Package 'stpphawkes'

Calculate area of polynomial

Description

Calculate area of polynomial

Usage

areapl(poly)

Arguments

poly	- matrix describing polynomial

Value

W - area of polynomial

---

Simulate a homogenous space-time Poisson process

Description

This function simulates a homogenous space-time Poisson process on $W$, defined by polygon

Usage

homog.STPP(
  mu,
  poly,
  t.region,
  xfrac = 0.1,
  yfrac = 0.1,
  remove = FALSE,
  checkpoly = TRUE,
  showplot = FALSE
)

Arguments

mu	- background parameter
poly	- matrix defining polygon ($N$ x $2$)
t.region	- vector of two elements describing time span
xfrac	- x fractional increase of polygon to handle boundary effects (default = .1)
yfrac	- y fractional increase (default = .1)
remove	- remove points outside polygon (default = FALSE)
checkpoly	- check if polygon is proper (default = TRUE)
showplot	- plot points (default = FALSE)

Value

A DataFrame containing $x$,$y$,$t$

Examples

out = homog.STPP(0.5,matrix(c(0,0,1,1,0,1,1,0),ncol=2),c(0,10))

---

Calculate intensity function for temporal Hawkes

Description

Calculate intensity function for temporal Hawkes

Usage

intensity_temporal(mu, alpha, beta, times, evalpt)

Arguments

mu	- background parameter
alpha	- alpha parameter
beta	- beta parameter
times	- history of previous times
evalpt	- point to evaluate

Value

lambda - intensity at evalpt

---

Bayesian Estimation of Spatio-Temporal Hawkes Model Parameters

Description

This function computes the posterior of a spatio-temporal exponential decay Hawkes model using Metropolis-with-in-Gibbs sampling.

Usage

mcmc_stpp(
  data,
  poly,
  t_max = max(data$t),
  t_mis = NULL,
  param_init = NULL,
  mcmc_param = NULL,
  branching = TRUE,
  print = TRUE,
  sp_clip = TRUE
)

Arguments

data	- A DataFrame containing $x$,$y$,$t$
poly	- matrix defining polygon ($N$ x $2$)
t_max	- maximum time value (default = max(times))
t_mis	- vector of two elements describing missing time range (default = NULL)
param_init	- list of parameters of initial guess (default = NULL, will start with MLE)
mcmc_param	- list of mcmc parameters
branching	- using branching structure in estimation (default = TRUE)
print	- print progress (default = TRUE)
sp_clip	- when simulating missing data spatial points, clip spatial region back to observed region (default = TRUE)

Details

The default is to estimate the branching structure. The model will also account to missing data if t_mis is provided.

Value

A DataFrame containing the mcmc samples

---

Bayesian Estimation of Spatio-Temporal Hawkes Model Parameters with non uniform spatial locations

Description

This function computes the posterior of a spatio-temporal exponential decay Hawkes model using Metropolis-with-in-Gibbs sampling.

Usage

mcmc_stpp_nonunif(
  data,
  poly,
  t_max = max(data$t),
  t_mis = NULL,
  param_init = NULL,
  mcmc_param = NULL,
  branching = TRUE,
  print = TRUE,
  sp_clip = TRUE
)

Arguments

data	- A DataFrame containing $x$,$y$,$t$
poly	- matrix defining polygon ($N$ x $2$)
t_max	- maximum time value (default = max(times))
t_mis	- vector of two elements describing missing time range (default = NULL)
param_init	- list of parameters of initial guess (default = NULL, will start with MLE)
mcmc_param	- list of mcmc parameters
branching	- using branching structure in estimation (default = TRUE)
print	- print progress (default = TRUE)
sp_clip	- when simulating missing data spatial points, clip spatial region back to observed region (default = TRUE)

Details

The default is to estimate the branching structure. The model will also account to missing data if t_mis is provided.

Value

A DataFrame containing the mcmc samples

---

Bayesian Estimation of Temporal Hawkes Model Parameters

Description

This function computes the posterior of the parameters of a temporal exponential decay Hawkes model using Metropolis-with-in-Gibbs sampling.

