We are concerned with the effect of a particulate matter on our health in Japan. When we estimate the effect of a particulate matter on our health, we would like to have observations of particulate matter concentrations in study areas. However, particulate matter concentrations are not observed in a part of cohort study areas, so we need to estimate PM concentrations in unobserved areas to estimate the effect of particulate matter on our health. In such a case, it is common to use some estimation method (e.g. Inverse distance weighting, land use regression) to obtain estimates of particulate matter concentrations at unobserved areas, then replace missing values with these estimates. However, the variance of the effect of particulate matters on our health may be underestimated using such methods. This paper discusses the problem when we substitute estimates as observed values to analyze the effect of particulate matters on our health through simulation, and construct the model for PM10 spatial distribution in Japan to use a Bayesian approach to avoid previously mentioned problems.