update_s | R Documentation |
This function updates the class weight vector by drawing from its posterior distribution.
update_s(delta, m)
delta |
A numeric for the concentration parameter vector |
m |
The vector of current class frequencies. |
Let m=(m_1,…,m_C) be the frequencies of C classes. Given the class weight (probability) vector s=(s_1,…,s_C), the distribution of m is multinomial and its likelihood is
L(m\mid s) \propto ∏_{i=1}^C s_i^{m_i}.
The conjugate prior p(s) for s is a Dirichlet distribution, which has a density function proportional to
∏_{i=1}^C s_i^{δ_i-1},
where δ = (δ_1,…,δ_C) is the concentration parameter vector. Note that in RprobitB, δ_1=…=δ_C. This restriction is necessary because the class number C can change. The posterior distribution of s is proportional to
p(s) L(m\mid s) \propto ∏_{i=1}^C s_i^{δ_i + m_i - 1},
which in turn is proportional to a Dirichlet distribution with parameters δ+m.
A vector, a draw from the Dirichlet posterior distribution for s
.
### number of classes C <- 4 ### current class sizes m <- sample.int(C) ### concentration parameter for Dirichlet prior (single-valued) delta <- 1 ### updated class weight vector update_s(delta = 1, m = m)
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