Usage

mcmc_temporal(
  times,
  t_max = max(times),
  t_mis = NULL,
  param_init = NULL,
  mcmc_param = NULL,
  branching = TRUE,
  print = TRUE
)

Arguments

times	- vector of arrival times
t_max	- maximum time value (default = max(times))
t_mis	- mx2 matrix, mth row contains two elements describing the mth missing time range (default = NULL)
param_init	- list of parameters of initial guess (default = NULL, will start with MLE)
mcmc_param	- list of mcmc parameters
branching	- using branching structure in estimation (default = TRUE)
print	- print progress (default = TRUE)

Details

The default is to estimate the branching structure which is much more computationally efficient. The model will also account to missing data if t_mis is provided.

Branching models specify gamma priors for mu, alpha and beta parameters.

Value

A DataFrame containing the mcmc samples

Examples

times = simulate_temporal(.5,.1,.5,c(0,10),numeric()) 
out = mcmc_temporal(times)

---

Bayesian Estimation of Temporal Hawkes Model Parameters with Categorical Marks

Description

This function computes the posterior of the parameters of a temporal exponential decay Hawkes model using Metropolis-with-in-Gibbs sampling.

Usage

mcmc_temporal_catmark(
  times,
  marks,
  t_max = max(times),
  t_mis = NULL,
  param_init = NULL,
  mcmc_param = NULL,
  branching = TRUE,
  print = TRUE
)

Arguments

times	- vector of arrival times
marks	- vector of marks
t_max	- maximum time value (default = max(times))
t_mis	- mx2 matrix, mth row contains two elements describing the mth missing time range (default = NULL)
param_init	- list of parameters of initial guess (default = NULL, will start with MLE)
mcmc_param	- list of mcmc parameters
branching	- using branching structure in estimation (default = TRUE)
print	- print progress (default = TRUE)

Details

The default is to estimate the branching structure which is much more computationally efficient. The model will also account to missing data if t_mis is provided.

Value

A DataFrame containing the mcmc samples

---

Bayesian Estimation of Temporal Hawkes Model Parameters with Categorical Marks

Description

This function computes the posterior of the parameters of a temporal exponential decay Hawkes model using Metropolis-with-in-Gibbs sampling.

Usage

mcmc_temporal_contmark(
  times,
  marks,
  wshape,
  t_max = max(times),
  t_mis = NULL,
  param_init = NULL,
  mcmc_param = NULL,
  branching = TRUE,
  dist = "Weibull",
  print = TRUE
)

Arguments

times	- vector of arrival times
marks	- vector of continuous marks
wshape	- fixed weibull shape parameter
t_max	- maximum time value (default = max(times))
t_mis	- mx2 matrix, mth row contains two elements describing the mth missing time range (default = NULL)
param_init	- list of parameters of initial guess (default = NULL, will start with MLE)
mcmc_param	- list of mcmc parameters
branching	- using branching structure in estimation (default = TRUE)
dist	- distribution for marks string (default = "Weibull")
print	- print progress (default = TRUE)

Details

The default is to estimate the branching structure which is much more computationally efficient. The model will also account to missing data if t_mis is provided.

Value

A DataFrame containing the mcmc samples

---

Point in polygon

Description

Determines if a point is in a polygon or on a polygon boundary

Usage

pip(x, y, poly)

Arguments

x	- vector of x positions
y	- vector of y positions
poly	- matrix defining polygon ($N$ x $2$)

Value

A list containing the x and y coordinates of the points inside the polygon @export

---

Calculate if points are in the polynomial

Description

Calculate if points are in the polynomial

Usage

ptinpoly(x, y, xp, yp, bb)

Arguments

x	- vector of x coordinates
y	- vector of y coordinates
xp	- vector of x coordinates of polynomial
yp	- vector of y coordinates of polynomial
bb	- matrix of bounding box of polynomial

Value

inout - vector of 1 if point is in polynomial and 0 if not

---

Simulate homogenous spatio-temporal hawkes model

Description

Simulate homogenous spatio-temporal hawkes model

Usage

simulate_hawkes_stpp(params, poly, t_region, d, history, seed = -1L)

