In diseases such as cancer, the design of new therapeutic strategies requires extensive, costly, and unfortunately sometimes deadly testing to reveal life threatening "off target" effects. A crucial first step in predicting toxicity are analyses of normal RNA and protein tissue expression, which are now possible using comprehensive molecular tissue atlases. However, no standardized approaches exist for target prioritization, which instead rely on ad-hoc thresholds and manual inspection. Such issues are compounded, given that genomic and proteomic data detection sensitivity and accuracy are often problematic. Thus, quantifiable probabilistic scores for tumor specificity that address these challenges could enable the creation of new predictive models for combinatorial drug design and correlative analyses. Here, we propose a Bayesian Tumor Specificity (BayesTS) score that can naturally account for multiple independent forms of molecular evidence derving from both RNA-Seq and protein expression while preserving the uncertainty of the inference. We applied BayesTS to 24,905 human protein-coding genes across 3,644 normal samples (GTEx and TCGA) spanning 63 tissues. These analyses demonstrate the ability of BayesTS to accurately incorporate protein, RNA and tissue distribution evidence, while effectively capturing the uncertainty of these inferences. This approach prioritized well-established drug targets, while deemphasizing those which were later found to induce toxicity. BayesTS allows for the adjustment of tissue importance weights for tissues of interest, such as reproductive and physiologically dispensable tissues (e.g., tonsil, appendix), enabling clinically translatable prioritizations. Our results show that BayesTS can facilitate novel drug target discovery and can be easily generalized to unconventional molecular targets, such as splicing neoantigens. We provide the code and inferred tumor specificity predictions as a database available online (https://github.com/frankligy/BayesTS). We envision that the widespread adoption of BayesTS will facilitate improved target prioritization for oncology drug development, ultimately leading to the discovery of more effective and safer drugs.