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Yun S Song - One of the best experts on this subject based on the ideXlab platform.
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efficiently inferring the demographic history of many populations with allele count data
Journal of the American Statistical Association, 2020Co-Authors: Jack Kamm, Jonathan Terhorst, Richard Durbin, Yun S SongAbstract:The Sample Frequency spectrum (SFS), or histogram of allele counts, is an important summary statistic in evolutionary biology, and is often used to infer the history of population size changes, mig...
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geometry of the Sample Frequency spectrum and the perils of demographic inference
Genetics, 2018Co-Authors: Zvi Rosen, Anand Bhaskar, Sebastien Roch, Yun S SongAbstract:: The Sample Frequency spectrum (SFS), which describes the distribution of mutant alleles in a Sample of DNA sequences, is a widely used summary statistic in population genetics. The expected SFS has a strong dependence on the historical population demography and this property is exploited by popular statistical methods to infer complex demographic histories from DNA sequence data. Most, if not all, of these inference methods exhibit pathological behavior, however. Specifically, they often display runaway behavior in optimization, where the inferred population sizes and epoch durations can degenerate to zero or diverge to infinity, and show undesirable sensitivity to perturbations in the data. The goal of this article is to provide theoretical insights into why such problems arise. To this end, we characterize the geometry of the expected SFS for piecewise-constant demographies and use our results to show that the aforementioned pathological behavior of popular inference methods is intrinsic to the geometry of the expected SFS. We provide explicit descriptions and visualizations for a toy model, and generalize our intuition to arbitrary Sample sizes using tools from convex and algebraic geometry. We also develop a universal characterization result which shows that the expected SFS of a Sample of size n under an arbitrary population history can be recapitulated by a piecewise-constant demography with only [Formula: see text] epochs, where [Formula: see text] is between [Formula: see text] and [Formula: see text] The set of expected SFS for piecewise-constant demographies with fewer than [Formula: see text] epochs is open and nonconvex, which causes the above phenomena for inference from data.
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efficiently inferring the demographic history of many populations with allele count data
bioRxiv, 2018Co-Authors: Jack Kamm, Jonathan Terhorst, Richard Durbin, Yun S SongAbstract:The Sample Frequency spectrum (SFS), or histogram of allele counts, is an important summary statistic in evolutionary biology, and is often used to infer the history of population size changes, migrations, and other demographic events affecting a set of populations. The expected multipopulation SFS under a given demographic model can be efficiently computed when the populations in the model are related by a tree, scaling to hundreds of populations. Admixture, back-migration, and introgression are common natural processes that violate the assumption of a tree-like population history, however, and until now the expected SFS could be computed for only a handful of populations when the demographic history is not a tree. In this article, we present a new method for efficiently computing the expected SFS and linear functionals of it, for demographies described by general directed acyclic graphs. This method can scale to more populations than previously possible for complex demographic histories including admixture. We apply our method to an 8-population SFS to estimate the timing and strength of a proposed "basal Eurasian" admixture event in human history. We implement and release our method in a new open-source software package momi2.
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geometry of the Sample Frequency spectrum and the perils of demographic inference
bioRxiv, 2017Co-Authors: Zvi Rosen, Anand Bhaskar, Sebastien Roch, Yun S SongAbstract:The Sample Frequency spectrum (SFS), which describes the distribution of mutant alleles in a Sample of DNA sequences, is a widely used summary statistic in population genetics. The expected SFS has a strong dependence on the historical population demography and this property is exploited by popular statistical methods to infer complex demographic histories from DNA sequence data. Most, if not all, of these inference methods exhibit pathological behavior, however. Specifically, they often display runaway behavior in optimization, where the inferred population sizes and epoch durations can degenerate to 0 or diverge to infinity, and show undesirable sensitivity of the inferred demography to perturbations in the data. The goal of this paper is to provide theoretical insights into why such problems arise. To this end, we characterize the geometry of the expected SFS for piecewise-constant demographic histories and use our results to show that the aforementioned pathological behavior of popular inference methods is intrinsic to the geometry of the expected SFS. We provide explicit descriptions and visualizations for a toy model with Sample size 4, and generalize our intuition to arbitrary Sample sizes n using tools from convex and algebraic geometry. We also develop a universal characterization result which shows that the expected SFS of a Sample of size n under an arbitrary population history can be recapitulated by a piecewise-constant demography with only κ n epochs, where κ n is between n/2 and 2n-1. The set of expected SFS for piecewise-constant demographies with fewer than κ n epochs is open and non-convex, which causes the above phenomena for inference from data.
