pi(t)=Pr(black horse=aiH(t)>Hc, I0),ipi(t)=1.p_i(t) = \Pr\big(\text{black horse}=a_i \mid H(t)>H_c,\ \mathcal{I}_0\big), \qquad \sum_i p_i(t)=1.
Both are computed via ensemble simulation or via semi-analytical first-passage approximations.
Key derived metrics
Mean first-passage time (MFPT): =E[min{t:H(t)>Hc}]\tau = \mathbb{E}[\min\{t: H(t)>H_c\}].
Hazard rate: h(t)=fT(t)1FT(t)h(t) = \frac{f_T(t)}{1-F_T(t)}, where FTF_T is CDF of first-passage time.
Actor likelihood score: computed from actor-specific mobilization potential hi(t)h_i(t) (see next section).
2) Data & signal construction for H(t)H(t) and actors
Build H(t)H(t) as a composite index:
H(t)=wsSsocial(t)+wmSmedia(t)+woSorgan(t)+wfSfund(t)H(t) \;=\; w_{s} \cdot S_{\text{social}}(t) \;+\; w_{m}\cdot S_{\text{media}}(t) \;+\; w_{o}\cdot S_{\text{organ}}(t) \;+\; w_{f}\cdot S_{\text{fund}}(t)
Components (normalized 0--1):
Social mobilization signal SsocialS_{\text{social}}: protest organizational metrics --- mobilization rate, event clustering, cross-sector alliances (student+labor+ojol).
Media attention signal SmediaS_{\text{media}}: velocity of mentions, sentiment divergence, follower growth rate of candidate actors, hashtag virality (use platform APIs).
Organizational capacity SorganS_{\text{organ}}: existence and activity of coordinating networks (NGO/ormas nodes, regional cadres), logistic capability proxies (crowdfunding, transport coordination).
Funding/logistics SfundS_{\text{fund}}: donation flows, crowdfunding spikes, sudden transfers to mobilization wallets.
Weights ww set from prior knowledge or via training (e.g., logistic regression on past emergence events). Normalize so H[0,1]H\in[0,1] (or scale to operational units).
Actor mobilization vector: for each candidate actor aia_i, compute actor-specific signals:
mi(t)m_i(t): growth rate of followers / engagement;
ni(t)n_i(t): leadership network centrality (mentions connecting to organizing nodes);
ri(t)r_i(t): rhetoric resonance index (sentiment + framing alignment with grievances).
Combine into actor score si(t)[0,1]s_i(t)\in[0,1]. Then actor conditional probability given HH is:
pi(t)=si(t)jsj(t)p_i(t) \;=\; \frac{s_i(t)^\gamma}{\sum_j s_j(t)^\gamma}
