Motion integration using competitive priors

Psychophysical experiments show that humans are better at perceiving rotation and expansion than translation [5][9]. These findings are inconsistent with standard models of motion integration which predict best performance for translation. To explain this discrepancy, our theory formulates motion perception at two levels of inference: we first perform model selection between the competing models (e.g. translation, rotation, and expansion) and then estimate the velocity using the selected model. We define novel prior models for smooth rotation and expansion using techniques similar to those in the slow-and-smooth model [23] (e.g. Green functions of differential operators). The theory gives good agreement with the trends observed in four human experiments

Galactic masers and the Milky Way circular velocity

Masers found in massive star-forming regions can be located precisely in six-dimensional phase space and therefore serve as a tool for studying Milky Way dynamics. The non-random orbital phases at which the masers are found and the sparseness of current samples require modeling. Here we model the phase-space distribution function of 18 precisely measured Galactic masers, permitting a mean velocity offset and a general velocity dispersion tensor relative to their local standards of rest, and accounting for different pieces of prior information. With priors only on the Sun's distance from the Galactic Center and on its motion with respect to the local standard of rest, the maser data provide a weak constraint on the circular velocity at the Sun of V_c = 246 +/- 30 km/s. Including prior information on the proper motion of Sgr A* leads to V_c = 244 +/- 13 km/s. We do not confirm the value of V_c \approx 254 km/s found in more restrictive models. This analysis shows that there is no conflict between recent determinations of V_c from Galactic Center analyses, orbital fitting of the GD-1 stellar stream, and the kinematics of Galactic masers; a combined estimate is V_c = 236 +/- 11 km/s. Apart from the dynamical parameters, we find that masers tend to occur at post-apocenter, circular-velocity-lagging phases of their orbits.Comment: ApJ in pres

Real Options under Choquet-Brownian Ambiguitys

Real options models characterized by the presence of “ambiguity” (or “Knightian uncertainty”) have been recently proposed. But based on recursive multiple-priors preferences, they typically describe ambiguity through a range of Geometric Brownian motions and solve it by application of a maxmin expected utility criterion among them (worst case). This reduces acceptable individual preferences to the single case of an extreme form of pessimism. In contrast, by relying on dynamically consistent “Choquet-Brownian” motions to represent the ambiguous cash flows expected from a project, we show that a much broader spectrum of attitudes towards ambiguity may be accounted for, improving the explanatory and application potentials of these appealing expanded real options models. In the case of a perpetual real option to invest, ambiguity aversion may delay the moment of exercise of the option, while the opposite holds true for an ambiguity seeking decision maker. Furthermore, an intricate relationship between risk and ambiguity appears strikingly in our model.

Real Options under Choquet-Brownian Ambiguity

Real options models characterized by the presence of ambiguity have been recently proposed. But based on recursive multiple-priors approaches to solve ambiguity, these seminal models reduce individual preferences to extreme pessimism by considering only the worst case scenario. In contrast, by relying on dynamically consistent Choquet-Brownian motions to model the dynamics of ambiguous expected cash flows, we show that a much broader spectrum of attitudes towards ambiguity may be accounted for. In the case of a perpetual real option to invest, ambiguity aversion delays the moment of exercise of the option, while the opposite holds true for an ambiguity lover.Real Options; Ambiguity; Irreversible investment; Optimal stopping; Knightian uncertainty; Choquet-Brownian motions