Pairwise Probability Research Articles

Detection of associations with rare and common SNPs for quantitative traits: a nonparametric Bayes-based approach

We propose a nonparametric Bayes-based clustering algorithm to detect associations with rare and common single-nucleotide polymorphisms (SNPs) for quantitative traits. Unlike current methods, our approach identifies associations with rare genetic variants at the variant level, not the gene level. In this method, we use a Dirichlet process prior for the distribution of SNP-specific regression coefficients, conduct hierarchical clustering with a distance measure derived from posterior pairwise probabilities of two SNPs having the same regression coefficient, and explore data-driven approaches to select the number of clusters. SNPs falling inside the largest cluster have relatively low or close to zero estimates of regression coefficients and are considered not associated with the trait. SNPs falling outside the largest cluster have relatively high estimates of regression coefficients and are considered potential risk variants. Using the data from the Genetic Analysis Workshop 17, we successfully detected associations with both rare and common SNPs for a quantitative trait. We conclude that our method provides a novel and broadly applicable strategy for obtaining association results with a reasonably low proportion of false discovery and that it can be routinely used in resequencing studies.

Consistent Community Identi¯cation in Complex Networks

We have found that known community identification algorithms produce inconsistent communities when the node ordering changes at input. We propose two metrics to quantify the level of consistency across multiple runs of an algorithm: pairwise membership probability and consistency. Based on these two metrics, we address the consistency problem without compromising the modularity. Our solution uses pairwise membership probabilities as link weights and generates consistent communities within six or fewer cycles. It offers a new tool in the study of community structures and their evolutions.

Spatial Optimization of Wildlife Populations with Probabilistic Habitat Connections

Abstract I consider a land area divided into cells and the problem that consists of determining the cells that must be harvested and the cells that must be left in old-growth to maximize the size of wildlife populations that depend on amounts of young- and old-growth forest. In each old-growth cell, the size of the old-growth-dependent population depends on the spatial arrangement of the old-growth cells, specifically of the probability that the cell is connected to at least one other old-growth cell. This problem suggested by Hof and Bevers can be easily formulated by a difficult nonlinear 0-1 program. These authors proposed a linear approximation of a special case of the pairwise connection probabilities. The aim of this article was to show that the problem can be solved simply and efficiently with any set of connection probabilities by using standard 0-1 linear programming software. The key feature to transform the nonlinear program into a linear program is an approximation of the logarithmic function curve by some of its tangents. Computational results on hypothetical grid forests with up to 900 cells are presented to illustrate potentialities of the approach. Near-optimal solutions guaranteed to be within 0.5% of the optimal solution are obtained in less than 10 minutes of computing time.

Pherotypes of pneumococcal strains co-existing in healthy children

Genetic diversity in the species Streptococcus pneumoniae is mainly driven by horizontal gene transfer. S. pneumoniae is naturally competent for transformation. Competence is induced by a pheromone termed competence stimulating peptide (CSP) by a quorum-sensing mechanism. Two CSP pherotypes predominate amongst clinical isolates of S. pneumoniae, CSP-1 and CSP-2, with ability to trigger competence in bacteria of the homologue pherotype. Opposing theories on the effect of pherotypes on speciation have been proposed, either as a barrier for intra-pherotype gene transfer, or as a mechanism for fratricide resulting in lysis of non-competent bacterial cells.The aim of the present study was to determine pherotype distribution in strains of S. pneumococci isolated from the nasopharynges of healthy children. We sequenced the locus encoding CSP, comC, in sets of strains obtained from children colonised by multiple pneumococcal strains simultaneously. The impact of pherotype on co-colonisation was determined by comparing the observed distribution of pherotypes in co-colonising strains with the estimated pair-wise probability based on the overall pherotype distribution in the sample set.Five distinct comC alleles were identified, encoding CSP belonging to the two dominating pherotypes, CSP-1 (62.7%) and CSP-2 (37.3%). The observed distribution of pherotypes in sets of co-colonising pneumococcal strains did not differ from the probability estimate. Thus, co-colonisation of S. pneumoniae in healthy children is not restricted by pherotype.

