How the model works

The comment at the top of models/model4.py lists what changed from earlier versions and why. Every number below comes from the result tables, which report/make_tables.py generates from the results files.

Files

models/model4.py the model (BASE priors with sources, run(P), vary, pool); models/chain4.py exact completion probabilities for a chain of exponential stages with an optional killing hazard; models/cosmo_tables.py and the .npz file it writes hold the LambdaCDM birth-date and reach tables.
models/run4.py driver: the base case (8 pooled seeds of 250,000 universes; the self-indication column comes from separate runs with a tilted sampler), all 16 on/off subsets of the four observation terms (Shapley values), 35 camps, one-at-a-time levers, a barrier by low-footprint grid, 14 possible future observations. Output integrate4_results.json.
models/scan4.py joint prior draws -> integrate4_scan.json; models/cells4.py -> cells4.json (cells for the in-browser prior playground); models/leverage4.py how far each measured input can move the answer.
The result tables are published in full.

Structure in one paragraph

One sample is one universe. Habitable planets around G, K and M hosts each run a biology chain: abiogenesis at a rate that is either fast (prior weight w_fast = 0.2) or log-uniform over up to 100 decades, then 0 to 4 candidate steps whose difficulty is log-uniform over 2 to 8 decades (a step counts as hard if its success probability in the window is below 0.3), or, with no hard step, an environmental gate with a delay. Persistence is a constant hazard with probability 0.5, otherwise a flat factor. A technological civilisation becomes a sustained expander with probability p_exp: zero-like under the universal-barrier atom (q_barrier = 0.15), otherwise 10^-(W x u). Expanders travel at v_gal inside a galaxy and v_ig between galaxies (q_ig = 0.6 that intergalactic travel is possible at all). Evidentness is per lineage: a fraction c ~ U(0,1) of lineages claim systems and would be evident; the rest are evident with probability p_here each; two universe-level atoms make all expansion low-footprint (q_cc = 0.05) or deliberately hidden (p_stealth = 0.03). Observation terms: (early) life appeared early on Earth; (late) we arrived late in the window; (local) nobody is visibly here, with pockets; (surveys) no harvested galaxy in three infrared bands plus optical scaling relations, and no radio detection.

Classes and the three answers

Seven classes: empty_universe (expected civilisations ever in the Galaxy, times the number of Milky-Way equivalents in the observable universe, 5e10 to 2e11, is below 1), rare (expected number ever in the Galaxy below 1), en_route (expanders hold at least 1% of the reachable universe, not here), stuck (civilisations arose in the Galaxy, no sustained expander here), unnoticed, hidden, excluded (claimed by evident settlers; we would be in a pocket). The page groups them into three answers that add to 1: nobody (empty_universe + rare), never spread (stuck), someone spread (en_route + unnoticed + hidden + excluded). "No other civilisation ever arose here" is a separate statistic (expected number ever in the Galaxy below 1) and overlaps the third answer by about 0.05.

Headline (8 x 250,000 universes)

Evident settlement: prior 0.360, posterior 0.005. That is nearly all the evidence does.
Three answers, Earth as a given: prior 0.469 / 0.097 / 0.434, posterior 0.726 / 0.164 / 0.110. Among the non-evident explanations only: 0.733 / 0.152 / 0.115 before, 0.729 / 0.165 / 0.106 after.
No other civilisation ever in the Galaxy: 0.580 -> 0.780 (odds times 2.57). Shapley shares in points: early life -7.3, late arrival +3.0, nobody visibly here +21.9, surveys and radio +2.3; as odds multipliers 0.70, 1.16, 2.83, 1.11.
P(life starts easily): prior 0.200, posterior 0.199. Early life alone favours an easy origin by 2.4 to 1 in this model; the silence cancels it.
Other conventions for counting ourselves: nobody 0.707 (typical among all civilisations), 0.722 (typical so far), 0.537 (typical observer, with never spread 0.452), and under self-indication about 0.70 never spread and 0.30 spread, nobody 0.
Monte Carlo standard error on the largest class: 0.0007 (Earth as a given), 0.005 (self-indication, which is quoted to the nearest 5 points).

Soft spots

The answer follows the prior that life starts easily (w_fast) and the 100-decade slow range: nobody falls from 0.80 to 0.35 as w_fast goes from 0.05 to 0.95, and at 0.9 "never spread" (0.41 in the pooled camp run; 0.42 on the single-run curve) passes "nobody" (0.38).
The +22 points from the silence is the redistribution of the 0.36 prior mass on evident settlement among the other classes roughly in proportion to their priors. If an unclaimed Earth is treated as a precondition for our existence, the silence carries no information.
"Unnoticed" returns about 0.5 to 0.8 times the prior put on forced low-footprint expansion; P(low-footprint regime) rises only from 0.05 to 0.084. The data do not test it. The same holds for the universal barrier (0.15 -> 0.26) and for hiding (0.03 -> 0.05).
Not modelled: the future star-formation prior, a minimum delay for hard-step rows, synchronised (reset) timing, waves that came and went (they sit inside "never spread"), partial harvesting with waste heat at 20 to 100 kelvin, any explanation not on the list. A 10% prior on an unlisted silent explanation would lower "no other ever" from 0.78 to about 0.66.
The typical-observer column depends on the assumed number of observers per expander: 1e3 to 1e10 moves nobody from 0.60 to 0.51.
The origin of life and the feasibility of expansion are independent in the prior. If they were strongly linked, the reading of a second origin of life as bad news could reverse.

What changed from 4.0 to 4.1 (after red team round 3)

Prior class masses and prior statistics now come from an unconditioned gate delay; Shapley values and forecasts are pooled over the 8 base seeds; forecasts report the chance that a discovery is true as well as the chance it is announced; new camps (life starts easily 90% sure, gradual evolution with no hard steps, classic SETI, a bounded origin-of-life prior, early life credited at 6, 9 and 13 to 1, long-lived hosts counted fully); the prior scan now draws the easy-life prior from 0.05 to 0.95. The page was rewritten around the fact that the evidence deletes one answer and the priors set the split among the rest.