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The compound Poisson process (CPP) is a common mathematical model for describing many phenomena in medicine, reliability theory and risk theory. However, in the case of low-frequency phenomena, we are often unable to collect a sufficiently large database to conduct analysis. In this article, we focused on methods for determining confidence intervals for the rate of the CPP when the sample size is small. Based on the properties of process parameter estimators, we proposed a new method for constructing such intervals and compared it with other known approaches. In numerical simulations, we used synthetic data from several continuous and discrete distributions. The case of CPP, in which rewards came from exponential distribution, was discussed separately. The recommendation of how to use each method to have a more precise confidence interval is given. All simulations were performed in R version 4.2.1. [ABSTRACT FROM AUTHOR]

We study a Markov decision problem in which the state space is the set of finite marked point patterns in the plane, the actions represent thinnings, the reward is proportional to the mark sum which is discounted over time, and the transitions are governed by a birth-death-growth process. We show that thinning points with large marks maximises the discounted total expected reward when births follow a Poisson process and marks grow logistically. Explicit values for the thinning threshold and the discounted total expected reward over finite and infinite horizons are also provided. When the points are required to respect a hard core distance, upper and lower bounds on the discounted total expected reward are derived. [ABSTRACT FROM AUTHOR]

In order to obtain functional limit theorems for heavy-tailed stationary processes arising from dynamical systems, one needs to understand the clustering patterns of the tail observations of the process. These patterns are well described by means of a structure called the pilling process introduced recently in the context of dynamical systems. So far, the pilling process has been computed only for observable functions maximised at a single repelling fixed point. Here, we study richer clustering behaviours by considering correlated maximal sets, in the sense that the observable is maximised in multiple points belonging to the same orbit, and we work out explicit expressions for the pilling process when the dynamics is piecewise linear and expanding (1-dimensional and 2-dimensional). [ABSTRACT FROM AUTHOR]

AbstractThis article studies the properties of Hawkes process with a gamma memory kernel and a shape parameter α∈(0,1]. This process, called rough Hawkes process, is nearly unstable since its intensity diverges to +∞ for a very brief duration when a jump occurs. First, we find conditions that ensure the stability of the process and provide a closed form expression of the expected intensity. Second, we next reformulate the intensity as an infinite dimensional Markov process. Approximating these processes by discretization and then considering the limit leads to the Laplace transform of the point process. This transform depends on the solution of an elegant fractional integro-differential equation. The fractional operator is defined by the gamma kernel and is similar to the left-fractional Riemann-Liouville integral. We provide a simple method for computing the Laplace transform. This is easily invertible by discrete Fourier transform so that the probability density of the process can be recovered. We also propose two methods of simulation. We conclude the article by presenting the log-likelihood of the rough Hawkes process and use it to fit hourly Bitcoin log-returns from 9/2/18 to 9/2/23. [ABSTRACT FROM AUTHOR]

In this article, convolution-type fractional derivatives generated by Dickman subordinator and inverse Dickman subordinator are discussed. The Dickman subordinator and its inverse are generalizations of stable and inverse stable subordinators, respectively. The series representations of densities of the Dickman subordinator and inverse Dickman subordinator are also obtained, which could be helpful for computational purposes. Moreover, the space and time-fractional Poisson-Dickman processes, space-fractional Skellam Dickman process and non-homogenous Poisson-Dickman process are introduced and their main properties are studied. [ABSTRACT FROM AUTHOR]

We consider a finite number of N statistically equal agents, each moving on a finite set of states according to a continuous-time Markov Decision Process (MDP). Transition intensities of the agents and generated rewards depend not only on the state and action of the agent itself, but also on the states of the other agents as well as the chosen action. Interactions like this are typical for a wide range of models in e.g. biology, epidemics, finance, social science and queueing systems among others. The aim is to maximize the expected discounted reward of the system, i.e. the agents have to cooperate as a team. Computationally this is a difficult task when N is large. Thus, we consider the limit for N → ∞. In contrast to other papers we treat this problem from an MDP perspective. This has the advantage that we need less regularity assumptions in order to construct asymptotically optimal strategies than using viscosity solutions of HJB equations. The convergence rate is 1 / N . We show how to apply our results using two examples: a machine replacement problem and a problem from epidemics. We also show that optimal feedback policies from the limiting problem are not necessarily asymptotically optimal. [ABSTRACT FROM AUTHOR]

