scholarly journals On asymptotic validity of naive inference with an approximate likelihood

Biometrika ◽  
2017 ◽  
Vol 104 (1) ◽  
pp. 153-164 ◽  
Author(s):  
H. E. Ogden
Keyword(s):  
Approximate Likelihood ◽  
Asymptotic Validity

scholarly journals Variational inference using approximate likelihood under the coalescent with recombination

2021 ◽  
pp. gr.273631.120
Author(s):  
Xinhao Liu ◽  
Huw A Ogilvie ◽  
Luay Nakhleh
Keyword(s):  
Simulated Data ◽  
Variational Inference ◽  
Divide And Conquer ◽  
Data Sets ◽  
Transition Rates ◽  
Data Set ◽  
Population Sizes ◽  
Novel Method ◽  
Approximate Likelihood ◽  
Promising Avenue

Coalescent methods are proven and powerful tools for population genetics, phylogenetics, epidemiology, and other fields. A promising avenue for the analysis of large genomic alignments, which are increasingly common, are coalescent hidden Markov model (coalHMM) methods, but these methods have lacked general usability and flexibility. We introduce a novel method for automatically learning a coalHMM and inferring the posterior distributions of evolutionary parameters using black-box variational inference, with the transition rates between local genealogies derived empirically by simulation. This derivation enables our method to work directly with three or four taxa and through a divide-and-conquer approach with more taxa. Using a simulated data set resembling a human-chimp-gorilla scenario, we show that our method has comparable or better accuracy to previous coalHMM methods. Both species divergence times and population sizes were accurately inferred. The method also infers local genealogies and we report on their accuracy. Furthermore, we discuss a potential direction for scaling the method to larger data sets through a divide-and-conquer approach. This accuracy means our method is useful now, and by deriving transition rates by simulation it is flexible enough to enable future implementations of all kinds of population models.

Simple formulae for the stress concentration factor for two- and three-dimensional holes in finite domains

2002 ◽  
Vol 37 (3) ◽  
pp. 259-264 ◽  
Author(s):  
Q. Z Wang
Keyword(s):  
Stress Concentration ◽  
Circular Hole ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Spherical Cavity ◽  
Three Dimensional ◽  
Finite Domain ◽  
Three Dimensional Models ◽  
Finite Domains ◽  
Asymptotic Validity

First, based on an approximate analysis, simple closed-form expressions of the stress concentration factor (SCF) for two- or three-dimensional models with a circular hole or a spherical cavity in a finite domain are derived. Then, an asymptotic method is adopted to improve the accuracy of the derived solutions for an extremely large circular hole or spherical cavity, when the remaining ligament approaches zero. Exact limit SCF values for these two kinds of models were given by Koiter; these values are used for the adjustment of the coefficients in the SCF expressions. Finally, simple SCF formulae for these finite domain problems are obtained, their accuracy is demonstrated to be very good by comparison with the available data from the literature, and the asymptotic validity is guaranteed.

scholarly journals An approximate likelihood perspective on ABC methods

2018 ◽  
Vol 12 (0) ◽  
pp. 66-104 ◽  
Author(s):  
George Karabatsos ◽  
Fabrizio Leisen
Keyword(s):  
Approximate Likelihood ◽  
Abc Methods
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