| Type: | Package |
| Title: | Diagnosis and Visualizations Tools for Temporal Point Processes |
| Version: | 0.1.1 |
| Description: | A suite of diagnostic tools for univariate point processes. This includes tools for simulating and fitting both common and more complex temporal point processes. We also include functions to visualise these point processes and collect existing diagnostic tools of Brown et al. (2002) <doi:10.1162/08997660252741149> and Wu et al. (2021) <doi:10.1002/9781119821588.ch7>, which can be used to assess the fit of a chosen point process model. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.1.1 |
| URL: | https://owenward.github.io/ppdiag/ |
| BugReports: | https://github.com/OwenWard/ppdiag/issues |
| Depends: | R (≥ 3.5) |
| Imports: | graphics, stats |
| Suggests: | testthat (≥ 2.1.0), knitr, rmarkdown, covr |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2021-08-12 13:15:10 UTC; owenw |
| Author: | Sally Sun [aut],
Owen G. Ward 
[aut, cre],
Jing Wu [aut],
Xiaoxi Zhao [aut],
Lihao Xiao [ctb],
Tian Zheng [aut] |
| Maintainer: | Owen G. Ward <owen.ward@columbia.edu> |
| Repository: | CRAN |
| Date/Publication: | 2021-08-12 13:50:02 UTC |
Draw the intensity of Hawkes Process
Description
Draw the intensity of a Hawkes Process
Usage
drawHPIntensity(
hp = NULL,
events,
int_title = "Hawkes Intensity",
start = 0,
end = max(events),
history = NULL,
color = 1,
i = 1,
add = FALSE,
fit = FALSE,
plot_events = TRUE,
verbose = FALSE
)
Arguments
hp |
object parameters for Hawkes process. |
events |
the event times happened in this state |
int_title |
title of the intensity plot |
start |
the start time of current state |
end |
the end time of current state |
history |
the past event times |
color |
specify the default plotting color. |
i |
state number, used only for drawUniMMHPIntensity |
add |
whether to add the hawkes intensity to an existing plot, used for drawUniMMHPIntensity |
fit |
a boolean indicating whether to fit a new HP to events |
plot_events |
indicate whether events will be plotted |
verbose |
whether to output informative messages as running |
Value
no return value, intensity plot of Hawkes process
Examples
set.seed(100)
hp_obj <- pp_hp(lambda0 = 0.5, alpha = 0.45, beta = 0.5)
events <- pp_simulate(hp_obj, start = 0, end = 20)
drawHPIntensity(hp_obj, events)
Draw intensity of homogeneous Poisson process
Description
Draw the intensity for a homogeneous Poisson process
Usage
drawHPPIntensity(
hpp = NULL,
events,
int_title = "Homogeneous Poisson Process",
start = 0,
end = max(events),
color = "red",
plot_events = TRUE,
fit = FALSE,
add = FALSE,
verbose = FALSE
)
Arguments
hpp |
object for homogeneous Poisson process |
events |
event times input |
int_title |
the plot title |
start |
start of events |
end |
end of events |
color |
a specification for the default plotting color. |
plot_events |
a boolean indicating whether input events will be plotted |
fit |
a boolean indicating whether to fit a hpp or use the passed object |
add |
whether to add the hpp intensity to an existing plot |
verbose |
whether to output informative messages as running |
Value
no return value, intensity plot of homogeneous Poisson process
Examples
pois_y <- pp_hpp(lambda = 1)
drawHPPIntensity(pois_y, events = pp_simulate(pois_y, end = 10))
Draw the intensity of the Markov-modulated Hawkes Process(MMHP)
Description
Take a mmhp object and draw its intensity accordingly
Usage
drawUniMMHPIntensity(
mmhp,
simulation,
int_title = "Intensity of MMHP",
leg_location = "topright",
color = 1,
add = FALSE
)
Arguments
mmhp |
a mmhp object including its state, state_time, events, lambda0, lambda1, beta and alpha. |
simulation |
the simulated Markov-modulated Hawkes Process(MMHP) |
int_title |
title of the plot. |
leg_location |
location of legend, if moving needed |
color |
A specification for the default plotting color. |
add |
logical; if TRUE add to an already existing plot; if NA start a new plot taking the defaults for the limits and log-scaling of the x-axis from the previous plot. Taken as FALSE (with a warning if a different value is supplied) if no graphics device is open. |