We study pair correlation functions for planar Coulomb systems in the pushed phase, near a ring-shaped impenetrable wall. We assume coupling constant Γ = 2 and that the number n of particles is large. We find that the correlation functions decay slowly along the edges of the wall, in a narrow interface stretching a distance of order 1/n from the hard edge. At distances much larger than 1 / n , the effect of the hard wall is negligible and pair correlation functions decay very quickly, and in between sits an interpolating interface that we call the “semi-hard edge”. More precisely, we provide asymptotics for the correlation kernel K n (z , w) as n → ∞ in two microscopic regimes (with either | z - w | = O (1 / n) or | z - w | = O (1 / n) ), as well as in three macroscopic regimes (with | z - w | ≍ 1 ). For some of these regimes, the asymptotics involve oscillatory theta functions and weighted Szegő kernels. [ABSTRACT FROM AUTHOR]

The discovery of gas in Groningen in 1959 has been a massive boon to the Dutch economy. From the 1990s onwards, though, gas production has led to induced seismicity. In this paper, we carry out a comprehensive exploratory analysis of the spatio-temporal earthquake catalogue. We develop a non-parametric adaptive kernel smoothing technique to estimate the spatio-temporal hazard map and to interpolate monthly well-based gas production statistics. Second- and higher-order inhomogeneous summary statistics are used to show that the state-of-the-art rate-and-state models for the prediction of seismic hazard fail to capture inter-event interaction in the earthquake catalogue. Based on these findings, we suggest a modified rate-and-state model that also takes into account changes in gas production volumes and uncertainty in the pore pressure field. [ABSTRACT FROM AUTHOR]

We consider Palm distributions arising in a Markov process with time homogeneous transitions which is jointly stationary with multiple point processes. Motivated by a BAR approach studied in the recent paper (Braverman et al. in the BAR approach for multi-class queueing networks with SBP service policies, 2023), we are interested in two problems; when this Markov process inherits the same Markov structure under the Palm distributions, and how the state changes at counting instants of the point processes can be handled to derive stationary equations when there are simultaneous counts and each of them influences the state changes. We affirmatively answer the first problem, and propose a framework for resolving the second problem, which is applicable to a general stationary process, which is not needed to be Markov. We also discuss how those results can be applied in deriving BAR's for the diffusion approximation of queueing models in heavy traffic. In particular, as their new application, the heavy traffic limit of the stationary distribution is derived for a single-server queue with a finite waiting room. [ABSTRACT FROM AUTHOR]

We propose an algorithm for the closed-form recursive computation of joint moments and cumulants of all orders of k-hop counts in the 1D unit disk random graph model with Poisson distributed vertices. Our approach uses decompositions of k-hop counts into multiple Poisson stochastic integrals. As a consequence, using the Stein and cumulant methods we derive Berry-Esseen bounds for the asymptotic convergence of renormalized k-hop path counts to the normal distribution as the density of Poisson vertices tends to infinity. Computer codes for the recursive symbolic computation of moments and cumulants of any orders are provided as an online resource. [ABSTRACT FROM AUTHOR]

Metric-based summary statistics such as mean and covariance have been introduced in neural spike train space. They can properly describe template and variability in spike train data, but are often sensitive to outliers and expensive to compute. Recent studies also examine outlier detection and classification methods on point processes. These tools provide reasonable result, whereas the accuracy remains at a low level in certain cases. In this study, we propose to adopt a well-established notion of statistical depth to the spike train space. This framework can naturally define the median in a set of spike trains, which provides a robust description of the ‘template’ of the observations. It also provides a principled method to identify ‘outliers’ and classify data from different categories. We systematically compare the new median, outlier detection and classification tools with state-of-the-art competing methods. The result shows the median has superior description for template than the mean. Moreover, the proposed outlier detection and classification perform more accurately than previous methods. [ABSTRACT FROM AUTHOR]

