57 research outputs found
Efficient Forward Simulation of Fisher-Wright Populations with Stochastic Population Size and Neutral Single Step Mutations in Haplotypes
In both population genetics and forensic genetics it is important to know how
haplotypes are distributed in a population. Simulation of population dynamics
helps facilitating research on the distribution of haplotypes. In forensic
genetics, the haplotypes can for example consist of lineage markers such as
short tandem repeat loci on the Y chromosome (Y-STR). A dominating model for
describing population dynamics is the simple, yet powerful, Fisher-Wright
model. We describe an efficient algorithm for exact forward simulation of exact
Fisher-Wright populations (and not approximative such as the coalescent model).
The efficiency comes from convenient data structures by changing the
traditional view from individuals to haplotypes. The algorithm is implemented
in the open-source R package 'fwsim' and is able to simulate very large
populations. We focus on a haploid model and assume stochastic population size
with flexible growth specification, no selection, a neutral single step
mutation process, and self-reproducing individuals. These assumptions make the
algorithm ideal for studying lineage markers such as Y-STR.Comment: 17 pages, 6 figure
A gentle introduction to the discrete Laplace method for estimating Y-STR haplotype frequencies
Y-STR data simulated under a Fisher-Wright model of evolution with a
single-step mutation model turns out to be well predicted by a method using
discrete Laplace distributions.Comment: 18 pages, 5 figure
Order quantity distributions:Estimating an adequate aggregation horizon
In this paper an investigation into the demand, faced by a company in the form of customer orders, is performed both from an explorative numerical and analytical perspective. The aim of the research is to establish the behavior of customer orders in first-come-first-serve (FCFS) systems and the impact of order quantity variation on the planning environment. A discussion of assumptions regarding demand from various planning and control perspectives underlines that most planning methods are based on the assumption that demand in the form of customer orders are independently identically distributed and stem from symmetrical distributions. To investigate and illustrate the need to aggregate demand to live up to these assumptions, a simple methodological framework to investigate the validity of the assumptions and for analyzing the behavior of orders is developed. The paper also presents an analytical approach to identify the aggregation horizon needed to achieve a stable demand. Furthermore, a case study application of the presented framework is presented and concluded on
sparta: Sparse Tables and their Algebra with a View Towards High Dimensional Graphical Models
A graphical model is a multivariate (potentially very high dimensional)
probabilistic model, which is formed by combining lower dimensional components.
Inference (computation of conditional probabilities) is based on message
passing algorithms that utilize conditional independence structures. In
graphical models for discrete variables with finite state spaces, there is a
fundamental problem in high dimensions: A discrete distribution is represented
by a table of values, and in high dimensions such tables can become
prohibitively large. In inference, such tables must be multiplied which can
lead to even larger tables. The sparta package meets this challenge by
implementing methods that efficiently handles multiplication and
marginalization of sparse tables. The package was written in the R programming
language and is freely available from the Comprehensive R Archive Network
(CRAN). The companion package jti, also on CRAN, was developed to showcase the
potential of sparta in connection to the Junction Tree Algorithm. We show, that
jti is able to handle highly complex graphical models which are otherwise
infeasible due to lack of computer memory, using sparta as a backend for table
operations
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