Simultaneous deconvolution

[pawel-czyz]

I wanted to open the issue on the simultaneous deconvolution model, so I understand it better.

The likelihood model

Is the following model valid?
Let $y(t) = (y_1(t), \dotsc, y_V(t))^T$ be a vector of proportions of variants and $A_{mv} = 1$ when variant $v$ has mutation $m$ and $A_{mv} = 0$ otherwise.
We have $p_m(t) = A y(t) = \sum_v A_{mv} y_v(t) \le 1$, which is the probability of observing mutation $m$.

Now, for some loci we observe some values. We want to use the quasibinomial model.

Handling non-existent values

How do we handle missing values in $x^{(n)}$, i.e., when some mutations are not observed? Do we set them to zero (more realistic if they are not detected due to low abundance) or try to do something like missing at random (assuming that the sequencing failed due to reasons independent on a given mutation and the abundance)?

Modeling the proportions of variants

A loose thought: it could be cool to have the loss being a function of the $y(t)$ time series, so that we can easily substitute the logistic model for something else, e.g., #15.