
Bayesian Logistic Regression Using Sequential Posterior Simulation 297
vector θ. In the standard setup θ
′
= (θ
′
1
, . . . , θ
′
C
) and
P (Y
t
= c | x
t
, θ) =
exp (θ
′
c
x
t
)
P
C
i=1
exp (θ
′
i
x
t
)
(c = 1, . . . , C; t = 1, . . . , T ) . (14 .13)
There is typically a normalization θ
c
= 0 for some c ∈ {1, 2 , . . . , C}, and there
could be further restrictions on θ, but these details are not important to the
main points of this s e c tion.
We use the specification (14.13) of the multinomial logit model throughout.
The binomial logit model is the specia l case C = 2. Going forward, denote
the observed outcomes y
t
= (y
1
, . . . , y
T
) and the full set of c ovariates X =
[x
1
, .