Characterizes measures preserving compound mixed renewal process properties.
problem Preserving compound mixed renewal process properties under different probability measures.
method Characterization of progressively equivalent probability measures.
result Any compound mixed renewal process can be converted into a compound mixed Poisson process through a change of measures.
Study examines ruin probability in insurance with stochastic premium and claim arrivals.
problem Analyzing ruin probability in insurance with dependent premium and claim arrivals.
method Adapted Cramer-Lundberg model for mixed Poisson processes with stochastic dependence.
result Explicit expression for ruin probability derived for exponential claim and premium sizes.
Study of mixed product Poisson structures on Lie group and bialgebra manifolds.
problem Exploring new Poisson structures on product manifolds.
method Introducing and analyzing mixed product Poisson structures on Poisson Lie groups and Lie bialgebras.
result Equivalence to fusion products of quasi-Poisson G-manifolds for quasitriangular Lie bialgebras.
Local Poisson groupoids over mixed product Poisson structures defined and applied.
problem Defining and studying Poisson structures on groupoids.
method Using a local Lagrangian bisection in a double symplectic groupoid to twist a direct product of Poisson groupoids.
result Proving Gu,u is a Poisson groupoid over Ou. Study improves Poisson equation solutions on various manifolds.
problem Improving solutions to Poisson equation on different types of manifolds.
method Established L1 estimates for mixed boundary conditions on manifolds with specific curvature properties. result Generalized existing theorems to broader Riemannian settings.
In this paper we study Backward Stochastic Differential Equations with two reflecting right continuous with left limits obstacles (or barriers) when the noise is given by Brownian motion and a Poisson random measure mutually independent. The jumps of the obstacle processes could be either predictable or inaccessible. W…
A new stochastic version of BPS improves sampling from big datasets.
problem Efficiently sampling Bayesian posteriors in large datasets.
method Stochastic Bouncy Particle Sampler using thinning method of Poisson process.
result The algorithm outperforms other samplers in efficiency and mixing.
Reformulates Fock-Rosly Poisson structure using quasi-triangular r-matrices.
problem Defining Fock-Rosly Poisson structure on moduli spaces.
method Using Lie algebra actions and quasi-triangular r-matrices.
result Shows Fock-Rosly structure as mixed product Poisson structure.
Estimates stationary mass and frequency from non-i.i.d. data.
problem Estimating stationary mass and frequency from non-i.i.d. data.
method Combines plug-in estimator with WingIt modification for exponentially α-mixing processes. result Universal consistency in n for total variation distance estimation. This paper shows that the time t map of the averaged Euler equations, with Dirichlet, Neumann, and mixed boundary conditions is canonical relative to a Lie-Poisson bracket constructed via a non-smooth reduction for the corresponding diffeomorphism groups. It is also shown that the geodesic spray for Neumann and mixed…
New PDMP samplers improve BNN inference with accelerated computation.
problem Inference on Bayesian Neural Networks violates independence and posterior assumptions.
method Piecewise Deterministic Markov Process (PDMP) with adaptive thinning for inhomogenous Poisson Process (IPPs) sampling.
result PDMP samplers accelerate inference in BNNs, improving accuracy and mixing performance.
We construct explicitly a bridge process whose distribution, in its own filtration, is the same as the difference of two independent Poisson processes with the same intensity and its time 1 value satisfies a specific constraint. This construction allows us to show the existence of Glosten-Milgrom equilibrium and its as…
Bayesian Tweedie mixed models are improved with adversarial variational inference.
problem Intractable likelihood function and hierarchical structure of mixed effects.
method Adversarial variational inference with reparameterization and flexible hyper prior.
result Proposed method reduces estimation bias and achieves state-of-the-art predictive performance.