The pairwise velocity probability density function in models with local primordial non-Gaussianity

We study how primordial non-Gaussianity affects the pairwise velocity probability density function (PDF) using an analytical model and cosmological N-body simulations. We adopt the local type non-Gaussian models characterized by fnl, and examine both the linear velocity difference PDF and the linear pairwise velocity PDF. We show explicitly how fnl induces correlations between originally independent velocities along the parallel and the perpendicular to the line of separation directions. We compare the model results with measurements from N-body simulations of the non-Gaussian models. Linear theory fails to predict the PDF in the fnl models. Therefore, we develop an analytic model based on the Zeldovich approximation to describe the evolution of the velocity PDF. Our analytical model and simulation results show remarkably good agreement in both the parallel and the perpendicular directions for the PDF profiles, as well as the change in the PDF due to primordial non-Gaussianity. The agreement is particularly good for relatively small separations (<10 h−1 Mpc). The inclusion of the evolution of the velocity PDF is important to obtain a good description on the signature of primordial non-Gaussianity in the PDF. Our model provides the foundation to constrain fnl using the peculiar velocity in future surveys.

Generalizations of the Goulden–Jackson cluster method

We give several modifications of the Goulden–Jackson cluster method for finding generating functions for words avoiding a given set of forbidden words. Our modifications include functions which can take into account various ‘weights’ on words, including single letter probability distributions, double letter (i.e. pairwise) probability distributions, and triple letter probability distributions. We also describe an alternative, recursive approach to finding such generating functions. We describe Maple implementations of the various modifications. The accompanying Maple package is available at the website for this paper.

Conditional Probability-Based Significance Tests for Sequential Patterns in Multineuronal Spike Trains

We consider the problem of detecting statistically significant sequential patterns in multineuronal spike trains. These patterns are characterized by ordered sequences of spikes from different neurons with specific delays between spikes. We have previously proposed a data-mining scheme to efficiently discover such patterns, which occur often enough in the data. Here we propose a method to determine the statistical significance of such repeating patterns. The novelty of our approach is that we use a compound null hypothesis that not only includes models of independent neurons but also models where neurons have weak dependencies. The strength of interaction among the neurons is represented in terms of certain pair-wise conditional probabilities. We specify our null hypothesis by putting an upper bound on all such conditional probabilities. We construct a probabilistic model that captures the counting process and use this to derive a test of significance for rejecting such a compound null hypothesis. The structure of our null hypothesis also allows us to rank-order different significant patterns. We illustrate the effectiveness of our approach using spike trains generated with a simulator.

New closed-form bounds on the performance of coding in correlated Rayleigh fading

New, simple bounds are presented for the probability of error in a binary hypothesis test for communications using diversity signaling in correlated Rayleigh fading. The bounds are developed in the context of pairwise error-event probabilities in decoding an error-correction code. A long-standing conjecture regarding the form of worst-case error events in exponentially correlated Rayleigh fading is also proven. The utility of the results is illustrated by their application to transfer-function bounds on the probability of bit error for a system using a convolutional code. The closed-form transfer-function bounds are shown to be tighter than previously developed transfer-function bounds for communications in exponentially correlated Rayleigh fading.

Statistical theory of neutral protein evolution by random site mutations

Understanding the features of the protein conformational space represents a key component to characterize protein structural evolution at the molecular level. This problem is approached in a twofold manner; simple lattice models are used to represent protein structures with the ability of a protein sequence to fold into the lowest energy native conformation, quantified as the foldability, which measures the fitness of the sequence. Alternatively, a self-consistent mean-field based theory is developed to evaluate the protein neutrality through random single-point and multiple-point mutations by calculating the pair-wise probability profile of the amino acid residues in a library of sequences, consistent with a particular foldability criterion. The theory predicts the change in sequence plasticity with the foldability criterion and also correlates the effect of hydrophobic residues on the variation of the free energy surface of the protein as a function of the number of cumulative mutations. The results obtained from the theory are compared with the exact enumeration results of 3 × 3 × 3 lattice protein and also with some small real proteins chosen from the protein databank. An excellent match of the results obtained from theory and exact enumeration with those of real proteins validates the range of applicability of the theory. The theory may provide a new perspective in de novo protein design, in-vivo/in-vitro protein evolution and site-directed mutagenesis experiments.

Statistical Theory of Protein Sequence Design by Random Mutation

A self-consistent mean-field based theory is developed to evaluate the site-specific amino acid pair probabilities in a library of sequences to consider the effect of correlated mutations. This approach computes the entire residue-residue substitution pattern by completely characterizing all possible residue-residue combinations consistent with a given protein structure. Design involves screening a library of sequences with different monomer types to estimate the number and composition of sequences as a function of a generalized foldability criterion. The theory is applied to a simple lattice model of proteins. The theoretical results are respectively compared with real sequences obtained from both the lysozyme protein fold and 1789 nonhomologous globular proteins. The pairwise sequence probability profile of the real proteins show a reasonably good match with that of the lattice proteins with a simple coarse-grained potential. The theory may provide a framework for exploring site directed mutagenesis strategies in engineering known proteins and designing them de novo.

