A Proof of Entropy Minimization for Outputs in Deletion Channels via Hidden Word Statistics

From the output produced by a memoryless deletion channel from a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that of the uniform prior measures the amount of information about the channel input which is conveyed by the output of length $m$, and it is natural to ask for which outputs this is extremized. This question was posed in a previous work, where it was conjectured on the basis of experimental data that the entropy of the posterior is minimized and maximized by the constant strings $\texttt{000}\ldots$ and $\texttt{111}\ldots$ and the alternating strings $\texttt{0101}\ldots$ and $\texttt{1010}\ldots$ respectively. In the present work we confirm the minimization conjecture in the asymptotic limit using results from hidden word statistics. We show how the analytic-combinatorial methods of Flajolet, Szpankowski and Vall\'ee for dealing with the hidden pattern matching problem can be applied to resolve the case of fixed output length and $n\rightarrow\infty$, by obtaining estimates for the entropy in terms of the moments of the posterior distribution and establishing its minimization via a measure of autocorrelation.Comment: 11 pages, 2 figure

Statistics local fisher discriminant analysis for industrial process fault classification

In order to effectively identify industrial process faults, an improved Fisher discriminant analysis (FDA) method, referred to as the statistics local Fisher discriminant analysis (SLFDA), is proposed for fault classification. For mining statistics information hidden in process data, statistics pattern analysis is firstly applied to transform the original measured variables into the corresponding statistics, including second-order and higher-order ones. Furthermore, considering the local structure characteristics of fault data, local FDA (LFDA) is performed which computes the discriminant vectors by modifying the optimization objective with local weighting factor. Simulation results on the benchmark Tennessee Eastman process show that the proposed SLFDA has a better fault classification performance than the FDA and LFDA methods

Spontaneous attribution of false beliefs in adults examined using a signal detection approach

Understanding other people have beliefs different from ours or different from reality is critical to social interaction. Previous studies suggest that healthy adults possess an implicit mentalising system, but alternative explanations for data from reaction time false belief tasks have also been given. In this study, we combined signal detection theory (SDT) with a false belief task. As application of SDT allows us to separate perceptual sensitivity from criteria, we are able to investigate how another person’s beliefs change the participant’s perception of near-threshold stimuli. Participants (n = 55) watched four different videos in which an actor saw (or did not see) a Gabor cube hidden (or not hidden) behind an occluder. At the end of each video, the occluder vanished revealing a cube either with or without Gabor pattern, and participants needed to report whether they saw the Gabor pattern or not. A pre-registered analysis with classical statistics weakly suggests an effect of the actor’s belief on participant’s perceptions. An exploratory Bayesian analysis supports the idea that when the actor believed the cube was present, participants made slower and more liberal judgements. Although these data are not definitive, these current results indicate the value of new measures for understanding implicit false belief processing

Radial Basis Neural Network for Availability Analysis

The appliance of radial basis neural network is demostrated in this paper. The method applies failure and repair rate signals to learn the hidden relationship presented into the input pattern. Statistics of availability of several years is considered and collected from the management of concern plant. This data is considered to train and calidate the radial basis neural network (RBNN). Subsequently validated RBNN is used to estimate the availability of concern plant. The main objective of using neural network approach is that it’s not require assumption, nor explicit coding of the problem and also not require the complete knowledge of interdependencies, only requirement is raw data of system functioning

An Algorithm to Compute the Character Access Count Distribution for Pattern Matching Algorithms

We propose a framework for the exact probabilistic analysis of window-based pattern matching algorithms, such as Boyer--Moore, Horspool, Backward DAWG Matching, Backward Oracle Matching, and more. In particular, we develop an algorithm that efficiently computes the distribution of a pattern matching algorithm's running time cost (such as the number of text character accesses) for any given pattern in a random text model. Text models range from simple uniform models to higher-order Markov models or hidden Markov models (HMMs). Furthermore, we provide an algorithm to compute the exact distribution of \emph{differences} in running time cost of two pattern matching algorithms. Methodologically, we use extensions of finite automata which we call \emph{deterministic arithmetic automata} (DAAs) and \emph{probabilistic arithmetic automata} (PAAs)~\cite{Marschall2008}. Given an algorithm, a pattern, and a text model, a PAA is constructed from which the sought distributions can be derived using dynamic programming. To our knowledge, this is the first time that substring- or suffix-based pattern matching algorithms are analyzed exactly by computing the whole distribution of running time cost. Experimentally, we compare Horspool's algorithm, Backward DAWG Matching, and Backward Oracle Matching on prototypical patterns of short length and provide statistics on the size of minimal DAAs for these computations

An Introduction to Psychological Statistics

This work has been superseded by Introduction to Statistics in the Psychological Sciences available from https://irl.umsl.edu/oer/25/. - We are constantly bombarded by information, and finding a way to filter that information in an objective way is crucial to surviving this onslaught with your sanity intact. This is what statistics, and logic we use in it, enables us to do. Through the lens of statistics, we learn to find the signal hidden in the noise when it is there and to know when an apparent trend or pattern is really just randomness. The study of statistics involves math and relies upon calculations of numbers. But it also relies heavily on how the numbers are chosen and how the statistics are interpreted. This work was created as part of the University of Missouri’s Affordable and Open Access Educational Resources Initiative (https://www.umsystem.edu/ums/aa/oer). The contents of this work have been adapted from the following Open Access Resources: Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University. Changes to the original works were made by Dr. Garett C. Foster in the Department of Psychological Sciences to tailor the text to fit the needs of the introductory statistics course for psychology majors at the University of Missouri – St. Louis. Materials from the original sources have been combined, reorganized, and added to by the current author, and any conceptual, mathematical, or typographical errors are the responsibility of the current author

Modeling Rainfall Variability over Urban Areas: A Case Study for Kuwait

This study examines the spatial and temporal variability of monthly total rainfall data obtained from weather stations located in the urban areas of Kuwait. The rainfall data are analyzed by considering statistics on a seasonal basis and by means of periodogram technique to reveal the periods responsible for the variable pattern. The results demonstrate similarity implying that a point estimate of rainfall data can be considered spatially representative over the urban areas of Kuwait. A sinusoidal model triggering the influence of the detected periods is developed accordingly for the time duration from January 1965 to December 2009. The model is capable of describing the rainfall data with some discrepancies between the actual and calculated values resulting from hidden periods that have not been taken into account. This finding suggests that the ability to construct a more reliable model would require a wider range of historical data to detect the other periods affecting the rainfall pattern