Improved Method to Estimating Parameters of a Poisson Hidden Markov Model Using Bayesian Approach
Bibliographic record
Abstract
Expectation-Maximization (EM) is a popular method for estimating parameters of the Poisson-Hidden Markov Model (P-HMM). However, over-dispersion in comparison to the Poisson distribution remains a concern. This study developed a Bayesian method to Poisson count models. The study compares the Mean Square Errors and sufficiency of the EM to the Gibbs sampler technique using Akaike Information Criterion, Bayesian Information Criterion, and Deviance Information Criterion as model selectors. The Maximum Likelihood Estimates and Maximum a \textit{posteriori} were calculated using both simulated and real data in this case. The study's findings indicate that using any of the two approaches depends on the data type and the sample size. Whereas the Poisson Hidden Markov model, which uses the EM algorithm is preferred when using Zero-inflated data with a sample size n ≤ 20 , the Bayesian Poisson-Hidden Markov Model, which uses a Gibbs sampler is better used for Heavy and Mixture data types irrespective of the sample size. The model predicted parameters of simulated data with remarkable accuracy and produced some unique statistical property results. This method is applicable to Poisson-hidden Markov models with homogeneous time series.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".