документация

$$\begin{array}{l}{\stackrel{}{}}_{\mathrm{k^FIC}}{(}_{}xi{,}_{}xj\text{'}\theta \mathcal{,}A){\stackrel{}{}}_{}{\mathrm{=k^SR}}_{}({}_{\mathrm{xi}},xj\mathcal{}\text{'}\theta ,A_{)}+{\mathrm{\delta ij}}_{}(k_{}(xi,{\stackrel{xj}{}}_{\mathrm{\text{'}\theta }}){}_{}{}_{}-k^SR(\mathcal{}xi,\\ \text{xj}\text{'θ}\text{,}\text{A}\text{)}{)}_{,}\begin{array}{ll}\mathrm{\delta ij}=\hfill & \text{{1}\text{,}если\hfill \\ \mathrm{}\hfill & \text{i=j,}0if\hfill \end{array}\end{array}$$i≠j.

$$\begin{array}{ll}{\left[\Omega (X\text{'}\theta \mathcal{,}A\right)}_{]}\hfill & {\mathrm{ij}}_{}\mathrm{=\delta ij}{(}_k{(}_{}xi,xj{\stackrel{\text{'}\theta }{}}_{)}{}_{}{\mathrm{-k^SR}}_{}(xi\mathcal{,}xj\hfill \\ \hfill & \text{'}\theta \begin{array}{ll},A{)}_{)}{=}_{\{}k({\stackrel{,}{\mathrm{xi}}}_{\mathrm{xj}}{\mathrm{\text{'}\theta }}_{)}{}_{}-k^SR\mathcal{}(\hfill & \text{xi}\text{,}xj\text{'}\theta \hfill \\ \mathrm{,}\hfill & \text{A)},\; если\hfill \end{array}\hfill \end{array}$$i=j, 0if i≠j.

$$\begin{array}{ll}{\stackrel{}{}}_{\mathrm{K^FIC}}(X,X\text{'}\theta \mathcal{,}A\hfill & ){\stackrel{}{}}_{}\mathrm{=K^SR}(X,X\mathcal{}\text{'}\theta ,\text{ A})+\Omega \mathcal{(}X\hfill \\ \hfill & \text{ 'θ},A){=}_{\mathcal{}}K(X{,{}_{\mathcal{XA}}{\mathrm{\text{'}\theta }}_{\mathcal{)}}K}^{(\mathrm{}}\mathrm{XA},{}_{\mathcal{XA}}\mathrm{\text{'}\theta })\mathrm{-1K}(\mathrm{XA},\mathcal{X}\text{'}\theta \hfill \end{array}$$) + Ω (X 'θ, A).

$$\begin{array}{ll}{}_{\mathrm{LogPIC}}(y\; \text{'}X,\beta ,{}^{\mathrm{\lambda }},\mathcal{}start2\hfill & ,\frac{\mathrm{}}{\mathrm{A}}{)=-}^{}{12{\stackrel{(}{}}_{y-}H\beta )T\mathcal{[}K{^}^{\mathrm{}}{}_{}FIC}^{\mathrm{(}}X,X\text{'}\; start\hfill \\ \hfill & ,\frac{}{\mathrm{A}}\mathrm{)\; +}\mathrm{}\frac{\mathrm{}}{\mathrm{\sigma 2In}}\mathrm{]\; -}{\stackrel{}{1}}_{(y}-\mathrm{H\beta })-\mathcal{}{}^{\mathrm{}}{}_{}N2log2\pi \hfill \end{array}$$− 12log 'K ^ FIC (X, X' start, A) + σ2In |.