Value
no return value, intensity plot of Markov-modulated Hawkes process
Examples
Q <- matrix(c(-0.4, 0.4, 0.2, -0.2), ncol = 2, byrow = TRUE)
x <- pp_mmhp(Q,
delta = c(1 / 3, 2 / 3), lambda0 = 0.9, lambda1 = 1.1,
alpha = 0.8, beta = 1.2
)
y <- pp_simulate(x, n = 25)
drawUniMMHPIntensity(x, y)
Draw the intensity of the Markov-modulated Poisson Process(MMPP)
Description
Take a mmpp object and draw its intensity accordingly
Usage
drawUniMMPPIntensity(
mmpp,
simulation,
add = FALSE,
color = 1,
fit = FALSE,
int_title = "Intensity Plot of MMPP"
)
Arguments
mmpp |
a mmpp object including its transition probability matrix, lambda0, delta, and c. |
simulation |
the simulated Markov-modulated Poisson Process(MMPP) |
add |
logical; if TRUE add to an already existing plot; if NA start a new plot taking the defaults for the limits and log-scaling of the x-axis from the previous plot. Taken as FALSE (with a warning if a different value is supplied) if no graphics device is open. |
color |
A specification for the default plotting color. |
fit |
a boolean indicating whether to fit the events provided |
int_title |
title of the plot. |
Value
no return value, intensity plot of Markov-modulated Poisson process
Examples
Q <- matrix(c(-0.4, 0.4, 0.2, -0.2), ncol = 2, byrow = TRUE)
x <- pp_mmpp(Q, delta = c(1 / 3, 2 / 3), lambda0 = 0.9, c = 1.2)
y <- pp_simulate(x, n = 10)
drawUniMMPPIntensity(x, y)
Determine the MLE of Hawkes process numerically
Description
Determine the MLE of Hawkes process numerically
Usage
fithp(events, end = max(events), vec = c(0.1, 0.2, 0.3))
Arguments
events |
event times |
end |
end of observation period starting from 0 (default last event) |
vec |
vector of initial parameter values |
Value
a hp object indicating the maximum likelihood parameter values (lambda0,alpha,beta) for Hawkes process. This is a non-convex problem and a (unique) solution is not guaranteed.
Examples
hp_obj <- pp_hp(lambda0 = 0.1, alpha = 0.45, beta = 0.5)
sims <- pp_simulate(hp_obj, start = 0, n = 10)
fithp(sims)
Fit a homogeneous poisson process to event data
Description
Compute maximum likelihood estimator of the rate of a homogeneous Poisson process for the given events.
Usage
fithpp(events, end = max(events))
Arguments
events |
vector containing the event times. |
end |
end of observation period, starting from 0 (default is last event) |
Value
a hpp object containing the events and the estimated parameter
Examples
pois_y <- pp_hpp(lambda = 1)
events <- pp_simulate(pois_y, end = 10)
fithpp(events)
max intensity of a hawkes process
Description
max intensity of a hawkes process
Usage
hawkes_max_intensity(object, events)
Arguments
object |
hawkes process object containing parameters for Hawkes process. |
events |
events for Hawkes process. |
Value
max of intensity
Draw intensity of fitted point process and QQ-Plot of rescaled events
Description
Draw the intensity and q-q plot for models
Usage
intensityqqplot(object, events, markov_states)
## Default S3 method:
intensityqqplot(object, events, markov_states)
## S3 method for class 'hp'
intensityqqplot(object, events, markov_states = NULL)
## S3 method for class 'hpp'
intensityqqplot(object, events, markov_states = NULL)
## S3 method for class 'mmpp'
intensityqqplot(object, events = markov_states$events, markov_states)
## S3 method for class 'mmhp'
intensityqqplot(object, events = markov_states$events, markov_states)
Arguments
object |
parameters for the models: hp, hpp, and mmhp |
events |
event times |
markov_states |
only for mmhp and mmpp, markov states simulation output |
Value
no return value, intensity and qq-plot in a single plot
Interpolate latent process of MMHP
Description
Interpolate latent process of MMHP
Usage
interpolate_mmhp_latent(params, events, zt)
Arguments
params |
parameters of the MMHP, an MMHP object |
events |
events (not including 0, but assumes start at 0) |
zt |
inferred latent state of events |
Value
list of the states of the Markov process (z.hat), including initial state and the times of the transitions between these times (x.hat).