Fechnerian Scaling inR: The Packagefechner

Fechnerian scaling is a procedure for constructing a metric on a set of objects (e.g., colors, symbols, X-ray films, or even statistical models) to represent dissimilarities among the objects "from the point of view" of a system (e.g., person, technical device, or even computational algorithm) "perceiving" these objects. This metric, called Fechnerian, is computed from a data matrix of pairwise discrimination probabilities or any other pairwise measure which can be interpreted as the degree with which two objects within the set are discriminated from each other. This paper presents the package fechner for performing Fechnerian scaling of object sets in R. We describe the functions of the package. Fechnerian scaling then is demonstrated on real and artificial data sets accompanying the package.

Statistical physics of pairwise probability models.

Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of data: knowledge of the mean values and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this paper, we describe how tools from statistical physics can be employed for studying and using pairwise models. We build on our previous work on the subject and study the relation between different methods for fitting these models and evaluating their quality. In particular, using data from simulated cortical networks we study how the quality of various approximate methods for inferring the parameters in a pairwise model depends on the time bin chosen for binning the data. We also study the effect of the size of the time bin on the model quality itself, again using simulated data. We show that using finer time bins increases the quality of the pairwise model. We offer new ways of deriving the expressions reported in our previous work for assessing the quality of pairwise models.

Relatedness mapping and tracts of relatedness for genome‐wide data in the presence of linkage disequilibrium

Estimates of relatedness have several applications such as the identification of relatives or in identifying disease related genes through identity by descent (IBD) mapping. Here we present a new method for identifying IBD tracts among individuals from genome-wide single nucleotide polymorphisms data. We use a continuous time Markov model where the hidden states are the number of alleles shared IBD between pairs of individuals at a given position. In contrast to previous methods, our method accurately accounts for linkage disequilibrium using pairwise haplotype probabilities. The method provides a map of the local relatedness along the genome. We illustrate the potential of the method for mapping disease genes on a real data set, and show that the method has the potential to map causative disease mutations using only a handful of affected individuals. The new IBD mapping method provides considerable improvement in mapping power in natural populations compared to standard association mapping methods.

Automatic Language Identification with Discriminative Language Characterization Based on SVM

Robust automatic language identification (LID) is the task of identifying the language from a short utterance spoken by an unknown speaker. The mainstream approaches include parallel phone recognition language modeling (PPRLM), support vector machine (SVM) and the general Gaussian mixture models (GMMs). These systems map the cepstral features of spoken utterances into high level scores by classifiers. In this paper, in order to increase the dimension of the score vector and alleviate the inter-speaker variability within the same language, multiple data groups based on supervised speaker clustering are employed to generate the discriminative language characterization score vectors (DLCSV). The back-end SVM classifiers are used to model the probability distribution of each target language in the DLCSV space. Finally, the output scores of back-end classifiers are calibrated by a pair-wise posterior probability estimation (PPPE) algorithm. The proposed language identification frameworks are evaluated on 2003 NIST Language Recognition Evaluation (LRE) databases and the experiments show that the system described in this paper produces comparable results to the existing systems. Especially, the SVM framework achieves an equal error rate (EER) of 4.0% in the 30-second task and outperforms the state-of-art systems by more than 30% relative error reduction. Besides, the performances of proposed PPRLM and GMMs algorithms achieve an EER of 5.1% and 5.0% respectively.

Pulse position modulated space–time trellis coding for ultra-wideband impulse radio multiple-input multiple-output communication systems

The design of pulse position modulated (PPM) space-time trellis codes (STTC) for ultra-wideband impulse radio (UWB-IR) multiple-input multiple-output (MIMO) communication systems over slow and fast fading multipath channels is considered. First, A probability of error analysis is carried out to derive upper bounds on pairwise symbol error probability at high and low signal-to-noise ratios (SNRs). From the upper bounds, A new distance notion is introduced and novel design criteria for optimal (in error rate performance) M-ary PPM STTC are deduced for UWB. An optimal binary-PPM STTC is designed for two transmit antennas. Finally, simulation results of the UWB-IR MIMO system, using the optimal STTC, confirm significant improvement in bit-error-rate performance over the uncoded UWB-IR single-input single-output system and also over previously proposed space-time coding scheme for UWB, at higher SNR.

Using SVM as Back-End Classifier for Language Identification

Robust automatic language identification (LID) is a task of identifying the language froma short utterance spoken by an unknown speaker. One of the mainstream approaches named parallel phone recognition language modeling (PPRLM) has achieved a very good performance. The log-likelihood radio (LLR) algorithm has been proposed recently to normalize posteriori probabilities which are the outputs of back-end classifiers in PPRLM systems. Support vector machine (SVM) with radial basis function (RBF) kernel is adopted as the back-end classifier. But for the conventional SVM classifier, the output is not probability. We use a pairwise posterior probability estimation (PPPE) algorithm to calibrate the output of each classifier. The proposed approaches are evaluated on the 2005 National Institute of Standards and Technology (NIST). Language recognition evaluation databases and experiments show that the systems described in this paper produce comparable results to the existing arts.