Arguments

params	- list containing params ($\mu$, $a$, $b$, $\sigma$)
poly	- matrix defining polygon ($N$ x $2$)
t_region	- vector of two elements describing time region (e.g., c(0,10))
d	- generate parents on larger polygon by expanded observed polygon by d (default = R::qnorm(.95, 0, sig, 1, 0))
history	- history of process (e.g., numeric())
seed	- set random number seed (default=-1)

Value

A DataFrame containing $x$,$y$,$t$

---

Simulate inhomogenous spatio-temporal hawkes model

Description

Simulate inhomogenous spatio-temporal hawkes model

Usage

simulate_hawkes_stpp_nonunif(params, poly, t_region, d, history, seed = -1L)

Arguments

params	- list containing params ($\mu$, $a$, $b$, $\sigma$,$\mu x$, $\mu y$, $\sigma x$, $\sigma y$ )
poly	- matrix defining polygon ($N$ x $2$)
t_region	- vector of two elements describing time region (e.g., c(0,10))
d	- generate parents on larger polygon by expanded observed polygon by d (default = R::qnorm(.95, 0, sig, 1, 0))
history	- history of process (e.g., numeric())
seed	- set random number seed (default=-1)

Value

A DataFrame containing $x$,$y$,$t$

---

Simulates a temporal Hawkes process with an exponential correlation function

Description

Simulates a temporal Hawkes process with an exponential correlation function

Usage

simulate_temporal(mu, alpha, beta, tt, times, seed = -1L)

Arguments

mu	- background parameter
alpha	- $\alpha$ parameter
beta	- $\beta$ parameter
tt	- vector of two elements defining time span (e.g., c(0,10))
times	- history of previous times (e.g., numeric())
seed	- value to seed random number generation (default = -1)

Value

arrivals - vector of arrival times

Examples

times = simulate_temporal(.5,.1,.5,c(0,10),numeric())

---

MLE Estimation of Spatio-Temporal Hawkes Model Parameters

Description

Maximum likelihood estimation of the parameters of a spatio-temporal exponential decay Hawkes model.

Usage

stpp.mle(data, poly, t_max = max(data$t), initval = NA, print = TRUE)

Arguments

data	- A DataFrame containing $x$,$y$, and $t$
poly	- a matrix defining the polygon
t_max	- maximum time value (default = max(times))
initval	- vector of two elements describing missing time range (default = NA)
print	- print progress (default = TRUE)

Value

A list containing the parameter values and likelihood value

---

MLE Estimation of Nonuniform Spatio-Temporal Hawkes Model Parameters

Description

Maximum likelihood estimation of the parameters of a spatio-temporal exponential decay Hawkes model.

Usage

stpp.mle.nonunif(data, poly, t_max = max(data$t), initval = NA, print = TRUE)

Arguments

data	- A DataFrame containing $x$,$y$, and $t$
poly	- a matrix defining the polygon
t_max	- maximum time value (default = max(times))
initval	- vector of two elements describing missing time range (default = NA)
print	- print progress (default = TRUE)

Value

A list containing the parameter values and likelihood value

---

Marked Hawkes Process with Missing Data

Description

A library for estimation of spatio-temporal Hawkes process parameters with missing data support

References

J. D. Tucker, L. Shand, and J. R. Lewis, “Handling Missing Data in Self-Exciting Point Process Models,” Spatial Statistics, vol. 29. pp. 160-176, 2019.

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MLE Estimation of Temporal Hawkes Model Parameters with Categorical Marks

Description

Maximum likelihood estimation of the parameters of a temporal exponential decay Hawkes model

Usage

temporal.catmark.mle(t, marks, t_max = max(t), initval = NA, print = TRUE)

Arguments

t	- vector of arrival times
marks	- vector of marks
t_max	- maximum time value (default = max(times))
initval	- initial parameter values for likelihood optimization
print	- print progress (default = TRUE)

Value

A list containing the parameter values and likelihood value

---

MLE Estimation of Temporal Hawkes Model Parameters

Description

Maximum likelihood estimation of the parameters of a temporal exponential decay Hawkes model

Usage

temporal.mle(t, t_max = max(t), initval = NA, print = TRUE)

Arguments

t	- vector of arrival times
t_max	- maximum time value (default = max(times))
initval	- vector of two elements describing missing time range (default = NA)
print	- print progress (default = TRUE)

Value

A list containing the parameter values and likelihood value

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