Examples
Q <- matrix(c(-0.4, 0.4, 0.2, -0.2), ncol = 2, byrow = TRUE)
mmhp_obj <- pp_mmhp(Q,
delta = c(1 / 3, 2 / 3), lambda0 = 0.9, lambda1 = 1.1,
alpha = 0.8, beta = 1.2
)
ppdiag:::interpolate_mmhp_latent(
params = mmhp_obj,
events = c(1, 2, 3, 5), zt = c(2, 1, 1, 2)
)
Estimate the latent state for events of an MMHP
Description
Given a MMHP object and events from that MMHP, infer the most likely state of the Markov Process and each event time, along with the probability of being in the active state.
Usage
mmhp_event_state(
params = list(lambda0, lambda1, alpha, beta, Q),
events,
start = 0
)
Arguments
params |
the parameters of the chosen MMHP |
events |
the event times |
start |
the start of observation |
Value
probability of being in state 1 (active state) at each event, along with most likely state
Examples
Q <- matrix(c(-0.4, 0.4, 0.2, -0.2), ncol = 2, byrow = TRUE)
mmhp_obj <- pp_mmhp(Q,
delta = c(1 / 3, 2 / 3), lambda0 = 0.9,
lambda1 = 1.1,
alpha = 0.8, beta = 1.2
)
## evaluate at some fake event times
ppdiag:::mmhp_event_state(params = mmhp_obj, events = c(1, 2, 3, 5))
Estimate the latent state for events of an MMPP
Description
Given a MMPP object and events from that MMPP, infer the most likely state of the Markov Process at each event time, along with the probability of being in the active state.
Usage
mmpp_event_state(params = list(lambda0, c, Q), events, start = 0)
Arguments
params |
the parameters of the chosen MMPP |
events |
the event times |
start |
the start of observation |
Value
probability of being in state 1 (active state) at each event, along with most likely state
Examples
Q <- matrix(c(-0.4, 0.4, 0.2, -0.2), ncol = 2, byrow = TRUE)
mmpp_obj <- pp_mmpp(Q,
delta = c(1 / 3, 2 / 3), lambda0 = 0.9,
c = 1.1
)
## evaluate at some fake event times
ppdiag:::mmpp_event_state(params = mmpp_obj, events = c(1, 2, 3, 5))
Estimate Latent process of MMPP
Description
Estimate Latent process of MMPP
Usage
mmpp_latent(params = list(lambda0, c, Q), events, zt, start = 0)
Arguments
params |
parameters of the MMPP, an MMPP object |
events |
events (not including 0, but assumes start at 0) |
zt |
inferred latent state of events |
Value
list of the states of the Markov process (z.hat) and the times of the transitions between these times (x.hat).
Examples
Q <- matrix(c(-0.04, 0.04, 0.02, -0.02), ncol = 2, byrow = TRUE)
mmpp_obj <- pp_mmpp(Q, delta = c(1 / 3, 2 / 3), lambda0 = 1, c = 1)
ppdiag:::mmpp_latent(params = mmpp_obj, events = c(1, 2, 3), zt = c(2, 1, 1))
Compute negative log likelihood for point process models
Description
Compute negative log likelihood for point process models with model specified time events or simulated time events
Usage
negloglik(object, events, end)
Arguments
object |
point process object containing the parameters |
events |
vector containing the event times. |
end |
the end time of event times |
Value
a scalar indicating the negative log likelihood
Fit a Hawkes process with exponential kernel to event data
Description
Compute the negative log likelihood parameter values for hawkes process.
Usage
negloglik_hp(vec, events, end = max(events))
Arguments
vec |
vector containing initial values for the object parameters (lambda0,alpha,beta) to be optimized. |
events |
vector containing event times. |
end |
the end time of event times. |
Compute Pearson residuals for point process models
Description
Compute Pearson residuals for point processes with specified parameters and events.