The coexistence of multiple phytoplankton species despite their reliance on similar resources is often explained with mean-field models assuming mixed populations. In reality, observations of phytoplankton indicate spatial aggregation at all scales, including at the scale of a few individuals. Local spatial aggregation can hinder competitive exclusion since individuals then interact mostly with other individuals of their own species, rather than competitors from different species. To evaluate how microscale spatial aggregation might explain phytoplankton diversity maintenance, an individual-based, multispecies representation of cells in a hydrodynamic environment is required. We formulate a three-dimensional and multispecies individual-based model of phytoplankton population dynamics at the Kolmogorov scale. The model is studied through both simulations and the derivation of spatial moment equations, in connection with point process theory. The spatial moment equations show a good match between theory and simulations. We parameterized the model based on phytoplankters’ ecological and physical characteristics, for both large and small phytoplankton. Defining a zone of potential interactions as the overlap between nutrient depletion volumes, we show that local species composition—within the range of possible interactions—depends on the size class of phytoplankton. In small phytoplankton, individuals remain in mostly monospecific clusters. Spatial structure therefore favours intra- over inter-specific interactions for small phytoplankton, contributing to coexistence. Large phytoplankton cell neighbourhoods appear more mixed. Although some small-scale self-organizing spatial structure remains and could influence coexistence mechanisms, other factors may need to be explored to explain diversity maintenance in large phytoplankton. [ABSTRACT FROM AUTHOR]

Let T be an n × n truncation of an (n + α) × (n + α) Haar distributed unitary matrix. We consider the disk counting statistics of the eigenvalues of T. We prove that as n → + ∞ with α fixed, the associated moment generating function enjoys asymptotics of the form exp (C 1 n + C 2 + o (1)) , where the constants C 1 and C 2 are given in terms of the incomplete Gamma function. Our proof uses the uniform asymptotics of the incomplete Beta function. [ABSTRACT FROM AUTHOR]

We introduce and study a fractional version of the Skellam process of order k by time-changing it with an independent inverse stable subordinator. We call it the fractional Skellam process of order k (FSPoK). An integral representation for its one-dimensional distributions and their governing system of fractional differential equations are obtained. We derive the probability generating function, mean, variance and covariance of FSPoK which are utilized to establish its long-range dependence property. Later, we consider two time-changed versions of the FSPoK. These are obtained by time-changing the FSPoK by an independent Lévy subordinator and its inverse. Some distributional properties and particular cases are discussed for these time-changed processes. [ABSTRACT FROM AUTHOR]

In this paper, we study the n-player game and the mean field game under the constant relative risk aversion relative performance on terminal wealth, in which the interaction occurs by peer competition. In the model with n agents, the price dynamics of underlying risky assets depend on a common noise and contagious jump risk modeled by a multi-dimensional nonlinear Hawkes process. With a continuum of agents, we formulate the mean field game problem and characterize a deterministic mean field equilibrium in an analytical form under some conditions, allowing us to investigate some impacts of model parameters in the limiting model and discuss some financial implications. Moreover, based on the mean field equilibrium, we construct an approximate Nash equilibrium for the n-player game when n is sufficiently large. The explicit order of the approximation error is also derived. [ABSTRACT FROM AUTHOR]

This article proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.

AbstractThe basketball game is rarely predictable due to the complexity of its scoring process. To deal with the complexity and forecast the game results, we develop a marked mutually exciting point process model for the scoring process. In the model, the dynamic of the scoring intensity is characterized by a mutually exciting point process. A time varying background rate is used in the intensity function to account for the non-homogeneity. The dependence between scoring events is incorporated into the model with two team-specific exponential exciting kernels. The distribution of the points obtained in each scoring event is modeled as a categorical distribution with parameters from a Dirichlet prior. An empirical Bayesian method and an expectation-maximization algorithm are developed to estimate the model parameters. We design a simulation algorithm to do pre-game and in-game predictions. An empirical study is conducted with National Basketball Association games in four seasons. It is showed that the proposed model outperforms the benchmark model both in the win-loss prediction and score prediction. Moreover, our model can obtain positive returns when betting in the point spread market. Besides forecasting, an index called added winning probability is designed based on the model to evaluate the players’ performance. [ABSTRACT FROM AUTHOR]

The times of Brownian local minima, maxima and their union are three distinct examples of local, stationary, dense, random countable sets associated with classical Wiener noise. Being local means, roughly, determined by the local behavior of the sample paths of the Brownian motion, and stationary means invariant relative to the Lévy shifts of the sample paths. We answer to the affirmative Tsirelson's question, whether or not there are any others, and develop some general theory for such sets. An extra ingredient to their structure, that of an honest indexation, leads to a splitting result that is akin to the Wiener–Hopf factorization of the Brownian motion at the minimum (or maximum) and has the latter as a special case. Sets admitting an honest indexation are moreover shown to have the property that no stopping time belongs to them with positive probability. They are also minimal: they do not have any non-empty proper local stationary subsets. Random sets, of the kind studied in this paper, honestly indexed or otherwise, give rise to nonclassical one-dimensional noises, generalizing the noise of splitting. Some properties of these noises and the inter-relations between them are investigated. In particular, subsets are connected to subnoises. [ABSTRACT FROM AUTHOR]