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efficient computation of the joint Sample Frequency spectra for multiple populations
Journal of Computational and Graphical Statistics, 2017Co-Authors: Jack Kamm, Jonathan Terhorst, Yun S SongAbstract:ABSTRACTA wide range of studies in population genetics have employed the Sample Frequency spectrum (SFS), a summary statistic which describes the distribution of mutant alleles at a polymorphic site in a Sample of DNA sequences and provides a highly efficient dimensional reduction of large-scale population genomic variation data. Recently, there has been much interest in analyzing the joint SFS data from multiple populations to infer parameters of complex demographic histories, including variable population sizes, population split times, migration rates, admixture proportions, and so on. SFS-based inference methods require accurate computation of the expected SFS under a given demographic model. Although much methodological progress has been made, existing methods suffer from numerical instability and high computational complexity when multiple populations are involved and the Sample size is large. In this article, we present new analytic formulas and algorithms that enable accurate, efficient computation...
Jonathan Terhorst - One of the best experts on this subject based on the ideXlab platform.
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efficiently inferring the demographic history of many populations with allele count data
Journal of the American Statistical Association, 2020Co-Authors: Jack Kamm, Jonathan Terhorst, Richard Durbin, Yun S SongAbstract:The Sample Frequency spectrum (SFS), or histogram of allele counts, is an important summary statistic in evolutionary biology, and is often used to infer the history of population size changes, mig...
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efficiently inferring the demographic history of many populations with allele count data
bioRxiv, 2018Co-Authors: Jack Kamm, Jonathan Terhorst, Richard Durbin, Yun S SongAbstract:The Sample Frequency spectrum (SFS), or histogram of allele counts, is an important summary statistic in evolutionary biology, and is often used to infer the history of population size changes, migrations, and other demographic events affecting a set of populations. The expected multipopulation SFS under a given demographic model can be efficiently computed when the populations in the model are related by a tree, scaling to hundreds of populations. Admixture, back-migration, and introgression are common natural processes that violate the assumption of a tree-like population history, however, and until now the expected SFS could be computed for only a handful of populations when the demographic history is not a tree. In this article, we present a new method for efficiently computing the expected SFS and linear functionals of it, for demographies described by general directed acyclic graphs. This method can scale to more populations than previously possible for complex demographic histories including admixture. We apply our method to an 8-population SFS to estimate the timing and strength of a proposed "basal Eurasian" admixture event in human history. We implement and release our method in a new open-source software package momi2.
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efficient computation of the joint Sample Frequency spectra for multiple populations
Journal of Computational and Graphical Statistics, 2017Co-Authors: Jack Kamm, Jonathan Terhorst, Yun S SongAbstract:ABSTRACTA wide range of studies in population genetics have employed the Sample Frequency spectrum (SFS), a summary statistic which describes the distribution of mutant alleles at a polymorphic site in a Sample of DNA sequences and provides a highly efficient dimensional reduction of large-scale population genomic variation data. Recently, there has been much interest in analyzing the joint SFS data from multiple populations to infer parameters of complex demographic histories, including variable population sizes, population split times, migration rates, admixture proportions, and so on. SFS-based inference methods require accurate computation of the expected SFS under a given demographic model. Although much methodological progress has been made, existing methods suffer from numerical instability and high computational complexity when multiple populations are involved and the Sample size is large. In this article, we present new analytic formulas and algorithms that enable accurate, efficient computation...
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fundamental limits on the accuracy of demographic inference based on the Sample Frequency spectrum
Proceedings of the National Academy of Sciences of the United States of America, 2015Co-Authors: Jonathan Terhorst, Yun S SongAbstract:The Sample Frequency spectrum (SFS) of DNA sequences from a collection of individuals is a summary statistic that is commonly used for parametric inference in population genetics. Despite the popularity of SFS-based inference methods, little is currently known about the information theoretic limit on the estimation accuracy as a function of Sample size. Here, we show that using the SFS to estimate the size history of a population has a minimax error of at least O(1/log s), where s is the number of independent segregating sites used in the analysis. This rate is exponentially worse than known convergence rates for many classical estimation problems in statistics. Another surprising aspect of our theoretical bound is that it does not depend on the dimension of the SFS, which is related to the number of Sampled individuals. This means that, for a fixed number s of segregating sites considered, using more individuals does not help to reduce the minimax error bound. Our result pertains to populations that have experienced a bottleneck, and we argue that it can be expected to apply to many populations in nature.
