Inference in a Partially Observed Queuing Model with Applications in Ecology

Kevin Winner, Garrett Bernstein, Dan Sheldon
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:2512-2520, 2015.

Abstract

We consider the problem of inference in a probabilistic model for transient populations where we wish to learn about arrivals, departures, and population size over all time, but the only available data are periodic counts of the population size at specific observation times. The underlying model arises in queueing theory (as an M/G/inf queue) and also in ecological models for short-lived animals such as insects. Our work applies to both systems. Previous work in the ecology literature focused on maximum likelihood estimation and made a simplifying independence assumption that prevents inference over unobserved random variables such as arrivals and departures. The contribution of this paper is to formulate a latent variable model and develop a novel Gibbs sampler based on Markov bases to perform inference using the correct, but intractable, likelihood function. We empirically validate the convergence behavior of our sampler and demonstrate the ability of our model to make much finer-grained inferences than the previous approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-winner15, title = {Inference in a Partially Observed Queuing Model with Applications in Ecology}, author = {Winner, Kevin and Bernstein, Garrett and Sheldon, Dan}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {2512--2520}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/winner15.pdf}, url = {https://proceedings.mlr.press/v37/winner15.html}, abstract = {We consider the problem of inference in a probabilistic model for transient populations where we wish to learn about arrivals, departures, and population size over all time, but the only available data are periodic counts of the population size at specific observation times. The underlying model arises in queueing theory (as an M/G/inf queue) and also in ecological models for short-lived animals such as insects. Our work applies to both systems. Previous work in the ecology literature focused on maximum likelihood estimation and made a simplifying independence assumption that prevents inference over unobserved random variables such as arrivals and departures. The contribution of this paper is to formulate a latent variable model and develop a novel Gibbs sampler based on Markov bases to perform inference using the correct, but intractable, likelihood function. We empirically validate the convergence behavior of our sampler and demonstrate the ability of our model to make much finer-grained inferences than the previous approach.} }
Endnote
%0 Conference Paper %T Inference in a Partially Observed Queuing Model with Applications in Ecology %A Kevin Winner %A Garrett Bernstein %A Dan Sheldon %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-winner15 %I PMLR %P 2512--2520 %U https://proceedings.mlr.press/v37/winner15.html %V 37 %X We consider the problem of inference in a probabilistic model for transient populations where we wish to learn about arrivals, departures, and population size over all time, but the only available data are periodic counts of the population size at specific observation times. The underlying model arises in queueing theory (as an M/G/inf queue) and also in ecological models for short-lived animals such as insects. Our work applies to both systems. Previous work in the ecology literature focused on maximum likelihood estimation and made a simplifying independence assumption that prevents inference over unobserved random variables such as arrivals and departures. The contribution of this paper is to formulate a latent variable model and develop a novel Gibbs sampler based on Markov bases to perform inference using the correct, but intractable, likelihood function. We empirically validate the convergence behavior of our sampler and demonstrate the ability of our model to make much finer-grained inferences than the previous approach.
RIS
TY - CPAPER TI - Inference in a Partially Observed Queuing Model with Applications in Ecology AU - Kevin Winner AU - Garrett Bernstein AU - Dan Sheldon BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-winner15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 2512 EP - 2520 L1 - http://proceedings.mlr.press/v37/winner15.pdf UR - https://proceedings.mlr.press/v37/winner15.html AB - We consider the problem of inference in a probabilistic model for transient populations where we wish to learn about arrivals, departures, and population size over all time, but the only available data are periodic counts of the population size at specific observation times. The underlying model arises in queueing theory (as an M/G/inf queue) and also in ecological models for short-lived animals such as insects. Our work applies to both systems. Previous work in the ecology literature focused on maximum likelihood estimation and made a simplifying independence assumption that prevents inference over unobserved random variables such as arrivals and departures. The contribution of this paper is to formulate a latent variable model and develop a novel Gibbs sampler based on Markov bases to perform inference using the correct, but intractable, likelihood function. We empirically validate the convergence behavior of our sampler and demonstrate the ability of our model to make much finer-grained inferences than the previous approach. ER -
APA
Winner, K., Bernstein, G. & Sheldon, D.. (2015). Inference in a Partially Observed Queuing Model with Applications in Ecology. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:2512-2520 Available from https://proceedings.mlr.press/v37/winner15.html.

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