We consider a two-dimensional determinantal point process arising in the random normal matrix model and which is a two-parameter generalization of the complex Ginibre point process. In this paper, we prove that the probability that no points lie on any number of annuli centered at 0 satisfies large n asymptotics of the form exp (C 1 n 2 + C 2 n log n + C 3 n + C 4 n + C 5 log n + C 6 + F n + O (n - 1 12 )) , where n is the number of points of the process. We determine the constants C 1 , ... , C 6 explicitly, as well as the oscillatory term F n which is of order 1. We also allow one annulus to be a disk, and one annulus to be unbounded. For the complex Ginibre point process, we improve on the best known results: (i) when the hole region is a disk, only C 1 , ... , C 4 were previously known, (ii) when the hole region is an unbounded annulus, only C 1 , C 2 , C 3 were previously known, and (iii) when the hole region is a regular annulus in the bulk, only C 1 was previously known. For general values of our parameters, even C 1 is new. A main discovery of this work is that F n is given in terms of the Jacobi theta function. As far as we know this is the first time this function appears in a large gap problem of a two-dimensional point process. [ABSTRACT FROM AUTHOR]

Inspired by issues of formal kinetics in materials science, we consider a class of processes with density with respect to an inhomogeneous finite Poisson point process, which may be regarded as a generalization of the classical Strauss hard-core process. We prove expressions for the intensity measure and the void probabilities, together with upper and lower bounds. A discussion on some special cases of interest, links with literature and a comparison between Matérn I and Strauss hard-core process are also provided. We apply such a special class of point processes in modeling patterns of non-overlapping grains and in the study of the mean volume density of particular birth-and-growth processes. [ABSTRACT FROM AUTHOR]

The Hawkes process models have been recently become a popular tool for modeling and analysis of neural spike trains. In this article, motivated by neuronal spike trains study, we propose a novel multivariate generalized linear Hawkes process model, where covariates are included in the intensity function. We consider the problem of simultaneous variable selection and estimation for the multivariate generalized linear Hawkes process in the high-dimensional regime. Estimation of the intensity function of the high-dimensional point process is considered within a nonparametric framework, applying B-splines and the SCAD penalty for matters of sparsity. We apply the Doob-Kolmogorov inequality and the martingale central limit theory to establish the consistency and asymptotic normality of the resulting estimators. Finally, we illustrate the performance of our proposal through simulation and demonstrate its utility by applying it to the neuron spike train data set. [ABSTRACT FROM AUTHOR]

We study a family of Fredholm determinants associated to deformations of the sine kernel, parametrized by a weight function w. For a specific choice of w, this kernel describes bulk statistics of finite temperature free fermions. We establish a connection between these determinants and a system of integro-differential equations generalizing the fifth Painlevé equation, and we show that they allow us to solve an integrable PDE explicitly for a large class of initial data. [ABSTRACT FROM AUTHOR]

We consider a class of semi-Markov processes (SMP) such that the embedded discrete-time Markov chain may be non-homogeneous. The corresponding augmented processes are represented as semi-martingales using a stochastic integral equation involving a Poisson random measure. The existence and uniqueness of the equation are established. Subsequently, we show that the solution is indeed a SMP with desired transition rate. Finally, we derive the law of the bivariate process obtained from two solutions of the equation having two different initial conditions. [ABSTRACT FROM AUTHOR]

We derive quantitative bounds in the Wasserstein distance for the approximation of stochastic integrals with respect to Hawkes processes by a normally distributed random variable. In the case of deterministic and nonnegative integrands, our estimates involve only the third moment of the integrand in addition to a variance term using a squared norm of the integrand. As a consequence, we are able to observe a "third moment phenomenon" in which the vanishing of the first cumulant can lead to faster convergence rates. Our results are also applied to compound Hawkes processes, and improve on the current literature where estimates may not converge to zero in large time or have been obtained only for specific kernels such as the exponential or Erlang kernels. [ABSTRACT FROM AUTHOR]

