  In spite of significant progress in the research of fast radio bursts (FRBs)
in recent decade, their origin is still under extensive debate. Investigation
on the population of FRBs can provide new insight into this interesting
problem. In this paper, based on the first CHIME/FRB catalog, we construct a
Bayesian framework to analyze the FRB population, with the selection effect of
the CHIME telescope being properly taken into account. The energy function is
modeled as the power-law with an exponential cutoff. Four redshift distribution
models are considered, i.e., the star formation history (SFH) model, and three
time-delayed models (Gaussian delay, log-normal delay, and power-law delay).
The free parameters are simultaneously constrained using Bayesian inference
method, and the Bayesian information criterion (BIC) is used in model
comparison. According to BIC, the log-normal delay model fits the data best.
The power-law delay model and Gaussian delay model can also give reasonable
fits, although they are not as good as the log-normal delay model. However, the
SFH model is strongly disfavored compared with the three time-delayed models.
The energy function is tightly constrained and is almost independent of the
redshift models, with the best-fitting power-law index $\alpha\approx 1.8$, and
cut-off energy $\log(E_c/{\rm erg})\approx 42$. The FRB population shows on
average $3\sim 5$ billion years time delay with respect to the SFH. Therefore,
the hypothesis that the FRB population traces the SFH is conclusively ruled
out.
