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halasadi / ancient-structure

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Investigate the affect of drift on the model #6

Closed halasadi closed 9 years ago

halasadi commented 9 years ago

(1) Simulate data under drift to investigate whether our simple model can accommodate drift. For example, let the number of ancestral populations be 3 and simulate drift from the ancestral populations in a TreeMix like way.

(2) Think about incorporating drift by:

X{i,j} ~ Binomial(2, p) where p = \sum{k} q{ik} f{kj} + e{ij}, where e{ij} is the random effect, following e_{ij} ~ N(0, t \sigma^2). t is known.

Furthermore, we can estimate \sigma^2 jointly (on individuals from all time periods).

halasadi commented 9 years ago

It seems like drift doesn't really affect the inference. However, it seems like this model is very susceptible to noise. For example, when the true number of clusters = 2 and we model it so K_known = 2 and K_unknown = 1, then the K_unknown is a large proportion of the plot. Ideally we would like to shrink this proportion, perhaps by adding a LASSO like penalty term? See file:///Users/halasadi/ancient-structure/src/example_sim_drift.html