Mixed-precision CA-SGD for generalized linear models on GPUs
problem SGD communication bottleneck
method Mixed-precision CA-SGD
result Matches FP32 SGD loss within 0.5% on various problems
The claim experience of the past is a very important information to calculate the fair price of an insurance contract. In a lot of European countries for instance the prices for motor car insurance depend on the number of claims the driver has reported to the insurance company during the last years. Classically these p…
The paper develops new inequalities for Markov chain sums, linking them to mixing time.
problem Establishing concentration inequalities for Markov chain sums.
method Developed novel concentration inequalities for geometrically ergodic Markov chains, linking bounds to mixing time constants.
result Explicit bounds for additive functionals of Markov chains, linked to Rosenthal inequality constants and mixing properties.
This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson proc…
Study of Batalin-Vilkovisky algebra on Poisson manifolds with diagonalizable modular symmetry.
problem Exploring Batalin-Vilkovisky algebra structures on Poisson manifolds with specific symmetry conditions.
method Analysis of twisted Poincaré duality and mixed complex structure, combined with Kontsevich's deformation quantization and Koszul duality.
result Generalization of Batalin-Vilkovisky algebra structure to Poisson manifolds with diagonalizable modular symmetry.
Holistic GLMs add constraints for better model quality.
problem Improving classical linear regression models.
method Sparsity-inducing, sign-coherence, and linear constraints.
result Holistic GLMs reliably solve GLMs for various responses.
New model distinguishes Poisson processes from self-similar ones.
problem Distinguishing Poisson point processes from self-similar processes.
method Machine learning model based on inhomogeneous, compound Poisson point process.
result The model can distinguish Poisson point processes from self-similar processes.
Method proposed for pricing insurance products covering both foreseeable and unforeseeable risks.
problem Pricing insurance products that include unforeseeable risks.
method Mixed Poisson process with Bayesian setup and linear exponential family distributions.
result Bayesian premiums are more reactive to claim trends than traditional ones.
Exact simulation method for market impact estimation under various execution strategies.
problem Estimating market impact from observed price trajectories under different execution strategies.
method Conditional simulation of point processes under perturbed intensities.
result Exact, event-driven algorithm for reconstructing counterfactual paths.
We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying re…
The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical physics including models for anomalous diffusion. Contrary to the well-known Poiss…
A deep Neyman-Scott process uses Poisson processes for efficient inference in complex point processes.
problem Efficient inference in complex hierarchical point processes.
method Developed an efficient posterior sampling via Markov chain Monte Carlo for likelihood-based inference.
result More hidden Poisson processes improve likelihood fitting and event prediction.
A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infi…
We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of two possibly correlated assets: one liquid and one illiquid. The liquid asset is observed and can be traded continuously, while the illiquid one can be traded only at discrete random times corresponding to the jumps …
Study shows convergence rates for BSDEs approximated by compound Poisson processes.
problem Analyzing convergence rates of BSDEs driven by Lévy processes.
method Approximating Lévy processes by compound Poisson processes and studying BSDEs.
result Optimal convergence rates derived for BSDEs in L2-norm and Wasserstein distance. Developed shrinkage methods for Poisson regression models with experts to handle multicollinearity.
problem Multicollinearity in Poisson regression models with experts.
method Ridge and Liu-type shrinkage methods.
result Shrinkage methods offer more reliable estimates for coefficients in multicollinearity.
The paper provides approximations for pricing Asian options using a mixed fractional Brownian motion with jumps.
problem Pricing Asian options under a mixed fractional Brownian motion with jumps.
method Approximate closed-form solutions for arithmetic Asian options and power options.
result Analytical formulas for pricing arithmetic Asian options and power options are derived.
New method models Poisson intensity using RKHS for high-dimensional data.
problem Tractable nonparametric modeling of inhomogeneous Poisson intensity functions.
method Reproducing Kernel Hilbert Space (RKHS) formulation for intensity functions.
result Optimization of penalized likelihood can be cast as a tractable finite-dimensional problem.
