Tumor segmentation in oncological PET is challenging, a major reason being the partial-volume effects due to the low system resolution and finite voxel size. The latter results in tissue-fraction effects, i.e. voxels contain a mixture of tissue classes. Most conventional methods perform segmentation by exclusively assigning each voxel in the image as belonging to either the tumor or normal tissue classes. Thus, these methods are inherently limited in modeling the tissue-fraction effects. To address this inherent limitation, we propose an estimation-based approach to segmentation. Specifically, we develop a Bayesian method that estimates the posterior mean of fractional volume that the tumor occupies within each image voxel. The proposed method, implemented using an encoder-decoder network, was first evaluated using clinically realistic 2-D simulation studies with known ground truth, in the context of segmenting the primary tumor in PET images of patients with lung cancer. The evaluation studies demonstrated that the method accurately estimated the tumor-fraction areas and significantly outperformed widely used conventional methods, including a U-net-based method, on the task of segmenting the tumor. In addition, the proposed method was relatively insensitive to partial-volume effects and yielded reliable tumor segmentation for different clinical-scanner configurations. The method was then evaluated using clinical images of patients with stage II and III non-small cell lung cancer from ACRIN 6668/RTOG 0235 multi-center clinical trial. Here, the results showed that the proposed method significantly outperformed all other considered methods and yielded accurate tumor segmentation on patient images with dice similarity coefficient of 0.82 (95% CI: 0.78, 0.86). Overall, this study demonstrates the efficacy of the proposed method to accurately segment tumors in PET images.