Usage
pearsonresidual(object, events, start, end, steps = 1000)
Arguments
object |
point process model |
events |
vector of event times |
start |
start of observation period (default 0) |
end |
termination time (default final event) |
steps |
number of steps for numeric integration (if needed) |
Value
the Pearson residual
Examples
Q <- matrix(c(-0.4, 0.4, 0.2, -0.2), ncol = 2, byrow = TRUE)
x <- pp_mmhp(Q,
delta = c(1 / 3, 2 / 3), lambda0 = 0.9,
lambda1 = 1.1, alpha = 0.8, beta = 1.2
)
y <- pp_simulate(x, n = 10)
ppdiag:::pearsonresidual.mmhp(x, events = y$events[-1])
Compensators for point processes
Description
Computes the compensator for included point processes
Usage
pp_compensator(object, events)
## Default S3 method:
pp_compensator(object, events)
## S3 method for class 'mmpp'
pp_compensator(object, events)
## S3 method for class 'hp'
pp_compensator(object, events)
## S3 method for class 'mmhp'
pp_compensator(object, events)
## S3 method for class 'hpp'
pp_compensator(object, events)
Arguments
object |
a point process model |
events |
event times, which can have first value as 0 |
Value
compensator vector of rescaled interevent times
Examples
hpp_obj <- pp_hpp(lambda = 1)
events <- pp_simulate(hpp_obj, end = 10)
comp <- pp_compensator(hpp_obj, events)
Summarise diagnostics for point process models
Description
Generate diagnostic tools for different point process models, including quantile-quantile plot, ks plot, raw residual and pearson residual.
Usage
pp_diag(object, events)
## Default S3 method:
pp_diag(object, events)
## S3 method for class 'hp'
pp_diag(object, events)
## S3 method for class 'mmhp'
pp_diag(object, events)
## S3 method for class 'mmpp'
pp_diag(object, events)
## S3 method for class 'hpp'
pp_diag(object, events)
Arguments
object |
a point process model |
events |
event times |
Value
Invisibly returns NULL. Outputs plots and summary of diagnostics to console
Examples
hpp_obj <- pp_hpp(lambda = 1)
events <- pp_simulate(hpp_obj, end = 50)
pp_diag(hpp_obj, events)
Create a Hawkes process object
Description
Create a Hawkes Process with an exponential kernel according to the given parameters: lambda0, alpha, beta and events. If events are missing, then it means that data will be added later(simulated from this process)
Usage
pp_hp(lambda0, alpha, beta, events = NULL)
Arguments
lambda0 |
initial intensity at the start time |
alpha |
jump size in increase of intensity |
beta |
exponential decay of intensity |
events |
vector containing the event times. Note that the first event is at time zero. Alternatively, events could be specified as NULL, meaning that the data will be added later (e.g. simulated). |
Value
hp object
Examples
pp_hp(lambda0 = 0.1, alpha = 0.45, beta = 0.5)
Create a homogeneous Poisson process object
Description
Create a homogeneous Poisson object according to given parameters: lambda, and events. If events are missing, then it means that data will be added later(simulated from this process).
Usage
pp_hpp(lambda, events = NULL)
Arguments
lambda |
rate of the Poisson process |
events |
event times, optional |
Value
hpp object
Examples
pp_hpp(lambda = 1)
KS plot of empirical and theoretical cdf curve of fitted point process
Description
Plot empirical cdf plot for rescaled-inter-event-times and exponential cdf as a reference curve
Usage
pp_ksplot(r, ...)
Arguments
r |
rescaled-inter-event-times |
... |
other arguments for plots |
Value
no return value, KS plot for rescaled-inter-event-times and exponential cdf curve
Create a Markov-modulated Hawkes Process(MMHP) object
Description
Create a Markov-modulated Hawkes Process(MMHP) model according to the given parameters: lambda0, lambda1, alpha, beta, event times and transition probability matrix. If event time events is missing, then it means that data will be added later(e.g. simulated)
Usage
pp_mmhp(lambda0, lambda1, alpha, beta, Q = NULL, delta = NULL, events = NULL)
Arguments
lambda0 |
intensity for homogeneous Poisson process. |
lambda1 |
base intensity for Hawkes process. |
alpha |
jump size of the increase in intensity in the hawkes process |
beta |
exponential decrease of intensity in the hawkes process |
Q |
transition probability matrix. |
delta |
initial state probability. |
events |
vector containing the event times. Note that the first event is at time zero. Alternatively, events could be specified as NULL, meaning that the data will be added later (e.g. simulated). |
Value
mmhp object
Examples
Q <- matrix(c(-0.4, 0.4, 0.2, -0.2), ncol = 2, byrow = TRUE)
pp_mmhp(Q,
delta = c(1 / 3, 2 / 3), lambda0 = 0.9, lambda1 = 1.1,
alpha = 0.8, beta = 1.2
)
Create a Markov-modulated Poisson Process(MMPP) object
Description
Create a Markov-modulated Poisson Process(MMPP) model according to the given parameters: lambda0, c, q1, q2 and event times. If event time tau is missing, then it means that data will be added later(e.g. simulated)
Usage
pp_mmpp(lambda0, c, Q, events = NULL, delta = NULL)
Arguments
lambda0 |
parameters for Poisson process. |
c |
the proportion of intensity 1 over intensity 2 |
Q |
transition probability matrix |
events |
vector containing the event times. Note that the first event is often specified as zero. Alternatively, events could be specified as NULL, meaning that the data will be added later (e.g. simulated). |
delta |
initial state probability. |
Value
mmpp object
Examples
Q <- matrix(c(-0.4, 0.4, 0.2, -0.2), ncol = 2, byrow = TRUE)
pp_mmpp(Q = Q, lambda0 = 1, c = 1.5, delta = c(1 / 3, 2 / 3))
Plot QQ-plot for rescaled-inter-event-times of fitted point process
Description
Generate Quantile-quantile plot for rescaled-inter-event-times, which are independently and identically distributed as exponential random variables with rate 1 under the true point process.
