= Survival selection in a heterogeneous population
{title2=$w_i(t)=\frac{p_iS_i(t)}{\sum_jp_jS_j(t)}$}
= Survival selection
{synonym}
In a population mixture with initial component probabilities $p_i$, conditioning on survival to time $t$ changes them to the displayed probabilities by <Bayes theorem>. Components with larger <survivor functions> receive greater relative weight among survivors. The population <hazard function> is the weighted mean of the component hazards with these time-dependent weights. This selection can change the population hazard even when all component hazards are constant, as shown by the <hazard derivative for a mixture of exponential distributions>.
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