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A probabilistic query may not be estimable from observed data corrupted by missing values if the data are not missing at random (MAR). It is therefore of theoretical interest and practical importance to determine in principle whether a…
Motivated by DNA-based storage applications, we study the problem of reconstructing a coded sequence from multiple traces. We consider the model where the traces are outputs of independent deletion channels, where each channel deletes each…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
Under the effect of strong genetic drift, it is highly probable to observe gene fixation or gene loss in a population, shown by infinite peaks on a coherently constructed potential energy landscape. It is then important to ask what such…
Hi-C experiments are used to infer the contact probabilities between loci separated by varying genome lengths. Contact probability should decrease as the spatial distance between two loci increases. However, studies comparing Hi-C and FISH…
For a genetic locus carrying a strongly beneficial allele which has just fixed in a large population, we study the ancestry at a linked neutral locus. During this ``selective sweep'' the linkage between the two loci is broken up by…
We consider the maximum coding rate achievable by uniformly-random codes for the deletion channel. We prove an upper bound that's within 0.1 of the best known lower bounds for all values of the deletion probability $d,$ and much closer for…
In the trace reconstruction problem, the goal is to reconstruct an unknown string $x$ of length $n$ from multiple traces obtained by passing $x$ through the deletion channel. In the relaxed problem of $approximate$ trace reconstruction, the…
Mixture models have received considerable attention recently and Newton [Sankhy\={a} Ser. A 64 (2002) 306--322] proposed a fast recursive algorithm for estimating a mixing distribution. We prove almost sure consistency of this recursive…
The paper suggests a frequency criterion of error-free recoverability of a missing value for sequences, i.e. discrete time processes, in a pathwise setting without probabilistic assumptions. The paper establishes error-free recoverability…
Probability estimation is an elementary building block of every statistical data compression algorithm. In practice probability estimation is often based on relative letter frequencies which get scaled down, when their sum is too large.…
The fitness of a biological strategy is typically measured by its expected reproductive rate, the first moment of its offspring distribution. However, strategies with high expected rates can also have high probabilities of extinction. A…
The stationary sampling distribution of a neutral decoupled Moran or Wright-Fisher diffusion with neutral mutations is known to first order for a general rate matrix with small but otherwise unconstrained mutation rates. Using this…
We propose methods for estimating correspondence between two point sets under the presence of outliers in both the source and target sets. The proposed algorithms expand upon the theory of the regression without correspondence problem to…
In this paper, we derive an expression for the expected number of runs in a trace of a binary sequence $x \in \{0,1\}^n$ obtained by passing $x$ through a deletion channel that independently deletes each bit with probability $q$. We use…
We consider models of nucleotidic substitution processes where the rate of substitution at a given site depends on the state of its neighbours. For a wide class of such nonreversible models, we show how to compute consistent, mathematically…
We propose a modification to the random destruction of graphs: Given a finite network with a distinguished set of sources and targets, remove (cut) vertices at random, discarding components that do not contain a source node. We investigate…
We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate the ultimate ruin probability in the Gerber-Dickson risk model is provided when claims follow a negative binomial mixture distribution. The…