Usage
pp_qqexp(r, ...)
Arguments
r |
rescaled-inter-event-times |
... |
other arguments for plots |
Value
no return value, quantile-quantile plot for rescaled-inter-event-times
Compute raw and pearson residuals for point process models
Description
Compute raw and pearson residuals for point process models
Usage
pp_residual(object, events, start = 0, end = max(events), steps = 1000)
Arguments
object |
point process model containing the parameters |
events |
vector of event times |
start |
start of observation period (default 0) |
end |
end of observation period (default final event) |
steps |
number of steps for numeric integration (if needed) |
Value
the raw and pearson residuals
Examples
Q <- matrix(c(-0.4, 0.4, 0.2, -0.2), ncol = 2, byrow = TRUE)
x <- pp_mmhp(Q,
delta = c(1 / 3, 2 / 3), lambda0 = 0.9,
lambda1 = 1.1, alpha = 0.8, beta = 1.2
)
y <- pp_simulate(x, n = 10)
pp_residual(x, events = y$events)
Simulate events from a temporal point process
Description
Currently available point processes are homogeneous Poisson, Hawkes with exponential kernel, MMHP and MMPP
Usage
pp_simulate(object, start = 0, end = 1, n = NULL, verbose = FALSE)
## Default S3 method:
pp_simulate(object, start = 0, end = 1, n = NULL, verbose = FALSE)
## S3 method for class 'hpp'
pp_simulate(object, start = 0, end = 1, n = NULL, verbose = FALSE)
## S3 method for class 'hp'
pp_simulate(object, start = 0, end = 1, n = NULL, verbose = FALSE)
## S3 method for class 'mmpp'
pp_simulate(object, start = 0, end = 1, n = NULL, verbose = FALSE)
## S3 method for class 'mmhp'
pp_simulate(object, start = 0, end = 1, n = NULL, verbose = FALSE)
Arguments
object |
point process model object of type hpp, hp, mmhp, or mmpp |
start |
start time of events simulated. Not used for Markov modulated models |
end |
end time of events simulated. Not used for Markov modulated models |
n |
number of events simulated. Required for Markov modulated models, optional otherwise |
verbose |
whether to output informative messages as running |
Value
a vector of event times for all models. For Markov modulated models, also returns details on the underlying latent process
Examples
hpp_obj <- pp_hpp(lambda = 1)
s <- pp_simulate(hpp_obj, n = 50)
Compute raw residuals for point process models
Description
Compute raw residuals for for point processes with specified parameters and events.
Usage
rawresidual(object, events, start, end, steps = 1000)
Arguments
object |
point process model containing the parameters |
events |
vector of event times |
start |
start of observation period (default 0) |
end |
end of observation period (default final event) |
steps |
number of steps for numeric integration (if needed) |
Value
the raw residual
Examples
Q <- matrix(c(-0.4, 0.4, 0.2, -0.2), ncol = 2, byrow = TRUE)
x <- pp_mmhp(Q,
delta = c(1 / 3, 2 / 3), lambda0 = 0.9,
lambda1 = 1.1, alpha = 0.8, beta = 1.2
)
y <- pp_simulate(x, n = 10)