Approach: treat expert judgment as a prior distribution and telemetry as likelihood; use Bayesian updating to compute a posterior that drives decisions (alerts, mitigation, rollout hold). For rare binary failure modes use a Beta-Bernoulli model; for rates/latencies use a Gamma-Poisson or hierarchical Gaussian.1) Elicit priors from experts- Calibrate experts first (short seed questions with known answers).- Ask for quantiles (e.g., median, 90% interval) and translate to a parametric prior (e.g., Beta(α,β) for failure probability p). Fit α,β by matching mean and variance from quantiles or using method-of-moments.- Capture disagreement via pooled or hierarchical prior: model expert i as Beta(α_i,β_i) with a hyperprior, or form a weighted mixture where weights reflect calibration scores and expertise.2) Combine telemetry (likelihood)- For n observed requests and k observed rare failures, likelihood is Binomial(k|n,p). Posterior ∝ Beta(α,β) × Binomial → Beta(α+k, β+n−k).- If zero failures observed, the prior prevents posterior collapsing to zero; quantify posterior credible intervals.3) Weighting experts vs telemetry- Effective sample size (ESS) of prior: for Beta, ESS = α+β. Elicit or set ESS to reflect confidence (e.g., high ESS for well-validated expert models). Calibration-based weights adjust ESS per expert.- Use hierarchical modeling to let data shrink expert beliefs toward pooled mean as telemetry grows (data-driven weighting).4) Updating & decision rules- Implement online Bayesian updates as telemetry arrives (batch or streaming). After each update compute posterior predictive risk of cascading failure (e.g., probability p > threshold).- Decision policies: if P(p > p_crit | data) > θ → trigger mitigation; otherwise continue monitoring.- Use sequential hypothesis control (Bayes factor or posterior odds) for early warning with controlled false-alarm trade-offs.5) Robustness & validation- Run sensitivity analysis across prior choices; use heavy-tailed/prior mixtures to reduce overconfidence.- Posterior predictive checks and backtesting on historical incidents.- Human-in-the-loop: surface posterior, confidence, and key assumptions to SRE/PM; allow expert reassessment when telemetry contradicts priors.Minimal code (Beta-Bernoulli update):python
from scipy.stats import beta
# prior parameters from elicitation
alpha, beta_param = 2.0, 198.0 # prior ~ mean 0.01, ESS=200
# telemetry
n, k = 10000, 0 # observe 0 failures in 10k requests
# posterior
post_a, post_b = alpha + k, beta_param + n - k
mean = post_a / (post_a + post_b)
ci = beta.ppf([0.05, 0.95], post_a, post_b)
print(mean, ci)
