spread_likelihood: Spread a likelihood vector across time with a chosen temporal pattern

Description

Expands a sectoral likelihood $L$ (length $K$) into a $T \times K$ matrix by applying a temporal weight profile and then row-normalizing to the simplex.

Usage

spread_likelihood(
  L,
  T_periods,
  pattern = c("constant", "recent", "linear", "bell")
)

Value

Numeric matrix $T \times K$; each row sums to 1.

Arguments

L: Numeric vector (length $K$); sectoral likelihood. It is normalized internally to sum to 1 before spreading.
T_periods: Integer; number of time periods $T$.
pattern: Temporal pattern for the weights across time; one of "constant", "recent", "linear", "bell".

Details

Given $L$ and a non-negative time-weight vector $w_t$, the function replicates $L$ across rows and applies $w$ elementwise, then row-normalizes using row_norm1(): $$LT_{t,k} \propto w_t \cdot L_k, \qquad \sum_k LT_{t,k} = 1 \ \forall t.$$

Patterns:

"constant": $w_t = 1$.
"recent": linearly increasing in $t$ (more weight to later periods).
"linear": affine ramp from first to last period.
"bell": symmetric bell-shaped profile centered at $T/2$.

Examples

Run this code

set.seed(1)
K <- 5; T <- 8
L <- runif(K); L <- L / sum(L)
LT <- spread_likelihood(L, T, "recent")
stopifnot(nrow(LT) == T, ncol(LT) == K, all(abs(rowSums(LT) - 1) < 1e-12))