HMMfilterSDE: Estimate states in a scalar stochastic differential equation...

In Uffe-H-Thygesen/SDEtools: Utilities for Stochastic Differential Equations

Estimate states in a scalar stochastic differential equation based on discretization to a HMM

Description

HMMfilterSDE computes the state estimation for a discretely observed stochastic differential equation

Usage

HMMfilterSDE(
  u,
  D,
  xi,
  bc,
  x0dist,
  tvec,
  yvec,
  lfun,
  do.smooth = FALSE,
  N.sample = 0,
  do.Viterbi = FALSE,
  pfun = NULL
)

Arguments

u	function mapping state (numeric scalar) to advective term (numeric scalar)
D	function mapping state (numeric scalar) to diffusivity (numeric scalar)
xi	The numerical grid. Numeric vector of increasing values, giving cell boundaries
bc	String indicating boundary conditions. See details.
x0dist	Prior distribution of the initial state. See details.
tvec	Vector of (increasing) time points where observations are taken
yvec	Vector of observations at each time point
lfun	Likelihood function so that lfun(x,y) gives the likelihood of y given x
do.smooth	Do we want smoothing, or only predictive filtering / estimation?
N.sample	Number of "typical tracks" sampled (defaults to 0)
do.Viterbi	Do we want the most probable state sequence, found with the Viterbi algorithm?
pfun	C.d.f. of observations given states, i.e. pfun(x,y) gives P(Y<=y | X = x). If supplied, pseudo-prediction residuals will be computed

Details

The distribution of the initial condition x0 can be specified in a number of ways: . If x0dist is a function, it is interpreted as the c.d.f. of the initial state . If x0dist is a single number, it is interpreted as a deterministic initial state . If x0dist is a numeric vector of the same length as xi, then it is interpreted as a c.d.f. . If x0dist is a numeric vector with one less element than xi, then it is interpreted as cell probabilities.

Value

A list containing: phi A tabulation of the predicitive probability densities psi A tabulation of the estimated probability densities pi (If do.smooth==TRUE) A tabulation of the smoothed probability densities c A vector containing the normalization constants at each time step loglik The total log-likelihood of the model Xmpt A vector containing the most probabile path (if do.Viterbi==TRUE) U A vector containint the pseudo-prediction residuals (if pfun is supplied)

Author(s)

Uffe Høgsbro Thygesen

Uffe-H-Thygesen/SDEtools documentation built on Jan. 15, 2025, 6:41 p.m.