Simulates paths of the event probability by composing the exact
transition law over n_steps clock increments: the outcome J is
drawn once per path, and conditional on J the log-odds follow a
Gaussian random walk with drift \(\pm a_i/2\) and variance
\(a_i\) per step, where \(\sum_i a_i = A\). Unconditionally, each
step is Bayes-consistent and \(q_t\) is a martingale.
Arguments
- n_paths
Integer, number of paths.
- n_steps
Integer, number of clock increments per path.
- q
Numeric vector of current event probabilities in \((0,1)\).
- A
Numeric vector of event-clock time (non-negative).
Numeric in \([0, 1)\): share of
Aarriving in jump steps (default 0 = smooth information flow).- n_jumps
Integer, number of jump steps per path (default 1; only used when
jump_share > 0).
Value
A tibble with columns path, step (0..n_steps), t_frac
(fraction of calendar steps elapsed), J, L, q, and is_jump
(TRUE for the jump steps; FALSE for step 0).
Details
With jump_share > 0, information arrives lumpily: a fraction
jump_share of total clock time A is concentrated in n_jumps
randomly placed steps (scheduled sub-events: debates, data releases),
and the rest flows evenly. Every step still follows the exact
Bayes-consistent transition, so all closed-form results continue to
hold; lumpiness only changes when the clock ticks. This is the
testbed for the jump-robust estimator variants of event_clock().
Examples
set.seed(1)
paths <- ec_simulate_path(n_paths = 3, n_steps = 50, q = 0.3, A = 1)
# realized clock of one path is close to A:
sum(diff(subset(paths, path == 1)$L)^2)
#> [1] 0.7973274
# lumpy information: half of A arrives in two jump steps
lumpy <- ec_simulate_path(2, 50, q = 0.3, A = 1,
jump_share = 0.5, n_jumps = 2)