the Bayes factor is simplified to be the ratio of the corresponding Bayesian evidence, $$K = \frac{P(M_2|D)}{P(M_1|D} = \frac{P(D|M_2)}{P(D|M_1)},$$ where $P(M_{1, 2}|D)$ is the posterior probability, $P(D|M_{1, 2})$ is called the Bayesian evidence, which has been marginalized over the whole model parameters, and $D$ represent the observed data. A large value of $K>1$ means that model $M_2$ is [preferable]{} to model $M_1$. A widely used [criterion for quantifying the degree of preference is]{} given by [@Kass1995]. The three PSD adopted models are 1) the single power-law (SPL) model with a form of, $$P_{\rm SPL}(f) = A f^{-\alpha},
\label{equ_spl}$$ 2) the damped random walk (DRW) model with a form of $$P_{\rm DRW}(f) = \frac{A}{1 + (f/f_{\rm b})^2},
\label{equ_drw}$$ and 3) the bending power-law (BPL) model with a form of $$P_{\rm BPL}(f) = A \left\{\begin{array}{cc}
          (f/f_{\rm b})^{-\alpha} & {\rm for}~f > f_{\rm b},\\
          (f/f_{\rm b})^{-\beta} & {\rm otherwise}.
         \end{array}\right.
\label{equ_bpl}$$ Here $A$, $\alpha$, $\beta$, and $f_{\rm b}$ are free parameters with a restriction $\alpha > \beta$. Throughout the calculations, the prior probabilities for $A$ and $f_{\rm b}$ are set to be logarithmic and the value of $f_{\rm b}$ is limited to the frequency range of the data; the prior probabilities for $\alpha$ 