arXiv subjects

Kwabena Doku-Amponsah

Publications and source records attributed to Kwabena Doku-Amponsah.

18 recordsLinked to original sources

arXiv2020

Large deviations, asymptotic bounds on the number of positive individuals in a Bernoulli sample via the number of positive pool samples drawn on the bernoulli sample

In this paper we define for a Bernoulli samples the \emph{ empirical infection measure}, which counts the number of positives (infections) in the Bernoulli sample and for the \emph{ pool samples} we define the empirical pool infection measure, which counts the number of positive (infected) pool samples. For this empirical measures we prove a joint large deviation principle for Bernoulli samples. We also found an asymptotic relationship between the \emph{ proportion of infected individuals } with respect to the samples size, $n$ and the \emph{ proportion of infected pool samples} with respect to the number of pool samples, $k(n).$ All rate functions are expressed in terms of relative entropies.

math.PR↗

arXiv2020

Large Deviation Principle for Empirical SINR Measure of Critical Telecommunication Networks

For a \emph{ powered Poisson process}, we define \emph{Signal-to-Interference-plus-Noise Ratio}(SINR) and thesinr network as a Telecommunication Network. We define the Empirical Measures (\emph{empirical powered measure}, \emph{empirical link measure} and \emph{empirical sinr measure}) of a class of Telecommunication Networks. For this class of Telecommunication Network we prove a joint large deviation principle for the empirical measures of the Telecommunication Networks. All our rate functions are expressed in terms of relative entropies.

cs.IT↗

arXiv2020

Local Large Deviation Principle, Large Deviation Principle and Information theory for the Signal -to- Interference -Plus- Noise Ratio Graph Models

Given devices space $D$, an intensity measure $λm\in(0,\infty)$, a transition kernel $Q$ from the space $D$ to positive real numbers $(0,\infty,$ a path-loss function (which depends on the Euclidean distance between the devices and a positive constant $α$), we define a Marked Poisson Point process (MPPP). For a given MPPP and technical constants $τ_λ,γ_λ:(0,\,\infty)\to (0,\infty),$ we define a Marked Signal-to- Interference and Noise Ratio (SINR) graph, and associate with it two empirical measures; the \emph{empirical marked measure} and the \emph{empirical connectivity measure}. For a class of marked SINR graphs, we prove a joint \emph{ large deviation principle}(LDP) for these empirical measures, with speed $λ$ in the $τ$-topology. From the joint large deviation principle for the empirical marked measure and the empirical connectivity measure, we obtain an Asymptotic Equipartition Property(AEP) for network structured data modelled as a marked SINR graph. Specifically, we show that for large dense marked SINR graph one require approximately about $λ^{2}H(Q\times Q)/\log 2$ bits to transmit the information contained in the network with high probability, where $ H(Q\times Q)$ is a properly defined entropy for the exponential transition kernel with parameter $c$. Further, we prove a \emph {local large deviation principle} (LLDP) for the class of marked SINR graphs on $D,$ where $λ[τ_λ(a)γ_λ(a)+λτ_λ(b)γ_λ(b)]\to β(a,b),$ $ a,b\in (0,\infty)$, with speed $λ$ from a \emph{ spectral potential} point. From the LLDP we derive a conditional LDP for the marked SINR graphs.

cs.IT↗

arXiv2018

Local Large deviations for empirical locality measure of typed Random Graph Models

In this article, we prove a local large deviation principle (LLDP) for the empirical locality measure of typed random networks on $n$ nodes conditioned to have a given \emph{ empirical type measure} and \emph{ empirical link measure.} From the LLDP, we deduce a full large deviation principle for the typed random graph, and the classical Erdos-Renyi graphs, where $nc/2$ links are inserted at random among $n$ nodes. No topological restrictions are required for these results.

cs.IT↗

arXiv2017

Lossy Asymptotic Equipartition Property For Geometric Networked Data Structures

This article extends the Generalized Asypmtotic Equipartition Property of Networked Data Structures to cover the Wireless Sensor Network modelled as coloured geometric random graph (CGRG). The main techniques used to prove this result remains large deviation principles for properly defined empirical measures on CGRGs. As a motivation for this article, we apply our results to some data from Wireless Sensor Network for Monitoring Water Quality from a Lake..

