neg_log_likelihood: Negative log likelihood
In mrc-ide/epihawkes: Hawkes Processes model for outbreak analysis

Description Usage Arguments Value Examples

The log likelihood is written as:

log L = ∑_{i = 1}^{n} log (μ(t_{i}) + ∑_{t_{i} - t_{j}} g(t_{i} - t_{j})) - \int_{0}^{T} μ(t_{i}) dτ - ∑_{i=1}^{n} \int_{t_{i}}^{T} g(τ - t_{i}) dτ

Therefore, the negative log likelihood is - log L.

neg_log_likelihood(
  parameters,
  events,
  delay = 0,
  kernel,
  mu_fn = mu_none,
  mu_diff_fn = mu_diff_none,
  mu_int_fn = mu_int_none,
  print_level = 0
)

`parameters`	Parameters of the Hawkes kernel.
`events`	Vector of event times.
`delay`	Fixed delay
`kernel`	Kernel function for Hawkes Process.
`mu_fn`	Function that returns exogenous part of Hawkes Process.
`mu_diff_fn`	Function that returns differential of exogenous part.
`mu_int_fn`	Function that returns integral of exogenous part.
`print_level`	Level at which logger will print

Returns negative log-likelihood for optimising parameters.

neg_log_likelihood(parameters = list("alpha" = 1, "delta" = 1, "delay" = 0),
    events = c(0, 1.5, 6, 9), kernel = exp_kernel)
neg_log_likelihood(parameters = list("alpha" = 1, "delta" = 1, "A" = 3, "delay" = 0),
    events = c(0, 2, 5, 9), kernel = ray_kernel,
    mu_fn = mu_constant, mu_int_fn = mu_int_constant)