detect.bayes: Bayesian Stopping Rule for Continuous Data
In daining0905/chgdetn: Sequential Change-Point Detection, Analysis, Simulation

Description Usage Arguments Value Examples

View source: R/bayes.R

Change-point detection for continuous data with unknown post-change distributions using the Bayesian stopping rule.

detect.bayes(GEN, alpha, nulower = NULL, nuupper = NULL,
  score = "hyvarinen", c = 0.5, n = 1000, lenth, thlower = NULL,
  thupper = NULL, GENTH = NULL, ULPTH = NULL, ULP0 = NULL,
  GLP0 = NULL, LLP0 = NULL, ULP1 = NULL, GLP1 = NULL,
  LLP1 = NULL, par0 = NULL, par1 = NULL, lenx = NULL,
  lower0 = NULL, upper0 = NULL, lower1 = NULL, upper1 = NULL)

`GEN`	A function of time that returns an observation.
`alpha`	A numeric parameter in `(0,1)` that controls the probability of false alarm.
`nulower, nuupper`	Optional nonnegative numerics: The earliest and latest time of change-point based on prior belief. The default is `nulower=0` and `nuupper=18` which corresponds to the geometric prior distribution with `p=0.1`.
`score`	An optional character specifying the type of score to be used: The default `"hyvarinen"` or the conventional `"logarithmic"`. Can be abbreviated. Case insensitive.
`c, n`	Optional parameters of the Sequentital Monte Carlo algorithm: ESS threshold `0<c<1` and sample size `n>0`. Default is `c=0.5` and `n=1000`. The resample-move step is triggered whenever the ESS goes below `c*n`.
`lenth`	A positive numeric: The length of the variable of the unknown parameter in the post-change model.
`thlower, thupper`	Optional numeric vectors of length `lenth`: The lower and upper limits of the unknown parameter in the post-change model. The defaults are infinite.
`GENTH`	An optional function that takes a sample size and returns a random sample from the prior distribution of the unknown parameter in the post-change model. Default is standard normal on the unconstrained space. Required if `ULPTH` is specified.
`ULPTH`	An optional function: The log unnormalized probability function of the prior distribution of the unknown parameter in the post-change model. Default is standard normal on the unconstrained space. Required if `GENTH` is specified.
`ULP0, GLP0, LLP0`	Functions of an observation: The log unnormalized probability function, its gradient and its laplacian for the pre-change model. If `score="hyvarinen"`, either {`GLP0,LLP0`} or `ULP0` is required. The former is recommended. In the latter case, {`GLP0,LLP0`} will be computed via `grad` and `laplacian`. If `score="logarithmic"`, only `ULP0` is required.
`ULP1, GLP1, LLP1`	Functions of an observation and a numeric parameter: The log unnormalized probability function, its gradient and its laplacian for the post-change model. If `score="hyvarinen"`, either {`GLP1,LLP1`} or `ULP1` is required. The former is recommended. In the latter case, {`GLP1,LLP1`} will be computed via `grad` and `laplacian`. If `score="logarithmic"`, only `ULP1` is required.
`par0, par1`	Optional numeric parameters for the pre-change (`par0`) and post-change (`par1`) models, except if `score="logarithmic"` that `par1` is a function of the unknown parameter in the post-change model. If `score="hyvarinen"`, the positive tuning parameter with a default of 1. If `score="logarithmic"`, the negative log normalizing constant. If omitted, will be computed via `integrate` (if `lenx=1`) or `hcubature` (if `lenx>1`).
`lenx`	A positive numeric: The length of the variable of an obervation. Optional if `score="hyvarinen"` or if `score="logarithmic"` and `par0,par1` are specified.
`lower0, upper0, lower1, upper1`	Optional numeric vectors of length `lenx`: The lower and upper limits of an observation from the pre-change (`lower0,upper0`) and post-change (`lower1,upper1`) models. The defaults are infinite.

A named numeric vector with components

t A positive numeric: The stopping time.
LER A numeric in (0,1): The low ESS rate, i.e., the proportion of iterations that ESS drops below c*n.
AAR A numeric in (0,1): The average acceptance rate of the Metropolis-Hastings sampling in the move step. NaN if ESS never drops below c*n.

##Change from N(0,1) to 2*N(0,1)+1 at t=15.
##Prior knowledge suggests change occurs between 10 and 25.
##The mean and standard deviation of the post-change normal distribution are unknown.

GEN=function(t){ if(15>=t) rnorm(1) else 2*rnorm(1)+1 }
ULP1=function(x,th) -(x-th[1])^2/2/th[2]^2
GLP1=function(x,th) -(x-th[1])/th[2]^2
LLP1=function(x,th) -1/th[2]^2
ULP0=function(x) ULP1(x,c(0,1))
GLP0=function(x) GLP1(x,c(0,1))
LLP0=function(x) LLP1(x,c(0,1))
par0=log(2*pi)/2
par1=function(th) log(2*pi)/2+log(th[2])

#using hyvarinen score
detect.bayes(GEN=GEN,alpha=0.1,nulower=10,nuupper=25,lenth=2,
thlower=c(-Inf,0),GLP0=GLP0,LLP0=LLP0,GLP1=GLP1,LLP1=LLP1)

#using log score, normalizing constant unknown
detect.bayes(GEN=GEN,alpha=0.1,nulower=10,nuupper=25,lenth=2,
thlower=c(-Inf,0),score="log",ULP0=ULP0,ULP1=ULP1,lenx=1)

#using log score, normalizing constant known
detect.bayes(GEN=GEN,alpha=0.1,nulower=10,nuupper=25,lenth=2,
thlower=c(-Inf,0),score="log",ULP0=ULP0,ULP1=ULP1,par0=par0,par1=par1)