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Probability Histograms01:17

Probability Histograms

8.6K
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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Histogram01:05

Histogram

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The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data represents (for instance, distance from your home to school). The vertical y-axis is labeled either frequency or relative frequency (or percent frequency or probability).
A histogram graph consists of contiguous (adjoining) boxes. The heights of the bars correspond to frequency values. The graph will have the same shape with respective labels. The...
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Elements of Block Diagrams01:25

Elements of Block Diagrams

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Block diagrams serve as a visual representation of the input-output relationships within a system. An illustrative example is a heating system, where the set temperature activates the furnace to warm the room to the desired level. Block diagrams are versatile, modeling linear systems through Laplace transform variables and nonlinear systems using time domain variables.
A block diagram typically includes essential elements such as comparators, blocks, and feedback loops. Each of these elements...
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Block Diagram Reduction01:22

Block Diagram Reduction

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The process of deriving the transfer function of a control system often involves reducing its block diagram to a single block. This simplification can be achieved through a series of strategic operations, including relocating branch points and comparators. These operations preserve the overall function of the system while allowing for easier manipulation and combination of blocks.
The first step in this process is the identification and relocation of a branch point. A branch point, where a...
712
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

327
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
327
Central Limit Theorem01:14

Central Limit Theorem

17.5K
The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample means says that if you repeatedly draw samples of a given size and calculate their means, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape. In other words, as sample sizes increase, the distribution of means follows the normal distribution more closely.
The sample size, n, that...
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Updated: Apr 23, 2026

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
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Network histograms and universality of blockmodel approximation.

Sofia C Olhede1, Patrick J Wolfe2

  • 1Departments of Statistical Science and Computer Science, University College London, London WC1E 6BT, United Kingdom.

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|October 3, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces the network histogram, a novel statistical tool for analyzing network data. It uses stochastic blockmodels to summarize network interactions, aiding in exploratory data analysis and community detection.

Keywords:
community detectiongraph limitsgraphonsnonparametric statisticssparse networks

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Area of Science:

  • Network science
  • Statistical modeling
  • Data analysis

Background:

  • Exploratory data analysis of complex networks is challenging.
  • Existing methods may not capture the full range of network structures.
  • Statistical summaries are needed for understanding network interactions.

Purpose of the Study:

  • Introduce the network histogram as a novel statistical summary for network data.
  • Develop methods for automatic bandwidth selection in network histograms.
  • Explore the interpretation of network communities and the trade-off between fidelity and interpretability.

Main Methods:

  • Fitting a stochastic blockmodel to network data to create a network histogram.
  • Utilizing blocks of edges as histogram bins and community sizes as bandwidths.
  • Implementing automatic bandwidth selection for approximating exchangeable random graphs.

Main Results:

  • The network histogram provides a universal representation for unlabeled graphs.
  • Different blockmodel estimates can represent valid underlying probability models.
  • Analysis of political weblogs and student friendship networks demonstrates practical application.

Conclusions:

  • The network histogram offers a flexible tool for network data exploration.
  • Understanding community structures requires considering multiple valid representations.
  • The method aids in interpreting network properties with varying levels of detail.