Our aim is to analyze the link between optimism and risk aversion in a subjective expected utility setting and to estimate the average level of optimism when weighted by risk tolerance. Its estimation leads to a non-trivial statistical problem. We start from a large lottery survey (1536 individuals). We assume that individuals have true unobservable characteristics. We adopt a Bayesian approach and use a hybrid MCMC approximation method to numerically estimate the distributions of the unobservable characteristics. We find that individuals are on average pessimistic and that pessimism and risk tolerance are positively correlated.