This paper presents a robust optimization approach for linear optimization problems affected by uncertain probabilities, using ϕ-divergences. The authors show that uncertainty regions based on ϕ-divergences naturally arise as confidence sets when uncertain parameters include elements of a probability vector. These problems are common in areas such as inventory control and finance, where terms involving moments of random variables or expected utility are present. The robust counterpart of such problems is shown to be tractable for most ϕ-divergences typically considered in the literature. The approach is extended to nonlinear problems and illustrated with applications, including an asset pricing example and a numerical multi-item newsvendor example. The paper discusses the construction of uncertainty regions as confidence sets using ϕ-divergences, and shows that these regions can be used to formulate tractable robust optimization problems. The authors also discuss the tractability of the robust counterpart for different ϕ-divergences, and show that for most significant ϕ-divergences, the resulting robust counterpart problem is polynomially solvable. The paper concludes with a discussion of further research topics.This paper presents a robust optimization approach for linear optimization problems affected by uncertain probabilities, using ϕ-divergences. The authors show that uncertainty regions based on ϕ-divergences naturally arise as confidence sets when uncertain parameters include elements of a probability vector. These problems are common in areas such as inventory control and finance, where terms involving moments of random variables or expected utility are present. The robust counterpart of such problems is shown to be tractable for most ϕ-divergences typically considered in the literature. The approach is extended to nonlinear problems and illustrated with applications, including an asset pricing example and a numerical multi-item newsvendor example. The paper discusses the construction of uncertainty regions as confidence sets using ϕ-divergences, and shows that these regions can be used to formulate tractable robust optimization problems. The authors also discuss the tractability of the robust counterpart for different ϕ-divergences, and show that for most significant ϕ-divergences, the resulting robust counterpart problem is polynomially solvable. The paper concludes with a discussion of further research topics.