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In this paper, we discuss an extension of the Split Hamiltonian Monte Carlo (Split HMC) method for Gaussian process model (GPM). This method is based on splitting the Hamiltonian in a way that allows much of the movement around the state…
This paper deals the implementation of \emph{homotopy perturbation transform method} (HPTM) for numerical computation of initial valued autonomous system of time-fractional partial differential equations (TFPDEs) with proportional delay,…
We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…
Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme…
Recently non-reversible samplers based on simulating piecewise deterministic Markov processes (PDMPs) have shown potential for efficient sampling in Bayesian inference problems. However, there remains a lack of guidance on how to best…
In this paper we present an application of the use of autocopulas for modelling financial time series showing serial dependencies that are not necessarily linear. The approach presented here is semi-parametric in that it is characterized by…
A simple data-aided scheme for sampling clock synchronisation in reduced-guard-interval coherent optical orthogonal frequency division multiplexing (RGI-CO-OFDM) systems is proposed. In the proposed scheme, the sampling clock offset (SCO)…
The performances of a new data processing technique, namely the Empirical Mode Decomposition, are evaluated on a fully developed turbulent velocity signal perturbed by a numerical forcing which mimics a long-period flapping. First, we…
Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior,…
Decomposition, statically dividing a program into multiple units, is a common programming technique for realizing parallelism and refining programs. The decomposition of a sequential program into components is tedious, due to the…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
Analyzing multivariate time series data is important to predict future events and changes of complex systems in finance, manufacturing, and administrative decisions. The expressiveness power of Gaussian Process (GP) regression methods has…
We propose a setup for fractionally cointegrated time series which is formulated in terms of latent integrated and short-memory components. It accommodates nonstationary processes with different fractional orders and cointegration of…
In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…
Compositional minimisation can be an effective technique to reduce the state space explosion problem. This technique considers a parallel composition of several processes. In its simplest form, each sequential process is replaced by an…
We propose a time-adaptive, high-order compact finite difference scheme for option pricing in a family of stochastic volatility models. We employ a semi-discrete high-order compact finite difference method for the spatial discretisation,…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
We present the Causal Gaussian Process Convolution Model (CGPCM), a doubly nonparametric model for causal, spectrally complex dynamical phenomena. The CGPCM is a generative model in which white noise is passed through a causal,…
We propose a new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging, which is investigated along a general framework that we present with shape theory. This model consists of two components, one…
The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not…