NBFA addresses burstiness in count data using negative binomial likelihood.
problem Limitation of Poisson factorization in capturing burstiness.
method Constructs NBFA under negative binomial likelihood, proposes Gibbs samplers.
result NBFA provides clear advantages over Poisson models in burstiness.
New methods improve estimation of nonhomogeneous Poisson processes from limited data.
problem Estimating nonhomogeneous Poisson processes from limited data.
method Formulated as a learning generalization problem, proposed adaptive and data-driven binning methods.
result Improved estimation of nonhomogeneous Poisson processes with limited data.
The paper creates correlated Poisson processes from self-decomposable laws.
problem Creating non-independent Poisson processes with specific correlations.
method Using copulas and self-decomposable laws to pair exponential renewals.
result Explicit algorithms for applications in finance and queuing theory.
Proposes a model for predicting events from event streams.
problem Predicting events like part replacement and failure in manufacturing and teleservice systems.
method Non-parametric prognostic framework using MGCP modulated Poisson processes.
result MGCP prior facilitates sharing of information and analysis of flexible event patterns.
Study shows Merton model limits to Poisson process with log-normal intensity, improving default portfolio prediction.
problem Improving prediction of default portfolios using complex models.
method Applying Merton model with log-normal intensity function to Poisson process, discussing temporal correlation effects.
result Power decay model provides better generalization for long-term default portfolio data.
The paper introduces a model to measure ASR fairness, addressing key issues.
problem Measuring fairness in ASR systems for different subgroups.
method Mixed-effects Poisson regression to control nuisance factors and handle unobserved heterogeneity.
result The method effectively addresses WER gaps among subgroups and is flexible for practical analyses.
We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-formula optimal strategy describes in particular how one should react to the orders of other trader…
Paper improves fraud detection in imbalanced financial data.
problem Detecting fraud in imbalanced financial datasets.
method Uses time-varying Poisson processes for fraud prediction.
result Method outperforms baseline in imbalanced data.
Study of bandit problem with Poisson decision times and Lévy processes.
problem Continuous-time multi-armed bandit problem with Poisson decision times.
method Gittins index policy applied to spectrally one-sided Lévy processes.
result Gittins index converges to classical Lévy bandit index.
New algorithm improves mixing in Bayesian mixture models.
problem Slow mixing in Bayesian mixture models.
method A new Monte Carlo algorithm for sampling from the marginal posterior of a general integrable mixture.
result The new algorithm achieves excellent mixing times, outperforming standard Gibbs sampling in some cases.
Efficiently infers Poisson process intensity using Gaussian process with sigmoid link.
problem Estimating intensity of inhomogeneous Poisson processes efficiently.
method Variational free-form mean field optimization and sparse Laplace's method.
result Method is one order of magnitude faster than exact inference and competitive with quadratic link function models.
Random geodesics on curved surfaces form a pattern similar to random lines.
problem Understanding the geometry of random paths on curved surfaces.
method Scaling and analysis of tessellations induced by long geodesics.
result The global statistics of tessellations approach those of a Poisson line process.
We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of the time series. The process is composed of consecutive patches of variable length, each patch being described by a station…
We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously, while the illiquid one can only be traded and observed at discrete random times corresponding to the jumps of a Poisson pro…
We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient inference is feasible under this model with an EM algorithm. Moreover, the EM algorithm …
Establishes a microstructural foundation for a rough log-normal volatility model.
problem Developing a robust model for financial volatility under microstructural effects.
method Introduced a sequence of order-driven financial market models with Poisson process arrivals and analyzed their convergence to a log-normal rough volatility model.
result Weak convergence of price-volatility process to a log-normal rough volatility model with established weak error rates.
New method removes bias in Monte Carlo simulations of diffusion processes.
problem Bias in Monte Carlo simulations of diffusion processes.
method Using an auxiliary Poisson process, the method runs unbiased simulations.
result The method converges to the exact value and guarantees strong law of large numbers.