## Appendix B Bayesian Inference  
The parameter values of the APP model are estimated using Bayesian inference. Based on the model formulation in Section 3.2, the likelihood of observing paper citation histories are first calculated. Then, by imposing a conjugate prior, the posterior distribution of the latent affinity \(\xi^{f}\) is computed. Accordingly, Figure 3 illustrates the corresponding graphical model of the APP model. **Likelihood Distribution. ** As illustrated in Figure 2b, an individual paper \(i\)'s cited time moments, grouped into each citing field \(f\)'s citations \(D_{i}^{f}\), follows a Poisson process independently. Thus, the likelihood of observing all citation time moments \(\mathbf{D}^{f}\) of the cited field can be factorized as  
\[p\left(\mathbf{D}^{f}\;\left|\;\xi^{f}\right.\right)=\prod_{i=1}^{I}p\left(\mathbf{D}_{ i}^{f}\;\left|\;\xi^{f}\right.\right)=\prod_{i=1}^{I}\prod_{n=1}^{N_{i}^{f}}p \left(t_{n}^{f}\;\left|\;t_{n-1}^{f},\;\xi^{f}\right.\right)\;p\left(T\;\left| \;t_{N_{i}^{f}}^{f},\;\xi^{f}\right.\right)\;\;, \tag{13}\]  
where \(t_{0}^{f}=0\) denotes the publication time of the paper \(i\). In a nonhomogeneous Poisson process, the probability that a new event occurs after the previous event follows an exponential distribution as  
\[p\left(t_{n}^{f}\;\left|\;t_{n-1}^{f},\;\xi^{f}\right.\right)=\lambda_{i}^{f} \left(t_{n}^{f}\right)\;\exp\left(-\int_{t_{n-1}^{f}}^{t_{n}^{f}}\lambda_{i}^ {f}(s)\;ds\right)\;\;, \tag{14}\]  
while the probability that no event occurs between \(t_{N_{i}^{f}}^{f}\) and \(T\) is  
\[p\left(T\;\left|\;t_{N_{i}^{f}}^{f},\;\xi^{f}\right.\right)=\exp\left(-\int_{ t_{N_{i}^{f}}^{f}}^{T}\lambda_{i}^{f}(s)\;ds\right)\;\;. \tag{15}\]By substituting Equations (A7) and (A8) into Equation (A6), the likelihood is rewritten as  
\[ \begin{split} p\left(\mathbf{D}^{f}\ \Big{|}\ \xi^{f}\right)& =\prod_{i=1}^{I}\left(\prod_{n=1}^{N_{i}^{f}}\lambda_{i}^{f}(t_{n}^{f})\ \exp\left(-\int_{t_{n-1}^{f}}^{t_{n}^{f}}\lambda_{i}^{f}(t)dt\right)\right) \exp\left(-\int_{t_{N_{i}^{f}}^{f}}^{T}\lambda_{i}^{f}(t)dt\right)\\ &=\prod_{i=1}^{I}\exp\left(-\sum_{n=1}^{N_{i}^{f}}\int_{t_{n-1}^{f }}^{t_{n}^{f}}\lambda_{i}^{f}(t)dt-\int_{t_{N_{i}^{f}}^{T}}^{T}\lambda_{i}^{f} (t)dt\right)\prod_{n=1}^{N_{i}^{f}}\lambda_{i}^{f}(t_{n}^{f})\\ &=\prod_{i=1}^{I}\exp\left(-S_{i}^{f}\right)\prod_{n=1}^{N_{i}^{f }}\lambda_{i}^{f}\left(t_{n}^{f}\right)\.\end{split} \] (A9)  
According to Equation (4), the exponent \(S_{i}^{f}\) is rewritten as  
\[ \begin{split} S_{i}^{f}&=\sum_{n=1}^{N_{i}^{f}}\int _{t_{n-1}^{f}}^{t_{n}^{f}}\lambda_{i}^{f}(t)dt+\int_{t_{N_{i}^{f}}^{f}}^{T} \lambda_{i}^{f}(t)dt\\ &=\sum_{n=1}^{N_{i}^{f}}\int_{t_{n-1}^{f}}^{t_{n}^{f}}\xi^{f} \cdot(n_{0}+n-1)\cdot p(t;\theta_{i}^{f})dt+\int_{t_{N_{i}^{f}}^{f}}^{T}\xi^{f }\cdot(n_{0}+N_{i}^{f})\cdot p(t;\theta_{i}^{f})dt\\ &=\xi^{f}\left(\int_{0}^{t_{1}^{f}}n_{0}\cdot p(t;\theta_{i}^{f} )dt+\int_{t_{1}^{f}}^{t_{2}^{f}}(n_{0}+1)\cdot p(t;\theta_{i}^{f})dt+\cdots+ \int_{t_{N_{i}^{f}}^{f}}^{T}(n_{0}+N_{i}^{f})\cdot p(t;\theta_{i}^{f})dt\right) \\ &=\xi^{f}\left(\int_{0}^{t_{1}^{f}}n_{0}\cdot p(t;\theta_{i}^{f} )dt+\int_{0}^{t_{2}^{f}}(n_{0}+1)\cdot p(t;\theta_{i}^{f})dt+\cdots+\int_{0}^{ T}(n_{0}+N_{i}^{f})\cdot p(t;\theta_{i}^{f})dt\right)\\ &\quad-\xi^{f}\left(\int_{0}^{t_{1}^{f}}(n_{0}+1)\cdot p(t;\theta _{i}^{f})dt+\int_{0}^{t_{2}^{f}}(n_{0}+2)\cdot p(t;\theta_{i}^{f})dt+\cdots+ \int_{0}^{t_{N_{i}^{f}}^{f}}(n_{0}+N_{i}^{f})\cdot p(t;\theta_{i}^{f})dt\right) \\ &=\xi^{f}\Bigg{(}(n_{0}+N_{i}^{f})\cdot P(T;\theta_{i}^{f})-\sum_{ n=1}^{N_{i}^{f}}P(t_{n}^{f};\theta_{i}^{f})\Bigg{)}=\xi^{f}M_{i}^{f},\end{split} \] (A10)  
where  
\[ \begin{split}& M_{i}^{f}=\left(n_{0}+N_{i}^{f}\right)\cdot P\left( T;\theta_{i}^{f}\right)-\sum_{n=1}^{N_{i}^{f}}P\left(t_{n}^{f};\theta_{i}^{f} \right)\,\\ & P\left(t_{n}^{f};\theta_{i}^{f}\right)=\int_{0}^{t_{n}^{f}}p \left(s;\theta_{i}^{f}\right)ds=\Phi\left(\tau_{i}^{f}\right)\,\\ &\tau_{i}^{f}=\left(\ln t_{n}^{f}-\mu_{i}^{f}\right)/\sigma_{i}^{f }\.\end{split}