This article introduces a new class of diffusive processes with rough mutually exciting jumps for modeling financial asset returns. The novel feature is that the memory of positive and negative jump processes is defined by the product of a dampening factor and a kernel involved in the construction of the rough Brownian motion. The jump processes are nearly unstable because their intensity diverges to + ∞ for a brief duration after a shock. We first infer the stability conditions and explore the features of the dampened rough (DR) kernel, which defines a fractional operator, similar to the Riemann-Liouville integral. We next reformulate intensities as infinite-dimensional Markov processes. Approximating these processes by discretization and then considering the limit allows us to retrieve the Laplace transform of asset log-return. We show that this transform depends on the solution of a particular fractional integro-differential equation. We also define a family of changes of measure that preserves the features of the process under a risk-neutral measure. We next develop an econometric estimation procedure based on the peak over threshold (POT) method. To illustrate this work, we fit the mutually exciting rough jump-diffusion to time series of Bitcoin log-returns and compare the goodness of fit to its non-rough equivalent. Finally, we analyze the influence of roughness on option prices. [ABSTRACT FROM AUTHOR]

In this paper, we provide relations among the following properties: the tail triviality of a probability measure μ on the configuration space Υ ; the finiteness of a suitable L 2 -transportation-type distance d ¯ Υ ; the irreducibility of local μ -symmetric Dirichlet forms on Υ . As an application, we obtain the ergodicity (i.e., the convergence to the equilibrium) of interacting infinite diffusions having logarithmic interaction and arising from determinantal/permanental point processes including sine 2 , Airy 2 , Bessel α , 2 ( α ≥ 1 ), and Ginibre point processes. In particular, the case of the unlabelled Dyson Brownian motion is covered. For the proof, the number rigidity of point processes in the sense of Ghosh–Peres plays a key role. [ABSTRACT FROM AUTHOR]

We study the computation of the zero set of the Bargmann transform of a signal contaminated with complex white noise, or, equivalently, the computation of the zeros of its short-time Fourier transform with Gaussian window. We introduce the adaptive minimal grid neighbors algorithm (AMN), a variant of a method that has recently appeared in the signal processing literature, and prove that with high probability it computes the desired zero set. More precisely, given samples of the Bargmann transform of a signal on a finite grid with spacing δ , AMN is shown to compute the desired zero set up to a factor of δ in the Wasserstein error metric, with failure probability O (δ 4 log 2 (1 / δ)) . We also provide numerical tests and comparison with other algorithms. [ABSTRACT FROM AUTHOR]

In the present work, we develop a general spatial stochastic model to describe the formation and repair of radiation-induced DNA damage. The model is described mathematically as a measure-valued particle-based stochastic system and extends in several directions the model developed in Cordoni et al. (Phys Rev E 103:012412, 2021; Int J Radiat Biol 1–16, 2022a; Radiat Res 197:218–232, 2022b). In this new spatial formulation, radiation-induced DNA damage in the cell nucleus can undergo different pathways to either repair or lead to cell inactivation. The main novelty of the work is to rigorously define a spatial model that considers the pairwise interaction of lesions and continuous protracted irradiation. The former is relevant from a biological point of view as clustered lesions are less likely to be repaired, leading to cell inactivation. The latter instead describes the effects of a continuous radiation field on biological tissue. We prove the existence and uniqueness of a solution to the above stochastic systems, characterizing its probabilistic properties. We further couple the model describing the biological system to a set of reaction–diffusion equations with random discontinuity that model the chemical environment. At last, we study the large system limit of the process. The developed model can be applied to different contexts, with radiotherapy and space radioprotection being the most relevant. Further, the biochemical system derived can play a crucial role in understanding an extremely promising novel radiotherapy treatment modality, named in the community FLASH radiotherapy, whose mechanism is today largely unknown. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of computing a median of marked point process data under an edit distance. We formulate this problem as a binary linear program, and propose to solve it to optimality by software. We show results of numerical experiments to demonstrate the effectiveness of the proposed method and its application in earthquake prediction. [ABSTRACT FROM AUTHOR]

In this paper we compute the logarithmic energy of points in the unit interval [-1,1] chosen from different Gegenbauer Determinantal Point Processes. We check that all the different families of Gegenbauer polynomials yield the same asymptotic result to third order, we compute exactly the value for Chebyshev polynomials and we give a closed expression for the minimal possible logarithmic energy. The comparison suggests that DPPs cannot match the value of the minimum beyond the third asymptotic term. [ABSTRACT FROM AUTHOR]

