Key Empirical Findings

Part of Statistical Methods — MORIE’s statistical-methods reference.

Headline numerical results that the MORIE analysis surface produces on the public Toronto Police Service and Ontario Tracking and Information System (OTIS) data. Each item is the output of a specific module call.

Spatial autocorrelation (Toronto Police Service, 2024)

  • Polygon Moran’s \(I\) — Assault rate: \(+0.328\) (z = 90, p \(\approx 0\)). Strong positive spatial autocorrelation across neighbourhoods.

  • Polygon Moran’s \(I\) — Homicide rate: \(-0.005\) (z = 0.4). Spatially random — Toronto homicides do not cluster at the neighbourhood polygon scale.

Computed via morie.tps_spatial.morai over the TPS neighbourhood shapefile.

Hawkes self-exciting point processes (post-2014 TPS)

  • Markovian Hawkes branching ratio \(\hat{\eta} = 0.97\). Toronto Assault, classical Mohler exponential kernel + constant baseline (with U(0,1)-day jitter for tied OCC_DATE timestamps).

  • \(\Delta\mathrm{AIC}\) (non-Markovian over Markovian) \(\geq 80\). Holds across all 9 TPS categories. Weibull or Gamma kernel + sinusoidal baseline beats the classical Mohler-Bertozzi-Brantingham exponential + constant model under Kwan-Chen-Dunsmuir (2024).

Computed via morie.tps_hawkes_advanced.compare_hawkes_kernels; see Hawkes Self-Exciting Point Processes for the methodology and the companion paper at 10.5281/zenodo.20102198.

OTIS placements (Ontario Tracking and Information System)

  • Goffmanian power-law exponent \(\hat{\alpha} = 1.62\). Per-person placement-count distribution. Within the canonical 1.5–2.5 preferential-attachment range (Barabási-Albert / Goffman Asylums 1961 chapter on the mortified self).

  • Pareto distribution AIC = 197 k. Best fit for OTIS embedding-days distribution. Lognormal AIC = 207 k, Exponential AIC = 223 k.

  • RC / custody rate, Black individuals = 65.4 %. OTIS c03 race \(\times\) confinement breakdown. Versus 42.4 % for “Unknown / Not Reported”.

Computed via morie.otis_analyze and morie.otis_causal modules; the OTIS-RC OU diagnostic quads (residuals / Q-Q / scale-location / leverage) are produced by morie.otis_all_analyze.otis_rc_diagnostics.

How to reproduce

Each of the values above is the output of a single MORIE function call against the corresponding open-data feed. The morie run-module CLI subcommand executes any of the registered analysis modules end-to-end and writes a results table to --output-dir; the headline numbers are extracted from those tables.