scholarly journals A continuous-index hidden Markov jump process for modeling DNA copy number data

Biostatistics ◽  
2009 ◽  
Vol 10 (4) ◽  
pp. 773-778 ◽  
Author(s):  
S. Stjernqvist ◽  
T. Ryden
Keyword(s):  
Copy Number ◽  
Hidden Markov ◽  
Jump Process ◽  
Copy Number Data ◽  
Dna Copy Number ◽  
Markov Jump ◽  
Markov Jump Process ◽  
Continuous Index

scholarly journals Continuous-index hidden Markov modelling of array CGH copy number data

2007 ◽  
Vol 23 (8) ◽  
pp. 1006-1014 ◽  
Author(s):  
Susann Stjernqvist ◽  
Tobias Rydén ◽  
Martin Sköld ◽  
Johan Staaf
Keyword(s):  
Copy Number ◽  
Array Cgh ◽  
Hidden Markov ◽  
Copy Number Data ◽  
Markov Modelling ◽  
Continuous Index

scholarly journals Model-Integrated Estimation of Normal Tissue Contamination for Cancer SNP Allelic Copy Number Data

2011 ◽  
Vol 10 ◽  
pp. CIN.S6873 ◽  
Author(s):  
Susann Stjernqvist ◽  
Tobias Rydén ◽  
Chris D. Greenman
Keyword(s):  
Copy Number ◽  
Normal Tissue ◽  
Index Structure ◽  
Copy Number Data ◽  
Cancer Data ◽  
Unequally Spaced ◽  
Intensity Measurements ◽  
Tissue Contamination ◽  
Continuous Index ◽  
Allelic Copy Number

SNP allelic copy number data provides intensity measurements for the two different alleles separately. We present a method that estimates the number of copies of each allele at each SNP position, using a continuous-index hidden Markov model. The method is especially suited for cancer data, since it includes the fraction of normal tissue contamination, often present when studying data from cancer tumors, into the model. The continuous-index structure takes into account the distances between the SNPs, and is thereby appropriate also when SNPs are unequally spaced. In a simulation study we show that the method performs favorably compared to previous methods even with as much as 70% normal contamination. We also provide results from applications to clinical data produced using the Affymetrix genome-wide SNP 6.0 platform.

Deterministic limit of the stochastic model of chemical reactions with diffusion

1980 ◽  
Vol 12 (02) ◽  
pp. 367-379 ◽  
Author(s):  
L. Arnold ◽  
M. Theodosopulu
Keyword(s):  
Diffusion Equation ◽  
Stochastic Model ◽  
Chemical Reactions ◽  
Reaction Diffusion ◽  
Jump Process ◽  
Reaction Diffusion Equation ◽  
Markov Jump ◽  
Markov Jump Process ◽  
Deterministic Limit

Conditions are given for which the Markov jump process describing the stochastic model of chemical reactions with diffusion converges to the solution of the corresponding deterministic reaction–diffusion equation.

Characterization of the Output Rate Process for a Markovian Storage Model

1998 ◽  
Vol 35 (1) ◽  
pp. 184-199 ◽  
Author(s):  
Samuli Aalto
Keyword(s):  
Fluid Model ◽  
Jump Process ◽  
Rate Process ◽  
Output Rate ◽  
Markov Jump ◽  
Storage Model ◽  
Markov Jump Process ◽  
Queueing Process ◽  
Level Process

We consider storage models where the input rate and the demand are modulated by a Markov jump process. One particular example from teletraffic theory is a fluid model of a multiplexer loaded by exponential on-off sources. Although the storage level process has been widely studied, little attention has been paid to the output rate process. We will show that, under certain assumptions, there exists another Markov jump process that modulates the output rate. The modulating process is explicitly constructed. It turns out to be a modification of a GI/G/1 queueing process

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