Manuscript Psy04-A@1 · Psy04-A-v1.tex · section · d5800e2a

The classical factorization

The admitted delayed-query experiment › The classical factorization · lines 313–339

Psy04-A@1#eq:classicalfactor

Under Assumption ass:boundary, the binary response law has the form

p (b ∣ x, j) = \int μ (d λ) m = 1 \sum^{K} a_{λ} (m ∣ x) d_{λ} (b ∣ m, j) .

The kernels are arbitrary stochastic kernels.

A $K$ -state delay with kernel $D_{λ} (m^{'} ∣ m)$ is absorbed into

a_{λ}^{del} (m^{'} ∣ x) = m \sum D_{λ} (m^{'} ∣ m) a_{λ} (m ∣ x) .

More complicated delay dynamics are admitted whenever their complete decoder-accessible outcome still satisfies (eq:classicalfactor). An uncounted input-dependent delay record does not satisfy the stated boundary.

Displayed formulas in this passage

Psy04-A@1#eq:classicalfactor · line 317
$p (b ∣ x, j) = \int μ (d λ) m = 1 \sum^{K} a_{λ} (m ∣ x) d_{λ} (b ∣ m, j) .$
unlabeled · line 330
$a_{λ}^{del} (m^{'} ∣ x) = m \sum D_{λ} (m^{'} ∣ m) a_{λ} (m ∣ x) .$

Nearby in this section

remark: Remark: Probabilities are not extra observable memory