Get probability of parameter given new data

Questions
6

To complete the topic, here is the evolution of P(w_1) and P(w_2) wrt y.

ynew = np.asarray([0.51])

def prob_weights(model_mixed, trace_mixed, ynew):
    complogp = y_obs.distribution._comp_logp(theano.shared(ynew))
    f_complogp = model_mixed.model.fastfn(complogp)
    weight_ynew = []
    for ichain in range(trace_mixed.nchains):
        for point_idx in range(len(trace_mixed)):
            point  = trace_mixed._straces[ichain].point(point_idx)
            point.pop('sigma')
            point.pop('w')
            prob = np.exp(f_complogp(point))
            prob /= prob.sum()
            weight_ynew.append(prob)

    weight_ynew = np.asarray(weight_ynew).squeeze()

    return(weight_ynew.mean(axis=0))

n=1000
min_x = -0.5
max_x = 1.5
delta_x = (max_x - min_x )/n
probability_weights = np.array([[],[],[]])

for i in range(n):
    xx = min_x + i * delta_x
    res = prob_weights(model_mixed, trace_mixed, xx)
    res = np.append(xx, res).reshape(3,1)
    probability_weights = np.concatenate([probability_weights, res], axis=1)
print(probability_weights.shape)
probability_weights = pd.DataFrame(probability_weights.T, columns=['x', 'P(w_1)', 'P(w_2)'])
probability_weights


(3, 1000)
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x P(w_1) P(w_2)
0 -0.500 1.000000e+00 4.424003e-42
1 -0.498 1.000000e+00 5.257151e-42
2 -0.496 1.000000e+00 6.247663e-42
3 -0.494 1.000000e+00 7.425351e-42
4 -0.492 1.000000e+00 8.825689e-42
5 -0.490 1.000000e+00 1.049089e-41
6 -0.488 1.000000e+00 1.247121e-41
7 -0.486 1.000000e+00 1.482645e-41
8 -0.484 1.000000e+00 1.762779e-41
9 -0.482 1.000000e+00 2.095998e-41
10 -0.480 1.000000e+00 2.492392e-41
11 -0.478 1.000000e+00 2.963974e-41
12 -0.476 1.000000e+00 3.525045e-41
13 -0.474 1.000000e+00 4.192638e-41
14 -0.472 1.000000e+00 4.987038e-41
15 -0.470 1.000000e+00 5.932400e-41
16 -0.468 1.000000e+00 7.057496e-41
17 -0.466 1.000000e+00 8.396600e-41
18 -0.464 1.000000e+00 9.990538e-41
19 -0.462 1.000000e+00 1.188795e-40
20 -0.460 1.000000e+00 1.414678e-40
21 -0.458 1.000000e+00 1.683607e-40
22 -0.456 1.000000e+00 2.003811e-40
23 -0.454 1.000000e+00 2.385093e-40
24 -0.452 1.000000e+00 2.839139e-40
25 -0.450 1.000000e+00 3.379875e-40
26 -0.448 1.000000e+00 4.023903e-40
27 -0.446 1.000000e+00 4.791011e-40
28 -0.444 1.000000e+00 5.704790e-40
29 -0.442 1.000000e+00 6.793364e-40
... ... ... ...
970 1.440 2.567641e-38 1.000000e+00
971 1.442 2.194209e-38 1.000000e+00
972 1.444 1.875275e-38 1.000000e+00
973 1.446 1.602860e-38 1.000000e+00
974 1.448 1.370153e-38 1.000000e+00
975 1.450 1.171348e-38 1.000000e+00
976 1.452 1.001487e-38 1.000000e+00
977 1.454 8.563431e-39 1.000000e+00
978 1.456 7.323064e-39 1.000000e+00
979 1.458 6.262970e-39 1.000000e+00
980 1.460 5.356858e-39 1.000000e+00
981 1.462 4.582286e-39 1.000000e+00
982 1.464 3.920093e-39 1.000000e+00
983 1.466 3.353918e-39 1.000000e+00
984 1.468 2.869791e-39 1.000000e+00
985 1.470 2.455782e-39 1.000000e+00
986 1.472 2.101701e-39 1.000000e+00
987 1.474 1.798843e-39 1.000000e+00
988 1.476 1.539775e-39 1.000000e+00
989 1.478 1.318142e-39 1.000000e+00
990 1.480 1.128517e-39 1.000000e+00
991 1.482 9.662622e-40 1.000000e+00
992 1.484 8.274136e-40 1.000000e+00
993 1.486 7.085835e-40 1.000000e+00
994 1.488 6.068759e-40 1.000000e+00
995 1.490 5.198155e-40 1.000000e+00
996 1.492 4.452858e-40 1.000000e+00
997 1.494 3.814773e-40 1.000000e+00
998 1.496 3.268425e-40 1.000000e+00
999 1.498 2.800583e-40 1.000000e+00

1000 rows × 3 columns

probability_weights.set_index('x', inplace=True)
sns.scatterplot(data = probability_weights)

output_13_1

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