Understanding a Model Configuration

Questions
1

Hi all,

I’m looking through a notebook containing a number of different model types in both PyMC3 and STAN, link here:

I am hoping someone can help me understand a particular section.

In the Hierarchical Model of Parent and Manufacturer section, the PyMC3 model contains a variable as such:

b0 = pm.Normal('b0_mfr', mu=b0_parent[mfr_parent_map], sd=b0_mfr_sd, shape=n_mfr)

What i’m particularly confused about is this: mu=b0_parent[mfr_parent_map], specifically the reference in square brackets.

the b0_parent reference is a normal distribution initiated earlier in the model, which all makes sense to me:

b0_parent = pm.Normal('b0_parent', mu=b0_parent_mn, sd=b0_parent_sd, shape=n_parent)

but I don’t understand how the [mfr_parent_map] reference comes into play. This map is an array/list of label encoded values that map car manufacturers to their parent company.

I peeled the code out and remade the array without encoding to post here:

['fiat', 'fiat', 'aston martin lagonda', 'volkswagen', 'volkswagen',
       'bmw', 'fiat', 'peugeot-citroen', 'peugeot-citroen', 'fiat',
       'fiat', 'ford', 'honda', 'hyundai', 'tata', 'hyundai',
       'volkswagen', 'toyota', 'mazda', 'mclaren', 'daimler-ag', 'bmw',
       'mitsubishi', 'renault-nissan', 'peugeot-citroen', 'volkswagen',
       'renault-nissan', 'bmw', 'volkswagen', 'volkswagen', 'daimler-ag',
       'shanghai-auto', 'subaru', 'suzuki', 'toyota', 'gm', 'volkswagen',
       'geely']

Array is created from the table below.

idx mfr_enc parent_enc cnt
0 abarth fiat 12
1 alfa romeo fiat 10
2 aston martin lagonda aston martin lagonda 6
3 audi volkswagen 339
4 bentley motors volkswagen 18
5 bmw bmw 539
6 chrysler jeep fiat 29
7 citroen peugeot-citroen 93
8 ds peugeot-citroen 28
9 ferrari fiat 2
10 fiat fiat 27
11 ford ford 218
12 honda honda 13
13 hyundai hyundai 39
14 jaguar tata 27
15 kia hyundai 28
16 lamborghini volkswagen 2
17 lexus toyota 5
18 mazda mazda 31
19 mclaren mclaren 11
20 mercedes-benz daimler-ag 315
21 mini bmw 147
22 mitsubishi mitsubishi 4
23 nissan renault-nissan 4
24 peugeot peugeot-citroen 94
25 porsche volkswagen 67
26 renault renault-nissan 12
27 rolls royce bmw 7
28 seat volkswagen 63
29 skoda volkswagen 46
30 smart daimler-ag 5
31 ssangyong shanghai-auto 5
32 subaru subaru 21
33 suzuki suzuki 21
34 toyota toyota 27
35 vauxhall gm 73
36 volkswagen volkswagen 107
37 volvo geely 95

I just can’t understand how it’s being used in the context of this model. Is it basically created a b0 hyperprior for each Parent company as per the shape parameter, then the square bracket reference is accessing the b0_parent mu for the relevant manufacturer?

2

Yes, it’s just extending the prior to have the same shape of the index. You can do the same in numpy, which is called fancy indexing: Fancy Indexing | Python Data Science Handbook