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efficient computation of the joint Sample Frequency spectra for multiple populations
arXiv: Probability, 2015Co-Authors: Jack Kamm, Jonathan Terhorst, Yun S SongAbstract:A wide range of studies in population genetics have employed the Sample Frequency spectrum (SFS), a summary statistic which describes the distribution of mutant alleles at a polymorphic site in a Sample of DNA sequences. In particular, recently there has been growing interest in analyzing the joint SFS data from multiple populations to infer parameters of complex demographic histories, including variable population sizes, population split times, migration rates, admixture proportions, and so on. Although much methodological progress has been made, existing SFS-based inference methods suffer from numerical instability and high computational complexity when multiple populations are involved and the Sample size is large. In this paper, we present new analytic formulas and algorithms that enable efficient computation of the expected joint SFS for multiple populations related by a complex demographic model with arbitrary population size histories (including piecewise exponential growth). Our results are implemented in a new software package called momi (MOran Models for Inference). Through an empirical study involving tens of populations, we demonstrate our improvements to numerical stability and computational complexity.
Lars Wanhammar - One of the best experts on this subject based on the ideXlab platform.
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High-Speed Recursive Filter Structures for Interpolation and Decimation with Factors of Two
2014Co-Authors: Hakan Johansson, Lars WanhammarAbstract:Abstract – In this paper we propose high-speed recursive filter structures for interpolation and decimation with factors of two. The structures are composed of identical allpass subfilters and multipliers that interconnect these subfilters. In the simplest case, the overall transfer function corresponds to several half-band IIR filters in cascade. It can also be designed to have a smaller passband ripple than for the cascade approach. Recurrence formulas for computation of the multipliers from the overall transfer function, are given. One major advantage of the new structures over the corresponding single-stage structure is that the maximal Sample Frequency can be substantially increased. Further, the arithmetic complexity can be reduced in comparison with both the single-stage and the straightforward cascade structures. Examples are included which compare the new structure with the two above mentioned structures. I
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high speed low complexity fir filter using multiplier block reduction and polyphase decomposition
International Symposium on Circuits and Systems, 2000Co-Authors: Marcos Martinezpeiro, Lars WanhammarAbstract:In this paper we discuss the design and implementation of a highspeed FIR filter for both interpolation and decimation of the Sample Frequency. Several FIR filter structures are compared and various schemes for simplifying the implementation of the multiplications are evaluated. Carry-save adders with carryoverflow correction are used in the implementation. The results in terms of chip area and power consumption are compared using a standard 0.8 pm 3.3 V CMOS process.
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high speed recursive filter structures composed of identical all pass subfilters for interpolation decimation and qmf banks with perfect magnitude reconstruction
IEEE Transactions on Circuits and Systems Ii: Analog and Digital Signal Processing, 1999Co-Authors: Hakan Johansson, Lars WanhammarAbstract:High-speed recursive filter structures for interpolation and decimation with factors of two, and quadrature mirror filter (QMF) banks with perfect magnitude reconstruction, are proposed. The structures are composed of identical all-pass subfilters that are interconnected via extra multipliers. For the case of interpolation and decimation filters, the overall transfer function corresponds in the simplest case to several half-band infinite-impulse response (IIR) filters in cascade. To achieve a smaller passband ripple than for a cascade design, a design procedure that has been used earlier for single-rate filters is used. In this approach, the design is split into designs of a prototype finite-impulse response (FIR) filter and a half-band IIR filter. For the case of QMF banks, the design is again separated into designs of a prototype FIR filter and a half-band IIR filter. One major advantage of the proposed filter structures over the corresponding conventional (half-band filter) structures is that the required coefficient word length for the all-pass filters is substantially reduced, implying that the maximal Sample Frequency can he substantially increased for a given VLSI technology. Further, for interpolation and decimation, the arithmetic complexity may be reduced in comparison with both the conventional structures and straightforward cascade structures. Simple recurrence formulas for computation of the interconnecting multipliers, given the overall transfer function, are derived. Several examples are included which compare the proposed structures with the corresponding conventional and straightforward cascade structures.
Giorgio Bonmassar - One of the best experts on this subject based on the ideXlab platform.
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dual energy pulses for electrical impedance spectroscopy with the stochastic gabor function
International Conference of the IEEE Engineering in Medicine and Biology Society, 2012Co-Authors: Giorgio Bonmassar, Maria Ida Iacono, Michael H LevAbstract:This paper introduces the stochastic Gabor function (SGF), an excitation waveform that can be used to design optimal excitation pulses for Electrical Impedance Spectroscopy (EIS) of the brain. The SGF is a Gaussian function modulated by uniformly distributed noise; it has wide Frequency spectrum representation regardless of the stimuli pulse length. The SGF was studied in the time-Frequency domain. As shown by Frequency concentration measurements, the SGF is least compact in the Sample Frequency phase plane. Numerical results obtained by using a realistic human head model indicate that the SGF may allow for both shallow and deeper tissue penetration than is currently obtainable with conventional stimulus paradigms, potentially facilitating tissue subtraction assessment of parenchymal dielectric changes in Frequency. This could be of value in advancing EIS of stroke and hemorrhage.
