Using a per-subject empirical hourly rate prior \(\sim Normal(1198, 200)\) and the somewhat arbitrary word difficulty \(\sim Normal(1000,500)\), along with an accumulation startage \(\sim Uniform(0,12)\) (the same for all subjects), we will sample production scores for 10 words for 10 subjects for both the baseline model (uniform probability of each word occurring) and the CHILDES frequency model. The ages and production scores for the subjects (just their age, really) used in the simulation are shown below.

person age production
129968 21 71
130478 25 148
130637 20 261
130820 18 44
130935 19 18
132591 24 377
132795 20 72
134274 16 127
135044 24 399
135063 25 486

Baseline Model

Do we have our priors defined correctly?

Examine Simulated Production Values

are girl watch (action) wanna/want to deer make towel keys shirt hear ExpectedCDIVocab
0.04 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.06 0.05 31.60
0.06 0.06 0.07 0.06 0.06 0.06 0.06 0.06 0.07 0.07 44.20
0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.05 0.05 29.06
0.03 0.04 0.03 0.04 0.03 0.03 0.03 0.03 0.04 0.04 23.44
0.03 0.04 0.04 0.04 0.03 0.04 0.03 0.04 0.04 0.05 25.79
0.05 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.07 0.07 41.34
0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.05 0.05 29.01
0.02 0.03 0.03 0.03 0.02 0.02 0.02 0.03 0.03 0.03 18.22
0.05 0.06 0.06 0.06 0.06 0.06 0.06 0.05 0.07 0.07 41.32
0.05 0.07 0.07 0.06 0.07 0.06 0.07 0.06 0.07 0.07 44.88

Frequency Model

Do we have our priors defined correctly?

Examine Simulated Production Values

are girl watch (action) wanna/want to deer make towel keys shirt hear ExpectedCDIVocab
0.08 0.20 0.36 0.27 1.00 1.00 1.00 0.41 1 1 430.21
0.08 0.20 0.35 0.28 1.00 1.00 1.00 0.43 1 1 430.96
0.08 0.20 0.36 0.28 1.00 1.00 1.00 0.43 1 1 431.69
0.05 0.12 0.21 0.16 1.00 1.00 0.95 0.25 1 1 389.48
0.07 0.19 0.34 0.25 1.00 1.00 1.00 0.39 1 1 424.14
0.08 0.18 0.33 0.25 1.00 1.00 1.00 0.39 1 1 424.00
0.03 0.08 0.14 0.11 0.96 0.97 0.85 0.16 1 1 360.38
0.03 0.08 0.14 0.11 0.96 0.98 0.85 0.16 1 1 360.74
0.03 0.08 0.14 0.11 0.96 0.97 0.85 0.16 1 1 360.60
0.11 0.28 0.49 0.40 1.00 1.00 1.00 0.57 1 1 465.78