Implements a special kind of Markov chains where each state is a function. This is also known to be an infinite-dimensional Markov chain, or Markov chain in functional space (e.g. Banach space)
add "https://github.com/Clpr/FuncMarkov.jl.git#main"import FuncMarkov as fmv
fs = [
x -> x[1] + x[2],
x -> x[1] - x[2]
]
# test: construct from an AR(1) by Tauchen (1986)
fNames, P = fmv.tauchen(2, 0.9, 0.1, nσ = 0.5) # AR(1)
fNames, P = fmv.tauchen(2, 0.9, 0.1, nσ = 0.5) # log-AR(1)
mc = fmv.FunctionMarkovChain(fs, 2, P, names=fNames)
# test: change the names, functions, and Pr
mc.names .= [0.0, 1.0]
# test: standard manual verbose constructor
P = [0.9 0.1; 0.2 0.8]
mc = fmv.FunctionMarkovChain(fs, 2, P, names = [:f1, :f2])
# test: a human-friendly display
display(mc)
# test: overloaded Base methods
size(mc) # returns (D,K)
mc[1] # returns the first function
mc[:f1] # returns the first function (by name)
mc[:f1](rand(2)) # evaluate the first state function at a random point
# test: overloaded standard library functions
fmv.stationary(mc) # stationary distribution
# NOTE: `mean()` works only if `sum()` and scalar product are defined for the
# function return's type. I expect this package to be used with numerical
# functions which returns numeric values which almost always satisfy the above
# conditions.
import Statistics
Statistics.mean(mc, rand(2), 1) # E{f(x)|k = 1}, the conditional expectation.
Statistics.mean(mc, rand(2), :f1) # index by name
# test: non-scalar returns
fs = [
x -> sin.(x),
x -> cos.(x)
]
P = [0.9 0.1; 0.2 0.8]
mc = fmv.FunctionMarkovChain(fs, 2, P)
Statistics.mean(mc, rand(2), 1) # returns a mean array Use varinfo(FuncMarkov) to see what else functions are exported.
Every exported function or type has self-contained docstrings.
MIT license