Nitrous oxide (N2O) and nitric oxide (NO) play important roles in atmospheric chemical processes [Crutzen, 1979]. N2O is known as a greenhouse gas [Intergovernmental Panel on Climate Change, 2007] that contributes to global warming; its presence is the chief reason for ozone depletion in the stratosphere [Ravishankara et al., 2009]. On the other hand, accumulation of NO is a precursor to the development of acidic clouds and precipitation [Logan, 1983] and also acts as a catalyst in the synthesis of ozone in the troposphere [Holland and Lamarque, 1997].
 Agricultural soil is the major source of N2O and NO because N fertilizer strongly stimulates these N oxide gas emissions, which are derived from both nitrification and denitrification processes in the soil [e.g., Davidson and Verchot, 2000]. The fertilizer-induced N2O emission factor (EF), which is obtained by subtracting the emission of a zero-N control plot from the emission of a N fertilized plot expressed as the percentage of applied N, widely ranges from 0.003% to 0.083% [e.g., Bouwman et al., 2002; Zheng et al., 2004; Akiyama et al., 2006]. Many environmental and management factors such as the soil type, drainage, rainfall, temperature, and amount and type of fertilizers used affect N2O and NO fluxes [e.g., Akiyama et al., 2006; Toma et al., 2007]. For example, the mean annual temperature has a positive correlation with the EFs of N2O in onion fields [Toma et al., 2007]. In addition, a low soil pH leads to relatively higher EF values [Bouwman et al., 2002], which tend to occur in finely textured or poorly drained soil [Bouwman et al., 2002; Akiyama et al., 2006].
 The extent to which N2O and NO emissions from agricultural soil affect the global budget remains highly uncertain. One reason for this is the insufficient spatial resolution and representation of the flux data in field flux measurements with the conventional closed chamber method [Mosier, 1998]. In repeated chamber measurements conducted in previous studies, the variability in N2O and NO fluxes was significantly high and skewed [e.g., Yanai et al., 2003; Lark et al., 2004; Konda et al., 2008]. However, previous studies used the ensemble averaged N2O flux to analyze and adjust the parameters without considering the leptokurtic distribution of N2O fluxes. These approaches resulted in a bias because the distribution of the spatial N oxide flux was not approximated to a normal distribution and the information of variability was neglected. Nishina et al.  proposed that the hierarchical Bayesian (HB) model framework can be applied for the estimation of N2O flux from forest soil, in which the flux was assumed to follow a lognormal distribution and random variables were incorporated to compensate for the nonindependent data from the replication chambers. Their results showed that the HB model is an effective tool for the estimation of fluxes and evaluation of environmental parameters with less bias. Recently, micrometeorological methods have also been applied to measure the N oxide gas fluxes [e.g., Kroon et al., 2010] and are suitable for measuring long-term and spatially integrated fluxes. Comparison of the N oxide gas fluxes obtained using a micrometeorological method (e.g., eddy covariance) with those obtained using an automated closed chamber method reveals that avoiding the estimation bias of the closed chamber method is important.
 Bayesian estimation is one of the most effective analysis tools for evaluating uncertainties because it can simultaneously quantify variability and uncertainty in the observation data on the basis of stochasticity [Clark, 2005]. In previous reports, EFs have been calculated only from expected values by using a simple integration of the assembled observed data, known as area-under-curve (AUC) integration, with no evaluation of uncertainty. Precise evaluation of uncertainties in the observed fluxes and EFs is important for more plausible global budget estimation.
 An additional advantage of Bayesian estimation is that it can accommodate complex processes. The HB model reveals complex nonlinear relationships between the flux and environmental factors [Clark, 2005]. A previous innovative study on N2O flux using Bayes' theorem as a data assimilation method, known as Bayesian calibration, was performed by Lehuger et al. . They attempted to calibrate the N2O emission module of the CERES-EGC model and evaluated the responses of N2O flux to the environmental factors. In addition, Hashimoto et al.  applied the Bayesian calibration approach to a nonlinear equation for the inverse modeling of N2O flux in forest soil.
 In this study, we modeled the N2O and NO fluxes by assuming a lognormal distribution and incorporating random effects in the block (chamber position) to consider the spatial variability in the flux. Our HB model accommodated nonlinear relationships between the fluxes and environmental factors. In addition, it aimed (i) to quantify the response of the N2O and NO fluxes to the environmental factors and the N fertilization effect and (ii) to estimate the uncertainties in the N2O and NO fluxes and their fertilizer-induced EFs more accurately.