arXiv subjects

Tsz-Kit Jeffrey Kwan

Publications and source records attributed to Tsz-Kit Jeffrey Kwan.

3 recordsLinked to original sources

arXiv2026

Neural Networks for Parameter Estimation of the Discretely Observed Hawkes Process

When the sample path of a Hawkes process is observed discretely, such that only the total event counts in disjoint time intervals are known, the likelihood function becomes intractable. To overcome the challenge of likelihood-based inference in this setting, we propose to use a likelihood-free approach that uses simulated data to train a fully connected neural network (NN) to estimate the parameters of the Hawkes process from a summary statistic of the count data. A naive imputation estimate of the parameters forms the basis for our summary statistic, which is fast to generate and requires minimal expert knowledge to design. The resulting NN estimator is comparable to the best extant approximate likelihood estimators in terms of mean-squared error but requires significantly less computational time. We implement NN quantile estimation for fast uncertainty quantification. The proposed estimation procedure is applied to weekly count data for two infectious diseases, with a time-varying background rate used to capture seasonal fluctuations in infection risk.

stat.ME↗

arXiv2026

Parametric inference for the discretely observed multivariate Hawkes process using particle Markov Chain Monte Carlo

The multivariate Hawkes process (MHP) is a useful statistical model for analysing multidimensional event time sequences that exhibit self-excitation and cross-excitation. When the MHP is monitored discretely, only the total number of events for each dimension in disjoint time intervals is observed. The likelihood function relative to this data is intractable, so traditional inference techniques are not available. To address this, we design an unbiased estimate of the intractable likelihood function using sequential Monte Carlo (SMC) based on a representation of the unobserved event times as latent variables in a state-space model. The unbiasedness of the SMC estimate allows for its use in place of the true likelihood in a Metropolis-Hastings algorithm, enabling the construction of a Markov Chain Monte Carlo sample from the posterior distribution over the parameters of the MHP. Using simulated data, we assess the performance of our method and demonstrate that it outperforms existing approaches in terms of mean squared error and computational efficiency. Terrorist activity in Afghanistan and Pakistan from 2018 to 2021 is analysed based on daily count data to examine the dynamics of terrorism in the region.

stat.ME↗

arXiv2024

Likelihood inference of the non-stationary Hawkes process with non-exponential kernel

The Hawkes process is a popular point process model for event sequences that exhibit temporal clustering. The intensity process of a Hawkes process consists of two components, the baseline intensity and the accumulated excitation effect due to past events, with the latter specified via an excitation kernel. The classical Hawkes process assumes a constant baseline intensity and an exponential excitation kernel. This results in an intensity process that is Markovian, a fact that has been used extensively to establish the strong consistency and asymtpotic normality of maximum likelihood estimators or similar. However, these assumptions can be overly restrictive and unrealistic for modelling the many applications which require the baseline intensity to vary with time and the excitation kernel to have non-exponential decay. However, asymptotic properties of maximum likelihood inference for the parameters specifying the baseline intensity and the self-exciting decay under this setup are substantially more difficult since the resulting intensity process is non-Markovian. To overcome this challenge, we develop an approximation procedure to show the intensity process is asymptotically ergodic in a suitably defined sense. This allows for the identification of an ergodic limit to the likelihood function and its derivatives, as required for obtaining large sample inference under minimal regularity conditions.

math.ST↗