Classification With Finite Memory Revisited

We consider the class of strong-mixing probability laws with positive transitions that are defined on doubly infinite sequences in a finite alphabet A. A device called the classifier (or discriminator) observes a training sequence whose probability law Q is unknown. The classifier's task is to consider a second probability law P and decide whether P = Q, or P and Q are sufficiently different according to some appropriate criterion Delta(Q,P) > Delta. If the classifier has available an infinite amount of training data, this is a simple matter. However, here we study the case where the amount of training data is limited to N letters. We define a function NDelta(Q|P), which quantifies the minimum length sequence needed to distinguish Q and P and the class M(NDelta) of all probability laws pairs (Q,P) that satisfy NDelta(Q|P) les NDelta for some given positive number NDelta. It is shown that every pair Q,P of probability laws that are sufficiently different according to the Delta criterion is contained in M(NDelta). We demonstrate that for any universal classifier there exists some Q for which the classification probability lambda(Q) = 1 for some N-sequence emerging from Q, for some P : (Q,P) epsi M circ(NDelta).Delta(Q,P) > Delta, if N < NDelta. Conversely, we introduce a classification algorithm that is essentially optimal in the sense that for every (Q,P) epsi M(NDelta), the probability of classification error lambda(Q) is uniformly vanishing with N for every P : (Q,P) epsi M circ(NDelta) if N ges NDelta 1+O(log log N Delta /log N Delta ). The proposed algorithm finds the largest empirical conditional divergence for a set of contexts which appear in the tested N-sequence. The computational complexity of the classification algorithm is O(N2(log N)3). Also, we introduce a second simplified context classification algorithm with a computational complexity of only O(N(log N)4) that is efficient in the sense that for every pair (Q,P) epsi M(NDelta), the pairwise probability of classification error lambda(Q,P) for the pair Q,P vanishes with N if N ges NDelta 1+O(log log N Delta /log N Delta ). Conversely, lambda(Q,P) = 1 at least for some (Q,P) epsi M(NDelta), if N < NDelta.

A Generalized BCJR Algorithm and Its Use in Iterative Blind Channel Identification

The well-known Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm was generalized to compute joint posterior probabilities of arbitrary sets of symbols given noisy observations of those symbols at the output of an intersymbol interference (ISI) channel. This letter explores using pair-wise joint posterior probabilities produced by generalized BCJR together with expectation maximization for blind identification of the ISI channel impulse response and noise variance. Simulations indicate that the blind algorithm accurately estimates the channel response and noise variance and yields bit error rates comparable to a channel-informed BCJR equalizer.

Dissimilarity cumulation theory and subjective metrics

We present a new mathematical notion, dissimilarity function, and based on it, a radical extension of Fechnerian Scaling, a theory dealing with the computation of subjective distances from pairwise discrimination probabilities. The new theory is applicable to all possible stimulus spaces subject to the following two assumptions: (A) that discrimination probabilities satisfy the Regular Minimality law and (B) that the canonical psychometric increments of the first and second kind are dissimilarity functions. A dissimilarity function D ab for pairs of stimuli in a canonical representation is defined by the following properties: (1) a ≠ b ⟹ D ab > 0 ; (2) D aa = 0 ; (3) If D a n a n ′ → 0 and D b n b n ′ → 0 , then D a n ′ b n ′ - D a n b n → 0 ; and (4) for any sequence { a n X n b n } n ∈ N , where X n is a chain of stimuli, D a n X n b n → 0 ⟹ D a n b n → 0 . The expression D aXb refers to the dissimilarity value cumulated along successive links of the chain aXb . The subjective (Fechnerian) distance between a and b is defined as the infimum of D aXb + D bYa across all possible chains X and Y inserted between a and b .

A Tighter Bhattacharyya Bound for Decoding Error Probability

The Bhattacharyya bound has been widely used to upper bound the pair-wise probability of error when transmitting over a noisy channel. However, the bound as it appears in most textbooks on channel coding can be improved by a factor of 1/2 when applied to the frame error probability. For the particular case of symmetric channels, the pairwise error probability can also be improved by a factor of 1/2. This letter provides a simple proof of these tighter bounds that has the same simplicity as the proof of the standard Bhattacharyya bound currently found in textbooks