Systematic biases in perception can be either attractive or repulsive with respect to the immediate spatial or temporal context. There is an extensive amount of literature [1,2,3] on how to explain these differences in biases with a variety of mechanisms, ranging from sensory adaptation over efficient coding to various flavors of probabilistic estimation, variably called Bayesian or predictive or optimal. Here we want to demonstrate with several examples that some reasons for attraction vs. repulsion have been overlooked, neglected, or not acknowledged for specific domains. One example for strong biases is the perception of verticality assessed by the subjective visual vertical, where a repulsive bias, the E-effect, can occur close to the upright body position together with an attractive bias, the A-effect, for larger body tilt. While the attractive A-effect is explained as consequence of a prior for upright body orientation, explanations for the repulsive E-effect so far are based on sensory non-linearities [4] or uncompensated ocular torsion [5]. Here we show that a Bayesian model accounting for tilt-dependent sensory uncertainty explains the results, if the non-linear dependence of measurement noise on tilt angle is considered. This complete knowledge of noise distributions results in asymmetric likelihood functions, which cause the E-effect. Another example is sequential dependence, a bias due to temporal context, observed during consecutive magnitude estimations. While in most cases the current estimate is attracted toward the stimuli presented in the immediate previous past, we have recently shown that the sequential dependence becomes negative, if stimuli are presented in a random walk order rather than a randomized order [6]. Here we show that even for randomized stimuli, a repulsive sequential dependence can occur if stimuli comprise only a few distinct magnitudes. This repulsive sequential bias can be explained by the well-known sequential dependence for multiple-choice situations [7], if the perceptual process of participants incorporates the belief that stimuli are randomly drawn from few categories. Thus, individual beliefs of how stimuli are generated influence the sequential dependence and can even change its sign. In summary, both attractive and repulsive biases can be explained within the Bayesian framework, but with different reasons ranging from likelihood functions over stimulus properties to internal beliefs.