The recent gravitational wave signal detected by NANOGrav, Parkers Pulsar Timing Array, European Pulsar Timing Array, and Chinese Pulsar Timing Array collaborations can be explained by scalar induced secondary gravitational waves. The waveforms of scalar induced secondary gravitational waves exhibit a near-model-independent behavior in the infrared region $k\ll k_p$, $h^2\Omega_\text{GW} = A_\text{GW}\left(k/k_{\rm ref}\right)^{n_{\mathrm{GW}}}$, where the index $n_{\mathrm{GW}}$ is $n_{\mathrm{GW}} = 2 n_1$ for $n_1<3/2$, $n_{\mathrm{GW}} = 3-3/ \ln(k_p/k)$ for $n_1=3/2$, and $n_{\mathrm{GW}} =3-2/ \ln(k_p/k)$ for $n_1>3/2$ if the primordial curvature perturtation is parameterized as a power-law with the index $n_1$. Through Bayesian analysis, we discuss the parameter space that characterizes the behavior of scalar induced gravitational waves in the infrared region. The mean values and one sigma confidence intervals of parameters are $\log_{10} A_\mathrm{GW} = -7.18^{+0.24}_{-0.26}$ and $n_1 = 0.94^{+0.17}_{-0.17}$ for $n_1<3/2$, $\log_{10} A_\mathrm{GW} = -6.96^{+0.27}_{-0.30}$ and $\log_{10} k_p/ {\rm Mpc}^{-1} = 8.24^{+1.48}_{-0.58}$ for $n_1=3/2$, and $\log_{10} A_\mathrm{GW} = -6.77^{+0.19}_{-0.22}$ and $\log_{10} k_p/ {\rm Mpc}^{-1} = 8.37^{+1.69}_{-0.68}$ for $n_1>3/2$. Comparing with the interpretation of the detected signal as stochastic background from massive black hole binaries, the results for $n_1<3/2$, $n_1=3/2$, and $n_1>3/2$ give the support of scalar induced gravitational waves with the Bayes factor $\ln \mathcal{B}= 2.8$, $\ln \mathcal{B}= 2.9$, and $\ln \mathcal{B} = 1.8$, respectively.