Markov processes for modeling and analyzing a new genetic mapping method

1993 ◽  
Vol 30 (4) ◽  
pp. 766-779 ◽  
Author(s):  
Eleanor Feingold
Keyword(s):  
Markov Chains ◽  
Genetic Mapping ◽  
Stochastic Processes ◽  
Markov Processes ◽  
Mapping Method ◽  
Central Issue ◽  
Boundary Crossing ◽  
Crossing Probabilities

This paper describes a set of stochastic processes that is useful for modeling and analyzing a new genetic mapping method. Some of the processes are Markov chains, and some are best described as functions of Markov chains. The central issue is boundary-crossing probabilities, which correspond to p-values for the existence of genes for particular traits. The methods elaborated by Aldous (1989) provide very accurate approximate p-values, as spot-checked against simulations.

Markov processes for modeling and analyzing a new genetic mapping method

1993 ◽  
Vol 30 (04) ◽  
pp. 766-779 ◽  
Author(s):  
Eleanor Feingold
Keyword(s):  
Markov Chains ◽  
Genetic Mapping ◽  
Stochastic Processes ◽  
Markov Processes ◽  
Mapping Method ◽  
Central Issue ◽  
Boundary Crossing ◽  
Crossing Probabilities

This paper describes a set of stochastic processes that is useful for modeling and analyzing a new genetic mapping method. Some of the processes are Markov chains, and some are best described as functions of Markov chains. The central issue is boundary-crossing probabilities, which correspond to p-values for the existence of genes for particular traits. The methods elaborated by Aldous (1989) provide very accurate approximate p-values, as spot-checked against simulations.

Minimal distributions in a stochastic partial ordering and bounds for Gaussian processes

1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Partial Ordering ◽  
Boundary Crossing ◽  
Conditional Probabilities ◽  
Life Distribution ◽  
Life Distributions ◽  
Bounded Below ◽  
Crossing Probabilities

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.

scholarly journals Fast genetic mapping using insertion-deletion polymorphisms in Caenorhabditis elegans

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ho-Yon Hwang ◽  
Jiou Wang
Keyword(s):  
Caenorhabditis Elegans ◽  
Genetic Mapping ◽  
Whole Genome Sequencing ◽  
Genome Sequencing ◽  
Genetic Material ◽  
Mapping Method ◽  
Forward Genetics ◽  
Whole Genome ◽  
Nucleotide Polymorphisms ◽  
Large Populations

AbstractGenetic mapping is used in forward genetics to narrow the list of candidate mutations and genes corresponding to the mutant phenotype of interest. Even with modern advances in biology such as efficient identification of candidate mutations by whole-genome sequencing, mapping remains critical in pinpointing the responsible mutation. Here we describe a simple, fast, and affordable mapping toolkit that is particularly suitable for mapping in Caenorhabditis elegans. This mapping method uses insertion-deletion polymorphisms or indels that could be easily detected instead of single nucleotide polymorphisms in commonly used Hawaiian CB4856 mapping strain. The materials and methods were optimized so that mapping could be performed using tiny amount of genetic material without growing many large populations of mutants for DNA purification. We performed mapping of previously known and unknown mutations to show strengths and weaknesses of this method and to present examples of completed mapping. For situations where Hawaiian CB4856 is unsuitable, we provide an annotated list of indels as a basis for fast and easy mapping using other wild isolates. Finally, we provide rationale for using this mapping method over other alternatives as a part of a comprehensive strategy also involving whole-genome sequencing and other methods.

Approximations of boundary crossing probabilities for a Brownian motion

1999 ◽  
Vol 36 (4) ◽  
pp. 1019-1030 ◽  
Author(s):  
Alex Novikov ◽  
Volf Frishling ◽  
Nino Kordzakhia
Keyword(s):  
Brownian Motion ◽  
Power Series ◽  
Numerical Integration ◽  
Piecewise Linear ◽  
Boundary Crossing ◽  
Square Root ◽  
Girsanov Transformation ◽  
Piecewise Linear Approximations ◽  
Infinite Power ◽  
Crossing Probabilities

Using the Girsanov transformation we derive estimates for the accuracy of piecewise approximations for one-sided and two-sided boundary crossing probabilities. We demonstrate that piecewise linear approximations can be calculated using repeated numerical integration. As an illustrative example we consider the case of one-sided and two-sided square-root boundaries for which we also present analytical representations in a form of infinite power series.

scholarly journals On an approach to boundary crossing by stochastic processes

2016 ◽  
Vol 126 (12) ◽  
pp. 3843-3853 ◽  
Author(s):  
Mark Brown ◽  
Victor H. de la Peña ◽  
Michael J. Klass ◽  
Tony Sit
Keyword(s):  
Stochastic Processes ◽  
Boundary Crossing

scholarly journals Probability Models for Assessing Effectiveness of Advertising Channels in the Internet Environment

2018 ◽  
pp. 209-215
Keyword(s):  
Graph Theory ◽  
Markov Chains ◽  
Markov Processes ◽  
The Internet ◽  
Probability Models ◽  
Method Of Calculation ◽  
Internet Environment ◽  
The Impact ◽  
Theory Of Graphs ◽  
Selection Of

Nowadays, marketing specialists simultaneously use several channels to attract visitors to websites. There is a difficulty in assessing not only the efficiency and conversion of each channel separately, but also in their interconnection. The problem occurs when users visit a website from several sources and only after that do the key action. To assess the effectiveness and selection of the most optimal channels, different models of attribution are used. The models are reviewed in the article. However, we propose to use multi-channel attribution, which provides an aggregate assessment of multi-channel sequences, taking into account that they are interdependent. The purpose of the paper is to create an attribution model that comprehensively evaluates multi-channel sequences and shows the effect of each channel on the conversion. The presented model of attribution can be based on the theory of graphs or Markov chains. The first method of calculation is more visual, the second (based on Markov chains) allows for work with a large amount of data. As a result, a model of multi-channel attribution was presented, which is based on Markov processes or graph theory. It allows for maximum comprehensive assessing of the impact of each channel on the conversion. On the basis of the two methods, calculations were carried out, confirming the adequacy of the model used for the tasks assigned.

Sign in / Sign up

Export Citation Format

Share Document