This work focuses on kernel estimation of the pair correlation function (PCF) for inhomogeneous spatial point processes. We propose a bootstrap bandwidth selector based on minimizing the mean integrated squared error (MISE). The variance term is estimated by nonparametric bootstrap, and the bias by a plug-in approach using a pilot estimator of the PCF. Kernel estimators of the PCF also require a pilot estimator of the first-order intensity. We test the performance of the bandwidth selector and the role of the pilot intensity estimator in a simulation study. The bootstrap bandwidth selector is competitive with cross-validation procedures, but the contribution of the bandwidth parameter to the goodness-of-fit of the kernel PCF estimator is minor in comparison with that of the pilot intensity function. The data-based kernel intensity estimator leads to biased kernel PCF estimators, while both kernel and parametric covariate-based intensities provide accurate estimators of the PCF. [ABSTRACT FROM AUTHOR]

We show that there is no cyclically monotone stationary matching of two independent Poisson processes in dimension d = 2 . The proof combines the harmonic approximation result from Goldman et al. (Commun. Pure Appl. Math. 74:2483–2560, 2021) with local asymptotics for the two-dimensional matching problem for which we give a new self-contained proof using martingale arguments. [ABSTRACT FROM AUTHOR]

In this article, we introduce fractional Poisson fields of order k in n-dimensional Euclidean space of positive real valued vectors. We also work on time-fractional Poisson process of order k, space-fractional Poisson processes of order k and a tempered version of time-space fractional Poisson processes of order k. We discuss generalized fractional Poisson processes of order k in terms of Bernstein functions. These processes are defined in terms of fractional compound Poisson processes. The time-fractional Poisson process of order k naturally generalizes the Poisson process and the Poisson process of order k to a heavy-tailed waiting-times counting process. The space-fractional Poisson process of order k allows on average an infinite number of arrivals in any interval. We derive the marginal probabilities governing difference–differential equations of the introduced processes. We also provide the Watanabe martingale characterization for some time-changed Poisson processes. [ABSTRACT FROM AUTHOR]

In this paper we study an important global regulation mechanism of transcription of biological cells using specific macro-molecules, 6S RNAs. The functional property of 6S RNAs is of blocking the transcription of RNAs when the environment of the cell is not favorable. We investigate the efficiency of this mechanism with a scaling analysis of a stochastic model. The evolution equations of our model are driven by the law of mass action and the total number of polymerases is used as a scaling parameter. Two regimes are analyzed: exponential phase when the environment of the cell is favorable to its growth, and the stationary phase when resources are scarce. In both regimes, by defining properly occupation measures of the model, we prove an averaging principle for the associated multi-dimensional Markov process on a convenient timescale, as well as convergence results for “fast” variables of the system. An analytical expression of the asymptotic fraction of sequestrated polymerases in stationary phase is in particular obtained. The consequences of these results are discussed. [ABSTRACT FROM AUTHOR]

We prove that quadratic pair interactions for functions defined on planar Poisson clouds and taking into account pairs of sites of distance up to a certain (large-enough) threshold can be almost surely approximated by the multiple of the Dirichlet energy by a deterministic constant. This is achieved by scaling the Poisson cloud and the corresponding energies and computing a compact discrete-to-continuum limit. In order to avoid the effect of exceptional regions of the Poisson cloud, with an accumulation of sites or with ‘disconnected’ sites, a suitable ‘coarse-grained’ notion of convergence of functions defined on scaled Poisson clouds must be given. [ABSTRACT FROM AUTHOR]

Insurance loss distributions are characterized by a high frequency of small claim amounts and a lower, but not insignificant, occurrence of large claim amounts. Composite models, which link two probability distributions, one for the 'body' and the other for the 'tail' of the loss distribution, have emerged in the actuarial literature to take this specificity into account. The parameters of these models summarize the distribution of the losses. One of them corresponds to the breaking point between small and large claim amounts. The composite models are usually fitted using maximum likelihood estimation. A Bayesian approach is considered in this work. Sequential Monte Carlo samplers are used to sample from the posterior distribution and compute the posterior model evidence to both fit and compare the competing models. The method is validated via a simulation study and illustrated on an insurance loss dataset. [ABSTRACT FROM AUTHOR]