Bayesian structural inference for hidden processes
Christopher C Strelioff1, James P Crutchfield2
1Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA.
Summary
Bayesian structural inference (BSI) discovers complex process patterns using hidden Markov models. This method accurately estimates randomness and structure, reflecting uncertainty for better insights.
Area of Science:
- Complex Systems Analysis
- Computational Neuroscience
- Information Theory
Background:
- Inferring the structure of complex processes from data is challenging.
- Hidden Markov models (HMMs) are powerful tools for time series analysis.
- ε-machines provide a framework for understanding the dynamics of systems.
Purpose of the Study:
- To introduce a Bayesian approach for discovering patterns in structurally complex processes.
- To develop a method for inferring process structure from data series.
- To quantify process randomness and statistical complexity.
Main Methods:
- Bayesian structural inference (BSI) using candidate unifilar hidden Markov model (uHMM) topologies.
- Exact enumeration of topological ε-machines.
- Analytic expressions for estimating transition probabilities and inferring start states.
Main Results:
- BSI effectively estimates Shannon entropy rate (randomness) and statistical complexity (structure).
- The posterior distribution over models better reflects uncertainty than single maximum a posteriori estimation.
- The method was applied to finite- and infinite-order Markov processes and an infinite-state hidden process.
Conclusions:
- BSI provides a robust Bayesian framework for structural inference in complex systems.
- The approach guarantees inferred models are ε-machines.
- Accurate estimation of process properties and uncertainty is achievable.
Related Concept Videos
01:23Mechanistic Models: Compartment Models in Individual and Population Analysis
359
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
359
01:06Model Approaches for Pharmacokinetic Data: Distributed Parameter Models
333
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...
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...
333
01:24One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
1.5K
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
On...
1.5K
01:21Entropy Changes Accompanying Specific Processes
159
Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression...
159
01:16Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data
728
Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...
728
01:26Structuralism
3.6K
Structuralism, an early psychological theory developed by Wilhelm Wundt and his student Edward Bradford Titchener, sought to dissect the human mind into its most fundamental components. Wundt's groundbreaking work in his laboratory set the stage for Titchener to define structuralism's goal as cataloging the "atoms" of the mind—sensations, images, and feelings—akin to how chemists identify elements of matter.
Titchener's approach to structuralism was unique. He...
Titchener's approach to structuralism was unique. He...
3.6K