Determine Next State in a First-Order Markov Chain

Given the previous state and a random number `u_rand`, this function returns the next state in a 3-state first-order Markov chain. The transition probabilities are state- and index-specific.

Usage

markov_next_state(state_prev, u_rand, idx, p00, p01, p10, p11, p20, p21)

Arguments

state_prev

Integer. The current (previous) state (0, 1, or 2).

u_rand

Numeric. A random number in [0, 1] used to sample the next state.

idx

Integer. Index for selecting transition probabilities (e.g., time step or spatial location).

p00

Numeric vector. Probability of transition from state 0 to 0.

p01

Numeric vector. Probability of transition from state 0 to 1.

p10

Numeric vector. Probability of transition from state 1 to 0.

p11

Numeric vector. Probability of transition from state 1 to 1.

p20

Numeric vector. Probability of transition from state 2 to 0.

p21

Numeric vector. Probability of transition from state 2 to 1.

Value

Integer. The next state (0, 1, or 2).

Details

States are typically defined as: - 0: Dry - 1: Wet - 2: Extreme

The transition is determined using cumulative probabilities for the transitions to state 0 and 1. Any remaining probability is assigned to state 2.

Examples

set.seed(123)
u_rand <- runif(1)
markov_next_state(
  state_prev = 1,
  u_rand = u_rand,
  idx = 5,
  p00 = rep(0.7, 10),
  p01 = rep(0.2, 10),
  p10 = rep(0.3, 10),
  p11 = rep(0.4, 10),
  p20 = rep(0.1, 10),
  p21 = rep(0.3, 10)
)
#> [1] 0