Estimate daily proportions of weekly total

Questions
2

This seems to work:

with pm.Model(check_bounds=False) as model:
    probs = pm.Dirichlet('probs', np.ones(7))
    mu = probs[np.newaxis, :] * weekly[:, np.newaxis]
    pm.Normal('likelihood', mu=mu, sigma=1, observed=data)

I get this as the summary of my trace:

	mean	sd	hdi_3%	hdi_97%	mcse_mean	mcse_sd	ess_bulk	ess_tail	r_hat
probs[0]	0.10	0.003	0.095	0.106	0.0	0.0	3262.0	2966.0	1.0
probs[1]	0.10	0.003	0.095	0.105	0.0	0.0	3314.0	2847.0	1.0
probs[2]	0.20	0.003	0.194	0.205	0.0	0.0	4419.0	2688.0	1.0
probs[3]	0.10	0.003	0.094	0.105	0.0	0.0	3217.0	2735.0	1.0
probs[4]	0.05	0.003	0.044	0.055	0.0	0.0	2237.0	2362.0	1.0
probs[5]	0.05	0.003	0.045	0.055	0.0	0.0	2829.0	2758.0	1.0
probs[6]	0.40	0.003	0.394	0.406	0.0	0.0	3851.0	3777.0	1.0
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