cs.IT↗

arXiv2017

On Extreme Value Index Estimation under Random Censoring

Extreme value analysis in the presence of censoring is receiving much attention as it has applications in many disciplines, including survival and reliability studies. Estimation of extreme value index (EVI) is of primary importance as it is a critical parameter needed in estimating extreme events such as quantiles and exceedance probabilities. In this paper, we review several estimators of the extreme value index when data is subject to random censoring. In addition, four estimators are proposed, one based on the exponential regression approximation of log spacings, one based on a Zipf estimator and two based on variants of the moment estimator. The proposed estimators and the existing ones are compared under the same simulation conditions. The performance measures for the estimators include confidence interval length and coverage probability. The simulation results show that no estimator is universally the best as the estimators depend on the size of the EVI parameter, percentage of censoring in the right tail and the underlying distribution. However, certain estimators such as the proposed reduced-bias estimator and the adapted moment estimator are found to perform well across most scenarios. Moreover, we present a bootstrap algorithm for obtaining samples for extreme value analysis in the context of censoring. Some of the estimators that performed well in the simulation study are illustrated using a practical dataset from medical research

stat.CO↗

arXiv2017

Local Large deviation: A McMillian Theorem for Coloured Random Graph Processes

For a finite typed graph on $n$ nodes and with type law $μ,$ we define the so-called spectral potential $ρ_λ(\,\cdot,\,μ),$ of the graph.From the $ρ_λ(\,\cdot,\,μ)$ we obtain Kullback action or the deviation function, $\mathcal{H}_λ(π\,\|\,ν),$ with respect to an empirical pair measure, $π,$ as the Legendre dual. For the finite typed random graph conditioned to have an empirical link measure $π$ and empirical type measure $μ$, we prove a Local large deviation principle (LLDP), with rate function $\mathcal{H}_λ(π\,\|\,ν)$ and speed $n.$ We deduce from this LLDP, a full conditional large deviation principle and a weak variant of the classical McMillian Theorem for the typed random graphs. Given the typical empirical link measure, $λμ\otimesμ,$ the number of typed random graphs is approximately equal $e^{n\|λμ\otimesμ\|H\big(λμ\otimesμ/\|λμ\otimesμ\|\big)}.$ Note that we do not require any topological restrictions on the space of finite graphs for these LLDPs.

cs.IT↗

arXiv2017

Local Large Deviations: McMillian Theorem for multitype Galton-Watson Processes

In this article we prove a local large deviation principle (LLDP) for the critical multitype Galton-Watson process from spectral potential point. We define the so-called a spectral potential $U_{\skrik}(\,\cdot,\,π)$ for the Galton-Watson process, where $π$ is the normalized eigen vector corresponding to the leading \emph{Perron-Frobenius eigen value } $\1$ of the transition matrix $\skria(\cdot,\,\cdot)$ defined from ${\skrik},$ the transition kernel. We show that the Kullback action or the deviation function, $J(π,ρ),$ with respect to an empirical offspring measure, $ρ,$ is the Legendre dual of $U_{\skrik}(\,\cdot,\,π).$ From the LLDP we deduce a conditional large deviation principle and a weak variant of the classical McMillian Theorem for the multitype Galton-Watson process. To be specific, given any empirical offspring measure $\varpi,$ we show that the number of critical multitype Galton-Watson processes on $n$ vertices is approximately $e^{n\langle \skrih_{\varpi},\,π\rangle},$ where $\skrih_{\varpi}$ is a suitably defined entropy.

cs.IT↗

arXiv2017

Asymptotics of the partition function of Ising model on inhomogeneous random graphs

For a finite random graph, we defined a simple model of statistical mechanics. We obtain an annealed asymptotic result for the random partition function for this model on finite random graphs as n; the size of the graph is very large. To obtain this result, we define the empirical bond distribution, which enumerates the number of bonds between a given couple of spins, and empirical spin distribution, which enumerates the number of sites having a given spin on the spinned random graphs. For these empirical distributions we extend the large deviation principle(LDP) to cover random graphs with continuous colour laws. Applying Varandhan Lemma and this LDP to the Hamiltonian of the Ising model defined on Erdos-Renyi graphs, expressed as a function of the empirical distributions, we obtain our annealed asymptotic result.

math-ph↗

arXiv2016

Lossy Asymptotic Equipartition property for Hierarchical Data Structures

This paper presents a rate-distortion theory for hierarchical networked data structures modelled as tree-indexed multitype process. To be specific, this paper gives a generalized Asymptotic Equipartition Property (AEP) for the Process. The general methodology of proof of the AEP are process level large deviation principles for suitably defined empirical measures for muiltitype Galton-Watson trees.

cs.IT↗

arXiv2016

Joint large deviation result for empirical measures of the coloured random geometric graphs

We prove joint large deviation principle for the \emph{ empirical pair measure} and \emph{empirical locality measure} of the \emph{near intermediate} coloured random geometric graph models on $n$ points picked uniformly in a $d-$dimensional torus of a unit circumference.From this result we obtain large deviation principles for the \emph{number of edges per vertex}, the \emph{degree distribution and the proportion of isolated vertices } for the \emph{near intermediate} random geometric graph models.

