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Bernstein - von Mises theorems for statistical inverse problems II: Compound Poisson processes
[article]
2019
arXiv
pre-print
We study nonparametric Bayesian statistical inference for the parameters governing a pure jump process of the form Y_t = ∑_k=1^N(t) Z_k, t > 0, where N(t) is a standard Poisson process of intensity λ, and Z_k are drawn i.i.d. from jump measure μ. A high-dimensional wavelet series prior for the Lévy measure ν = λμ is devised and the posterior distribution arises from observing discrete samples Y_Δ, Y_2Δ, ..., Y_nΔ at fixed observation distance Δ, giving rise to a nonlinear inverse inference
arXiv:1709.07752v2
fatcat:piy6sfcaxngunjpt46ip54fsbm