Scalable Bayesian inference for self-excitatory stochastic processes applied to big American gunfire data [0.03%]
大型美国枪击事件数据的自激励随机过程的可扩展贝叶斯推理方法研究
Andrew J Holbrook,Charles E Loeffler,Seth R Flaxman et al.
Andrew J Holbrook et al.
The Hawkes process and its extensions effectively model self-excitatory phenomena including earthquakes, viral pandemics, financial transactions, neural spike trains and the spread of memes through social networks. The usefulness of these s...
Santeri Karppinen,Matti Vihola
Santeri Karppinen
Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in st...
Hans Kersting,T J Sullivan,Philipp Hennig
Hans Kersting
A recently introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution x and its first q deriv...
Peter F Craigmile,Debashis Mondal
Peter F Craigmile
Knowledge of the long range dependence (LRD) parameter is critical to studies of self-similar behavior. However, statistical estimation of the LRD parameter becomes difficult when the observed data are masked by short range dependence and o...
Robert Maidstone,Toby Hocking,Guillem Rigaill et al.
Robert Maidstone et al.
Many common approaches to detecting changepoints, for example based on statistical criteria such as penalised likelihood or minimum description length, can be formulated in terms of minimising a cost over segmentations. We focus on a class ...
Multivariate locally stationary 2D wavelet processes with application to colour texture analysis [0.03%]
多重局部平稳2D小波过程及其在颜色纹理分析中的应用
Sarah L Taylor,Idris A Eckley,Matthew A Nunes
Sarah L Taylor
In this article we propose a novel framework for the modelling of non-stationary multivariate lattice processes. Our approach extends the locally stationary wavelet paradigm into the multivariate two-dimensional setting. As such the framewo...
Statistical analysis of differential equations: introducing probability measures on numerical solutions [0.03%]
微分方程的统计分析：在数值解上引入概率测量
Patrick R Conrad,Mark Girolami,Simo Särkkä et al.
Patrick R Conrad et al.
In this paper, we present a formal quantification of uncertainty induced by numerical solutions of ordinary and partial differential equation models. Numerical solutions of differential equations contain inherent uncertainties due to the fi...
Andrej Aderhold,Dirk Husmeier,Marco Grzegorczyk
Andrej Aderhold
Inference of interaction networks represented by systems of differential equations is a challenging problem in many scientific disciplines. In the present article, we follow a semi-mechanistic modelling approach based on gradient matching. ...
High-dimensional regression in practice: an empirical study of finite-sample prediction, variable selection and ranking [0.03%]
高维回归的实证研究：有限样本预测、变量选择和排序
Fan Wang,Sach Mukherjee,Sylvia Richardson et al.
Fan Wang et al.
Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well developed, the relative efficacy of different approaches in finite-sample settin...
Spectral density-based and measure-preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs [0.03%]
基于谱密度与保持测度的ABC算法及其在Hamilton型随机微分方程中的应用
Evelyn Buckwar,Massimiliano Tamborrino,Irene Tubikanec
Evelyn Buckwar
Approximate Bayesian computation (ABC) has become one of the major tools of likelihood-free statistical inference in complex mathematical models. Simultaneously, stochastic differential equations (SDEs) have developed to an established tool...