Blackwell-MacQueen predictive rule

Formula: P(z_n = k | z_{1:n-1}) = n_k / (n - 1 + alpha)

Usage

Dpedt(partition, alpha = 1)

Arguments

partition: Block label of each of the n observations seated.
alpha: Concentration, strictly positive.

Value

List with estimate (probability of a new block), probs, p_new, counts, K, log_eppf, expected_K, n, method.

Details

with the remaining alpha/(n - 1 + alpha) going to a new block. The rule is exchangeable: the probability of a partition depends only on the block sizes, through the EPPF alpha^K prod (n_k - 1)! / (alpha)_n, and the expected number of blocks is sum_{i=1..n} alpha/(alpha + i - 1).

References

Blackwell & MacQueen (1973), Ann. Statist. 1(2):353-355; Pitman (2006), Combinatorial Stochastic Processes, Springer, ch. 3.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Dpedt(V)
#> $estimate
#> [1] 0.1111111
#> 
#> $probs
#> [1] 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111
#> [8] 0.1111111
#> 
#> $p_new
#> [1] 0.1111111
#> 
#> $counts
#> [1] 1 1 1 1 1 1 1 1
#> 
#> $K
#> [1] 8
#> 
#> $log_eppf
#> [1] -10.6046
#> 
#> $expected_K
#> [1] 2.717857
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Blackwell-MacQueen predictive rule of the DP"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"