Multivariate Posterior Probability Distribution Approximation
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Solution Overview
Problem
Handling large multivariate random samples generated from posterior probability distributions is challenging due to their size and complexity, making it difficult to store, transmit, and perform further analysis, especially when these samples are distributed across multiple computing devices.
Innovation Solution
The technique involves dividing the random sample into portions distributed across multiple computing devices, where each device fits partial marginal probability distributions and copula functions, allowing for parallel processing and reducing the data size through empirical distribution functions and copula modeling, enabling efficient storage, transmission, and further analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the random sample is divided into portions distributed across multiple computing devices, then the complexity of handling large data is reduced and processing can be performed in parallel, but the coordination and communication between devices increases system complexity
Solution Approach 1:
The patent divides the large random sample into multiple portions and distributes them across different computing devices. Each device independently fits marginal distributions and copula functions to its local sample portion, enabling parallel processing while reducing the data burden on each individual device. The segmentation is achieved by partitioning the sample data into disjoint subsets that can be processed autonomously.
2Quantity of substance
If empirical distribution functions and copula modeling are used to reduce data size, then storage and transmission requirements are reduced, but the precision of the probability distribution approximation may be compromised
Solution Approach 1:
The patent transforms the original large-scale sample data into a compact representation by estimating probability distribution parameters (marginal distributions and copula functions). This parameter-based approach reduces the data from millions of individual samples to a small set of statistical parameters that capture the essential distributional characteristics, achieving both compression and preservation of statistical properties.
3Productivity
If the copula function is divided into portions fitted on different computing devices, then parallel processing is enabled, but ensuring the overall fit accuracy across the entire sample becomes more difficult
Solution Approach 1:
The patent extracts the essential statistical properties (marginal distributions and copula parameters) from each local sample portion and combines them to form the overall distribution model. By extracting and aggregating the key parameters rather than exchanging the entire datasets, the method achieves parallel processing while maintaining overall fit accuracy through proper parameter integration.
Data Source
AI summary
Various embodiments are directed to techniques for deriving a sample representation from a random sample. A computer-program product includes instructions to cause a first computing device to fit an empirical distribution function to a marginal probability distribution of a variable within a first sample portion of a random sample to derive a partial marginal probability distribution approximation, wherein the random sample is divided into multiple sample portions distributed among multiple computing devices; fit a first portion of a copula function to a multivariate probability distribution of the first sample portion, wherein the copula function is divided into multiple portions; and transmit an indication of a first likelihood contribution of the first sample portion to a coordinating device to cause a second computing device to fit a second portion of the copula function to a multivariate probability distribution of a second sample portion. Other embodiments are described and claimed.