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Related Concept Videos

Probability Distributions01:32

Probability Distributions

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 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
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Poisson Probability Distribution01:09

Poisson Probability Distribution

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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
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Probability Histograms01:17

Probability Histograms

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A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
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Binomial Probability Distribution01:15

Binomial Probability Distribution

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A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
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There are only two possible outcomes,...
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Sampling Distribution01:12

Sampling Distribution

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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Prediction Intervals01:03

Prediction Intervals

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The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
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Creating Objects and Object Categories for Studying Perception and Perceptual Learning
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Probability Distribution Estimation for Autoregressive Pixel-Predictive Image Coding.

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    This study introduces advanced pixel prediction for lossless image compression, improving probability estimation for better results. The new methods achieve competitive compression ratios and the code is publicly available.

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    Area of Science:

    • Computer Science
    • Image Processing
    • Data Compression

    Background:

    • Pixelwise linear prediction with least-squares estimation is a leading lossless image compression technique.
    • Current methods often focus on mean intensity prediction, neglecting full probability distributions.
    • Accurate probability estimates are crucial for optimal lossless compression performance.

    Purpose of the Study:

    • To enhance lossless image compression by improving pixel intensity probability estimation.
    • To develop a method for deriving prediction error variance and complete probability distributions.
    • To introduce a novel weight computation formula for weighted least-squares and adapt models for sparse intensity distributions.

    Main Methods:

    • Utilized backward-adaptive least-squares and weighted least-squares estimation for prediction coefficients.
    • Derived prediction error variance estimates from (weighted) least-squares training regions.
    • Built complete probability distributions using an autoregressive image model and analyzed image stationarity.
    • Developed the C++ framework Volumetric, Artificial, and Natural Image Lossless Coder (Vanilc).

    Main Results:

    • Achieved competitive compression ratios compared to state-of-the-art lossless image codecs.
    • Demonstrated effective compression for diverse image types, including 16-bit medical 3D volumes and multichannel data.
    • The Vanilc framework provides a robust platform for evaluating lossless image compression techniques.

    Conclusions:

    • The proposed methods offer significant improvements in lossless image compression by accurately estimating intensity probabilities.
    • The developed autoregressive model and weight computation generalize existing approaches and handle sparse distributions effectively.
    • The public release of the Vanilc source code promotes reproducible research in the field of image compression.