$${\stackrel{}{}}_{\mathrm{\beta ^FIC}}(\theta {}^{\mathrm{}},\sigma 2\mathcal{,}A){\underset{)}{\underset{В}{{=}^{[}{{\stackrel{}{\mathrm{HT}}}_{(}K^FIC(X,\mathcal{X}\text{'}\theta {,}^{\mathrm{A}}\text{ )}{}_{+}}^{\sigma 2\mathrm{}}}}}^{\mathrm{}}\underset{\sigma 2}{\underset{}{{\mathrm{-1H}}^{︸}{*{\stackrel{}{}}_{\mathrm{]-1HT}}(K^FIC\mathcal{}(X{,}^{\mathrm{X}}{\mathrm{\text{'}\theta }}_{,}A}^{)\mathrm{}}+}}$$В) −1y ︸ **,

$$\begin{array}{l}*\; ={}^{}\mathrm{HT\Lambda }{(\theta {}^{\mathrm{}},\sigma 2\mathcal{,}A}^{)\mathrm{}}{}^{}{\mathrm{-1H-HT\Lambda }{(}^{\mathrm{\theta }}\mathcal{},\sigma 2}^{,\mathrm{A}}){\mathrm{-1K}}_{\mathcal{}}(X,{}_{\mathcal{XA}}^{\mathrm{\text{'}\theta }}){}_{\mathcal{}}BA-1K({XA,X{}^{\mathrm{\text{'}\theta }})\mathcal{}\Lambda }^{\mathrm{(}}\theta \\ ,\sigma 2,A^{)}{-1H{,}^{\mathrm{}}**\mathcal{}}^{\mathrm{=HT\Lambda }}({\theta }^{}{,\sigma 2,A{)}^{\mathrm{}}\mathcal{}}^{\mathrm{}}-1y-HT\Lambda ({\theta }_{\mathcal{}}\mathrm{,\sigma 2},A_{\mathcal{)}}^{\mathrm{}}-1K{}_{\mathcal{(}}X,\mathrm{XA}\mathrm{\text{'}\theta }{){}^{\mathrm{}}\mathcal{BA-1K}}^{(\mathrm{}}\mathrm{XA},\\ X_{\mathcal{}}\text{'}\theta ){\Lambda }_{\mathcal{}}({\theta }_{\mathcal{}}\mathrm{,\sigma 2},A){}_{\mathcal{}}-1y,\mathrm{BA=K}{({\mathrm{XA}}^{\mathrm{,}}\mathcal{XA}}^{\text{'}\theta \mathrm{)}}\mathrm{+K}{(}_{\mathcal{}}XA,X\\ \mathrm{\text{'}\theta })\Lambda {}^{\mathrm{(}}\theta \mathcal{},\sigma 2,A)\mathcal{-1K}(X^{\mathrm{,}}{}_{\mathrm{XA}}\end{array}$$'θ),Λ (θ,σ2, A) = Ω (X 'θ, A) + σ2In.

$$\begin{array}{l}{}_{\mathrm{logPFIC}}(y\text{'}X{\stackrel{}{,}}_{}\beta ^FIC({\theta }^{\mathrm{}}\mathcal{,\sigma 2},A),{\theta }^{\mathrm{}}\mathcal{,\sigma 2},\\ \begin{array}{ll}\hfill & A)\frac{\mathrm{}}{\mathrm{=}}{-12{\stackrel{}{(}}_{}{\mathrm{y-H\beta ^FIC}}^{\mathrm{}}(\mathcal{\theta }}^{\mathrm{,\sigma 2}}{,{\stackrel{)}{A}}_{)T}(K^FIC\mathcal{}(X{,}^{\mathrm{X}}{}_{\mathrm{\text{'}\theta }},}^{A\mathrm{)}}+{\stackrel{\sigma 2IN}{}}_{)}-1({}^{\mathrm{}}\mathcal{}\hfill \\ \hfill & \frac{\mathrm{y-H\beta ^FIC}}{\mathrm{}}\mathrm{(\theta }\mathrm{}\mathrm{,\sigma 2},\frac{\mathrm{A}}{\mathrm{)}}){\stackrel{}{}}_{}\mathcal{}{}^{\mathrm{}}{\mathrm{-N2log2\pi -12log\text{'}K^FIC}}_{}(X\hfill \end{array}\end{array}$$, X 'θ, A) + σ2IN |,

