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Estimating Motifs Under Order Restrictions (2005)

van Zwet, Erik W ; Kechris, Katherina J ; Bickel, Peter J ; [et al.]

Berkeley, Calif. : Berkeley Electronic Press (now: De Gruyter)

Statistical applications in genetics and molecular biology 4.2005, 1, art1

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ISSN: 1544-6115

Source: Berkeley Electronic Press Academic Journals

Topics: Biology

Notes: Transcription factors and many other DNA-binding proteins recognizemore than one specific sequence. Among sequences recognized by a givenDNA-binding protein, different positions exhibit varying degrees ofconservation. The reason is that base pairs that are more extensivelycontacted by the protein tend to be more conserved. This observationcan be used in the discovery of transcription factor bindingsites. Here we present a rigorous means to accomplish this. Inparticular, we constrain the order of the information (entropy) in thecolumns of the position specific weight matrix (PWM) whichcharacterizes the motif being sought. We then show how to compute themaximum likelihood estimate of a PWM under such orderrestrictions. This computation is easily integrated with the EMalgorithm or the Gibbs sampler to enhance performance in the searchfor motifs in unaligned sequences. We demonstrate our method on awell-known data set of binding sites of the transcription factor Crpin E. coli.

Type of Medium: Electronic Resource

URL: http://www.bepress.com/sagmb/vol4/iss1/art1

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Closure of Linear Processes (1997)

Bickel, Peter J. ; Bühlmann, Peter

Springer

Journal of theoretical probability 10 (1997), S. 445-479

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ISSN: 1572-9230

Keywords: AR process ; infinitely divisible law ; MA process ; distinction from nonlinear process

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We consider the sets of moving-average and autoregressive processes and study their closures under the Mallows metric and the total variation convergence on finite dimensional distributions. These closures are unexpectedly large, containing nonergodic processes which are Poisson sums of i.i.d. copies from a stationary process. The presence of these nonergodic Poisson sum processes has immediate implications. In particular, identifiability of the hypothesis of linearity of a process is in question. A discussion of some of these issues for the set of moving-average processes has already been given without proof in Bickel and Bühlmann.(2) We establish here the precise mathematical arguments and present some additional extensions: results about the closure of autoregressive processes and natural sub-sets of moving-average and autoregressive processes which are closed.