Related papers: Markovianness and Conditional Independence in Anno…
The aim of this work is to provide a rigorous mathematical analysis of a stochastic concatenation model presented by Sobottka and Hart (2011) which allows approximation of the first-order stochastic structure in bacterial DNA by means of a…
Chargaff's second parity rule for short oligonucleotides states that the frequency of any short nucleotide sequence on a strand is approximately equal to the frequency of its reverse complement on the same strand. Recent studies have shown…
Chargaff's second parity rule holds empirically for most types of DNA that along single strands of DNA the base contents are equal for complimentary bases, A = T, G = C. A Markov chain model is constructed to track the evolution of any…
The partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions. One of these conditions is that the variance is unbounded. A simple combinatorial…
We propose an interacting many-body space-time-discrete Markov chain model, which is composed of an integrable deterministic and reversible cellular automaton (the rule 54 of [Bobenko et al, CMP 158, 127 (1993)]) on a finite one-dimensional…
We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the…
The local Markov condition for a DAG to be an independence map of a probability distribution is well known. For DAGs with latent variables, represented as bi-directed edges in the graph, the local Markov property may invoke exponential…
The evolution in coding DNA sequences brings new flexibility and freedom to the codon words, even as the underlying nucleotides get significantly ordered. These curious contra-rules of gene organisation are observed from the distribution of…
We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this…
A general setting for nested subdivisions of a bounded real set into intervals defining the digits $X_1,X_2,...$ of a random variable $X$ with a probability density function $f$ is considered. Under the weak condition that $f$ is almost…
We present a framework based on conditional entropy and the Dirichlet distribution for classifying chromosomes based on the degree to which they use synonymous codons uniformly or preferentially, that is, whether or not codons that code for…
The stability of iterations of affine linear maps $\Psi_{n}(x)=A_{n}x+B_{n}$, $n=1,2,\ldots$, is studied in the presence of a Markovian environment, more precisely, for the situation when $(A_{n},B_{n})_{n\ge 1}$ is modulated by an ergodic…
We revisit the problem of finding the conditions under which synchronous probabilistic cellular automata indexed by the line $\mathbb{Z}$, or the periodic line $\cyl{n}$, depending on 2 neighbours, admit as invariant distribution the law of…
Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle…
Herein it is shown that in order to study the statistical properties of DNA sequences in bacterial chromosomes it suffices to consider only one half of the chromosome because they are similar to its corresponding complementary sequence in…
The rank ordered distribution of the codon usage frequencies for 123 bacteriae is best fitted by a three parameters function that is the sum of a constant, an exponential and a linear term in the rank n. The parameters depend (two…
We consider testing independence in group-wise selections with some restrictions on combinations of choices. We present models for frequency data of selections for which it is easy to perform conditional tests by Markov chain Monte Carlo…
We propose a general method to study dependent data in a binary tree, where an individual in one generation gives rise to two different offspring, one of type 0 and one of type 1, in the next generation. For any specific characteristic of…
The present work is devoted to describe a set of rules explaining the discriminating versus non-discriminating behavior of the di-basic stages and to characterize the role of each base in determining such a behavior. Bases are analyze as…
The fundamental concepts underlying in Markov networks are the conditional independence and the set of rules called Markov properties that translates conditional independence constraints into graphs. In this article we introduce the concept…