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The Stochastic Gabor Function Enhances Bandwidth In Finite-Difference-Time Domain $S$ -Parameter Estimation
IEEE Transactions on Microwave Theory and Techniques, 2007Co-Authors: Giorgio BonmassarAbstract:This paper introduces the stochastic Gabor function, an excitation waveform that can be used for finite-difference time-domain S-parameter estimation. The stochastic Gabor function is a Gaussian function modulated by uniformly distributed noise; it has wide Frequency spectrum representation regardless of the stimuli pulse length. The stochastic Gabor function was studied in the time-Frequency domain and was compared to Gaussian and Gabor stimuli functions with the same length. As shown by Frequency concentration measurements, the stochastic Gabor function is least compact in the Sample Frequency phase plane. Numerical results obtained by using a multilayer stripline indicate that the stochastic Gabor function provides convergence and stability similar to those provided by the Gabor and Gaussian functions, but produces a much wider Frequency band response when used as a pointwise hard voltage source stimulus
Jack Kamm - One of the best experts on this subject based on the ideXlab platform.
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efficiently inferring the demographic history of many populations with allele count data
Journal of the American Statistical Association, 2020Co-Authors: Jack Kamm, Jonathan Terhorst, Richard Durbin, Yun S SongAbstract:The Sample Frequency spectrum (SFS), or histogram of allele counts, is an important summary statistic in evolutionary biology, and is often used to infer the history of population size changes, mig...
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efficiently inferring the demographic history of many populations with allele count data
bioRxiv, 2018Co-Authors: Jack Kamm, Jonathan Terhorst, Richard Durbin, Yun S SongAbstract:The Sample Frequency spectrum (SFS), or histogram of allele counts, is an important summary statistic in evolutionary biology, and is often used to infer the history of population size changes, migrations, and other demographic events affecting a set of populations. The expected multipopulation SFS under a given demographic model can be efficiently computed when the populations in the model are related by a tree, scaling to hundreds of populations. Admixture, back-migration, and introgression are common natural processes that violate the assumption of a tree-like population history, however, and until now the expected SFS could be computed for only a handful of populations when the demographic history is not a tree. In this article, we present a new method for efficiently computing the expected SFS and linear functionals of it, for demographies described by general directed acyclic graphs. This method can scale to more populations than previously possible for complex demographic histories including admixture. We apply our method to an 8-population SFS to estimate the timing and strength of a proposed "basal Eurasian" admixture event in human history. We implement and release our method in a new open-source software package momi2.
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efficient computation of the joint Sample Frequency spectra for multiple populations
Journal of Computational and Graphical Statistics, 2017Co-Authors: Jack Kamm, Jonathan Terhorst, Yun S SongAbstract:ABSTRACTA wide range of studies in population genetics have employed the Sample Frequency spectrum (SFS), a summary statistic which describes the distribution of mutant alleles at a polymorphic site in a Sample of DNA sequences and provides a highly efficient dimensional reduction of large-scale population genomic variation data. Recently, there has been much interest in analyzing the joint SFS data from multiple populations to infer parameters of complex demographic histories, including variable population sizes, population split times, migration rates, admixture proportions, and so on. SFS-based inference methods require accurate computation of the expected SFS under a given demographic model. Although much methodological progress has been made, existing methods suffer from numerical instability and high computational complexity when multiple populations are involved and the Sample size is large. In this article, we present new analytic formulas and algorithms that enable accurate, efficient computation...
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efficient computation of the joint Sample Frequency spectra for multiple populations
arXiv: Probability, 2015Co-Authors: Jack Kamm, Jonathan Terhorst, Yun S SongAbstract:A wide range of studies in population genetics have employed the Sample Frequency spectrum (SFS), a summary statistic which describes the distribution of mutant alleles at a polymorphic site in a Sample of DNA sequences. In particular, recently there has been growing interest in analyzing the joint SFS data from multiple populations to infer parameters of complex demographic histories, including variable population sizes, population split times, migration rates, admixture proportions, and so on. Although much methodological progress has been made, existing SFS-based inference methods suffer from numerical instability and high computational complexity when multiple populations are involved and the Sample size is large. In this paper, we present new analytic formulas and algorithms that enable efficient computation of the expected joint SFS for multiple populations related by a complex demographic model with arbitrary population size histories (including piecewise exponential growth). Our results are implemented in a new software package called momi (MOran Models for Inference). Through an empirical study involving tens of populations, we demonstrate our improvements to numerical stability and computational complexity.
