Lossless Bayesian inference in infinite dimension without discretisation or truncation: a case study on Lambda-coalescents
نویسندگان
چکیده
In this talk I will introduce the class of Lambda-coalescents, which are naturally parametrised by infinite dimensional probability measures. I will show that these measures can be consistently inferred from data without discretising or truncating the problem under verifiable conditions on the prior. The method resembles the so-called Likelihood Informed Subspaces approach to Bayesian inverse problems under Gaussian measures, and we expect it to generalis beyond just the Lambda-coalescent setting without difficulty. I will conclude by providing an empirical comparison of noisy and exact pseudo-marginal MCMC algorithms for sampling the resulting posteriors. ∗Speaker sciencesconf.org:montecarlo16:110654
منابع مشابه
The site-frequency spectrum associated with Ξ-coalescents.
We give recursions for the expected site-frequency spectrum associated with so-called Xi-coalescents, that is exchangeable coalescents which admit simultaneous multiple mergers of ancestral lineages. Xi-coalescents arise, for example, in association with population models of skewed offspring distributions with diploidy, recurrent advantageous mutations, or strong bottlenecks. In contrast, the s...
متن کاملBayesian non-parametric inference for $\Lambda$-coalescents: consistency and a parametric method
We investigate Bayesian non-parametric inference for the Λ-measure of Λ-coalescent processes parametrised by probability measures on the unit interval and provide an implementable, provably consistent MCMC inference algorithm. We give verifiable criteria on the prior for posterior consistency when observations form a time series, and prove that any non-trivial prior is inconsistent when all obs...
متن کاملThe site-frequency spectrum associated with Xi-coalescents
1 We give recursions for the expected site-frequency spectrum associated with so2 called Xi-coalescents, that is exchangeable coalescents which admit simultaneous multi3 ple mergers of ancestral lineages. Xi-coalescents arise, for example, in association with 4 population models of skewed o spring distributions with diploidy, recurrent advanta5 geous mutations, or strong bottlenecks. In contras...
متن کاملCost Analysis of Acceptance Sampling Models Using Dynamic Programming and Bayesian Inference Considering Inspection Errors
Acceptance Sampling models have been widely applied in companies for the inspection and testing the raw material as well as the final products. A number of lots of the items are produced in a day in the industries so it may be impossible to inspect/test each item in a lot. The acceptance sampling models only provide the guarantee for the producer and consumer that the items in the lots are acco...
متن کاملUnbiased Bayesian inference for population Markov jump processes via random truncations
We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities, Bayesian inference for such systems remains challenging, as these are continuous time, discrete state systems with potentially infinite state-space. Here we prop...
متن کامل