math.PR↗

arXiv2016

Large deviation results for Critical Multitype Galton-Watson trees

In this article, we prove a joint large deviation principle in $n$ for the \emph{empirical pair measure} and \emph{ empirical offspring measure} of critical multitype Galton-Watson trees conditioned to have exactly $n$ vertices in the weak topology. From this result we extend the large deviation principle for the empirical pair measures of Markov chains on simply generated trees to cover offspring laws which are not treated by \cite[Theorem~2.1]{DMS03}. For the case where the offspring law of the tree is a geometric distribution with parameter \sfrac{1}{2}, we get an exact rate function. All our rate functions are expressed in terms of relative entropies.

math.PR↗

arXiv2015

Large deviation, Basic Information Theory for Wireless Sensor Networks

In this article, we prove Shannon-MacMillan-Breiman Theorem for Wireless Sensor Networks modelled as coloured geometric random graphs. For large $n,$ we show that a Wireless Sensor Network consisting of $n$ sensors in $[0,1]^d$ connected by an average number of links of order $n\log n $ can be coded by about $[n(\log n )^2π^{d/2}/(d/2)!]\,\mathcal{H}$ bits, where $\mathcal{H}$ is an explicitly defined entropy. In the process, we derive a joint large deviation principle (LDP) for the \emph{empirical sensor measure} and \emph{the empirical link measure} of coloured random geometric graph models.

cs.IT↗

arXiv2015

Statistical model for overdispersed count outcome with many zeros: an approach for direct marginal inference

Marginalized models are in great demand by most researchers in the life sciences particularly in clinical trials, epidemiology, health-economics, surveys and many others since they allow generalization of inference to the entire population under study. For count data, standard procedures such as the Poisson regression and negative binomial model provide population average inference for model parameters. However, occurrence of excess zero counts and lack of independence in empirical data have necessitated their extension to accommodate these phenomena. These extensions, though useful, complicates interpretations of effects. For example, the zero-inflated Poisson model accounts for the presence of excess zeros but the parameter estimates do not have a direct marginal inferential ability as its base model, the Poisson model. Marginalizations due to the presence of excess zeros are underdeveloped though demand for such is interestingly high. The aim of this paper is to develop a marginalized model for zero-inflated univariate count outcome in the presence of overdispersion. Emphasis is placed on methodological development, efficient estimation of model parameters, implementation and application to two empirical studies. A simulation study is performed to assess the performance of the model. Results from the analysis of two case studies indicated that the refined procedure performs significantly better than models which do not simultaneously correct for overdispersion and presence of excess zero counts in terms of likelihood comparisons and AIC values. The simulation studies also supported these findings. In addition, the proposed technique yielded small biases and mean square errors for model parameters. To ensure that the proposed method enjoys widespread use, it is implemented using the SAS NLMIXED procedure with minimal coding efforts.

stat.ME↗

arXiv2014

Some large deviation results for near intermediate random geometric graphs

We find large deviation principles for the degree distribution and the proportion of isolated vertices for the near intermediate random geometric graph models on n vertices placed uniformly in [0, 1]^d, for d in N. In the course of the proof of these large deviation results we find joint large deviation principle for the empirical locality measure of the coloured random geometric graphs,(Canning & Penman, 2003).

math.PR↗

arXiv2014

Large deviation result for the empirical locality measure of typed random geometric graphs

In this article for a finite typed random geometric graph we define the empirical locality distribution, which records the number of nodes of a given type linked to a given number of nodes of each type. We find large deviation principle (LDP) for the empirical locality measure given the empirical pair measure and the empirical type measure of the typed random geometric graphs. From this LDP, we derive large deviation principles for the degree measure and the proportion of detached nodes in the classical Erdos-Renyi graph defined on [0, 1]^d. This graphs have been suggested by (Canning and Penman, 2003) as a possible extension to the randomly typed random graphs.

math.PR↗

arXiv2010

Large deviation principles for empirical measures of colored random graphs

For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number of edges connecting each pair of colors. For a class of models of sparse colored random graphs, we prove large deviation principles for these empirical measures in the weak topology. The rate functions governing our large deviation principles can be expressed explicitly in terms of relative entropies. We derive a large deviation principle for the degree distribution of Erdős--Rényi graphs near criticality.

math.PR↗

arXiv2010

Asymptotic Equipartition Properties for simple hierarchical and networked structures

We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large $n$, a networked data structure consisting of $n$ units connected by an average number of links of order $n/log n$ can be coded by about $nH$ bits, where $H$ is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical measures.

cs.IT↗