$$\begin{array}{l}{{\stackrel{}{(}}_{}K^FIC(X,X\mathcal{\text{'}\theta },A{)}^{\mathrm{}}{+}_{}}^{\mathrm{\sigma 2IN}}\\ \text{)},\; -1{=\Lambda {(}^{\mathrm{\theta }}\mathcal{},\sigma 2}^{,\mathrm{A}}){{\mathrm{-1-\Lambda }}^{\mathrm{}}(\mathcal{\theta }}^{\mathrm{,\sigma 2}},A){}_{\mathcal{}}-1K(X_{\mathcal{,}}^{\mathrm{XA}}\text{'}\theta {)}_{\mathcal{}}BA-1K{\left(XA{,}^{\mathrm{X}}\mathcal{\text{'}\theta }\right)}^{\mathrm{\Lambda }}\\ \mathrm{(\theta }{\stackrel{,}{\mathrm{,\sigma 2}}}_{A)}\mathrm{-1},\mathcal{}{}^{\mathrm{log\text{'}K^FIC}}{}_{(}X,\mathrm{X\; \text{'}\theta },A\left)+{}^{\mathrm{}}\mathcal{\sigma 2IN}\right|=\mathrm{регистрируют}\text{'}\Lambda {}_{\mathcal{(}}\theta \mathrm{,\sigma 2,}A){|}_{\mathcal{}}{}_{\mathcal{}}+log\text{'}BA\end{array}$$|−log'K (XA, XA 'θ) |.

$$\begin{array}{ll}P{(}_{}ynew\; \text{'}y,X_{,}\hfill & \mathcal{xnew}){}_{=N}({{}_{}ynew\text{'}\; h}^{}({}_{\mathrm{xnew})}{}_{\mathrm{T\beta }+}^{\mathrm{}}{}_{}\hfill \end{array}$$

$${}_{\mathrm{\mu FIC}}=K{(}_{}^{}xnewT{,}_{\mathcal{}}XA\text{'}\theta \text{ )}{}_{\mathcal{}}^{\mathrm{}}\text{ BA−1}K{}_{\mathcal{(}}\mathrm{XA},X\text{ 'θ}){\Lambda {(}^{\mathrm{\theta }}\mathcal{},\sigma 2}^{,\mathrm{A}})\mathrm{-1}$$(y−Hβ),

$$\begin{array}{ll}{}_{}\hfill & \mathrm{\Sigma FIC=k}{(}_{}xnew{,}_{}xnew\text{'}\theta ){\mathrm{-K}}_{(}^{}{}_{\mathcal{xnewT}},XA{\text{'}\theta {)}_{\mathcal{}}K{}_{\mathcal{(}}\mathrm{XA},}^{\mathrm{XA}}\text{'}\theta {)}_{\mathcal{}}{}_{\mathrm{-1K}(}^{}XA,\hfill \\ \hfill & {}_{\mathrm{xnewT\; \text{'}\theta })}^{}{\mathrm{+K}}_{\mathcal{}}({}_{\mathcal{}}^{xnewT\mathrm{,}}XA{}_{\mathcal{\text{'}\theta }}){}_{}^{}BA-1K(\hfill \end{array}$$XA, xnewT 'θ),

$$\begin{array}{l}{}_{\mathcal{}}\mathrm{BA=K}{(}_{\mathcal{}}XA{,}_{\mathcal{}}XA\text{'}\theta ){\mathrm{+K}}_{\mathcal{}}(XA,X{\text{'}\theta ){\Lambda }^{\mathrm{}}(\mathcal{\theta }}^{\mathrm{,\sigma 2}},A){}_{\mathcal{}}-1K(X\\ ,\mathrm{XA}{\mathrm{\text{'}\theta }}^{\mathrm{)}}\mathcal{,\Lambda }(\theta ,\sigma 2,A\mathcal{)}={\Omega }^{\mathrm{}}{(}_X\end{array}$$'θ, A) + σ2In.