6. Caveats and interpretive guidance
These baseline numerics are illustrative and contingent on calibration quality. Local data mapping and continuous updating are essential.
Forecasts are probabilistic: policy should be guided by risk appetite and costs of Type I vs Type II errors (false alarms vs missed escalations).
Ethical caution: public release of forecasts may influence behavior; consider controlled dissemination to crisis managers and independent oversight.
The bifurcation-aware stochastic ensemble approach reveals a binary tendency in near-term Indonesian trajectories: one of managed recovery, achievable via rapid accommodative responses and information control, and one of entrenched escalation, triggered by slow relief, heavy repression, or an unlucky large shock. The operational value of the model lies in quantifying the probabilities of these paths, identifying sensitive policy levers (notably U\rho_U and K\rho_{\mathcal{K}}), and translating ensemble diagnostics into actionable early-warning rules.
B. Black-Horse Emergence --- Probability Mapping
This section turns the abstract variable H(t)H(t) --- the black-horse potential --- into an operational probabilistic forecast: what is the chance that (1) a black-horse actor emerges, and (2) which actor (or cluster) will become that black horse? The goal is a repeatable pipeline that converts data into probability trajectories Pr(H(t)>Hc)\Pr(H(t)>H_c) and actor-level shares Pr(actor iH(t)>Hc)\Pr(\text{actor } i \mid H(t)>H_c).
Below I present (1) a mathematical framing, (2) data and signal construction, (3) an algorithm to compute probabilities and MFPTs, (4) mapping to candidate actors, and (5) recommended visual products and decision thresholds.
1) Mathematical framing
We adopt the SDE for H(t)H(t) from Section III.A:
dHdt=PP(t)+EE(t)TT(t)HH(t)+H(t).\frac{dH}{dt} \;=\; \alpha_P P(t) + \alpha_E E(t) - \beta_T T(t) - \gamma_H H(t) + \xi_H(t).
Let HcH_c be the empirical emergence threshold (set from historical cases or calibrated). We want:
Emergence probability curve: pem(t)=Pr(H(t)>HcI0)p_{\text{em}}(t) = \Pr\big(H(t) > H_c \,\big|\, \mathcal{I}_0\big) given information I0\mathcal{I}_0 at model time 0.
Actor attribution vector: for a candidate set A={a1,...,an}\mathcal{A}=\{a_1,\dots,a_n\}, we want conditional probabilities
