Mortality: the oldest decay-prediction discipline
Actuarial science has been formally predicting human lifespan and validating those predictions against real outcomes since the 19th century — making it the most battle-tested field in this survey.
The core idea
Benjamin Gompertz observed in 1825 that human mortality risk rises roughly exponentially with age over the bulk of adult life. William Makeham later added a constant background term to account for age-independent causes of death (accidents, for instance). The resulting Gompertz-Makeham law is still the standard textbook model for the force of mortality in developed-nation populations across the core mortality-risk age range.
The formula
The force of mortality (instantaneous hazard rate) at age x:
where α is an age-dependent scale parameter, β is the exponential aging rate, and λ ≥ 0 is Makeham's age-independent background-mortality term (setting λ = 0 recovers Gompertz's original pure-exponential law, μ(x) = α·e^(βx)). The survival function derived from this hazard is:
with probability density function:
The model is well-approximated for ages roughly 40–90 in low-mortality developed-nation populations. A commonly cited empirical rule of thumb, following from typical fitted values of β (around 0.085 per year), is that mortality risk roughly doubles every 7 to 10 years between ages 30 and 80.
The parameters α, β, and λ are estimated by maximizing the log-likelihood against observed life-table death counts, or via a least-squares fit to log-mortality rates against grouped death counts.
How this field validates its predictions
Actuarial science's answer to "how do you validate a lifetime prediction" is the Actual-to-Expected (A/E) ratio — a backward-looking experience study that tracks a real cohort against the mortality table's predicted death count:
An A/E ratio above 100% means worse-than-predicted mortality (a loss for an insurer that priced against the table); a ratio below 100% means better-than-predicted (favorable) mortality. This is structurally the actuarial equivalent of a backtest. Formal statistical hypothesis tests for whether an observed A/E ratio deviates significantly from 100% trace back to Seligman & Kahn (1980).
No single universal A/E-ratio target is published as a hard pass/fail bar. Actuarial standards of practice — for example, ASOP No. 48, covering life-settlement mortality — instead require minimum data-collection and credibility periods, disclosed methodology for how the base table was selected or modified, and periodic re-validation through updated A/E studies rather than a one-time accuracy claim. Regulatory frameworks additionally require statistical credibility standards: a population must be large enough for its observed A/E ratio to be statistically meaningful before a mortality assumption can be relied on for pricing.