Appendix Figure 5.

Schematic of belief regions described in proofs of Propositions 3 and 4 and Theorem 3. Panel a: The line demarking half-space H_t, Cβ_t = 0, intersects the lines that form the edges of the belief space at points a, b and c. Panel b: The lines that define half-spaces $S_{t-1,H_t,SS+}$ and $S_{t-1,H_t,SS-}$ can be expressed as linear combinations of $a_{+}^{\prime }$ and $b_{+}^{\prime }$, and similarly for $a_{-}^{\prime }$ and $b_{-}^{\prime }$ (panel c). Panel d: We define the union of the two intersections (given in panel b and c) as U_t−1,t.