Estimating parameters from multiple time series of population dynamics using Bayesian inference

AbstractEmpirical time series of interacting entities, e.g. species abundances, are highly useful to study ecological mechanisms. Mathematical models are valuable tools to further elucidate those mechanisms and underlying processes. However, obtaining an agreement between model predictions and experimental observations remains a demanding task. As models always abstract from reality one parameter often summarizes several properties. Parameter measurements are performed in additional experiments independent of the ones delivering the time series. Transferring these parameter values to different settings may result in incorrect parametrizations. On top of that, the properties of organisms and thus the respective parameter values may vary considerably. These issues limit the use of a priori model parametrizations.In this study, we present a method suited for a direct estimation of model parameters and their variability from experimental time series data. We combine numerical simulations of a continuous-time dynamical population model with Bayesian inference, using a hierarchical framework that allows for variability of individual parameters. The method is applied to a comprehensive set of time series from a laboratory predator-prey system that features both steady states and cyclic population dynamics.Our model predictions are able to reproduce both steady states and cyclic dynamics of the data. Additionally to the direct estimates of the parameter values, the Bayesian approach also provides their uncertainties. We found that fitting cyclic population dynamics, which contain more information on the process rates than steady states, yields more precise parameter estimates. We detected significant variability among parameters of different time series and identified the variation in the maximum growth rate of the prey as a source for the transition from steady states to cyclic dynamics.By lending more flexibility to the model, our approach facilitates parametrizations and shows more easily which patterns in time series can be explained also by simple models. Applying Bayesian inference and dynamical population models in conjunction may help to quantify the profound variability in organismal properties in nature.

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Are predator-prey model predictions supported by empirical data? Evidence for a storm-driven shift to an alternative stable state in a crab-clam system

Marine Ecology Progress Series ◽

10.3354/meps13368 ◽

2020 ◽

Vol 645 ◽

pp. 83-90

Author(s):

CN Glaspie ◽

RD Seitz ◽

RN Lipcius

Keyword(s):

Time Series ◽

Empirical Data ◽

Time Series Data ◽

Steady States ◽

Series Data ◽

Low Density ◽

Predator Prey ◽

Predator Prey Model ◽

Model Predictions ◽

Analysis Of Time Series

A dynamic systems approach can predict steady states in predator-prey interactions, but there are very few examples of predictions from predator-prey models conforming to empirical data. Here, we examined the evidence for the low-density steady state predicted by a Lotka-Volterra model of a crab-clam predator-prey system using data from long-term monitoring, and data from a previously published field survey and field predation experiment. Changepoint analysis of time series data indicate that a shift to low density occurred for the soft-shell clam Mya arenaria in 1972, the year of Tropical Storm Agnes. A possible mechanism for the shift is that Agnes altered predator-prey dynamics between M. arenaria and the blue crab Callinectes sapidus, shifting from a system controlled from the bottom up by prey resources, to a system controlled from the top down by predation pressure on bivalves, which is supported by a correlation analysis of time series data. Predator-prey ordinary differential equation models with these 2 species were analyzed for steady states, and low-density steady states were similar to previously published clam densities and mortality rates, consistent with the idea that C. sapidus is a major driver of M. arenaria population dynamics. Relatively simple models can predict shifts to alternative stable states, as shown by agreement between model predictions (this study) and published field data in this system. The preponderance of multispecies interactions exhibiting nonlinear dynamics indicates that this may be a general phenomenon.

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Cosinor Analysis for Temperature Time Series Data of Long Duration

Biological Research For Nursing ◽

10.1177/1099800407303509 ◽

2007 ◽

Vol 9 (1) ◽

pp. 30-41 ◽

Cited By ~ 7

Author(s):

Nikhil S. Padhye ◽

Sandra K. Hanneman

Keyword(s):

Time Series ◽

Time Series Data ◽

Model Fit ◽

Series Data ◽

Model Parameters ◽

Cosinor Analysis ◽

Long Time ◽

Improved Model ◽

Data Length ◽

Cosinor Models

The application of cosinor models to long time series requires special attention. With increasing length of the time series, the presence of noise and drifts in rhythm parameters from cycle to cycle lead to rapid deterioration of cosinor models. The sensitivity of amplitude and model-fit to the data length is demonstrated for body temperature data from ambulatory menstrual cycling and menopausal women and from ambulatory male swine. It follows that amplitude comparisons between studies cannot be made independent of consideration of the data length. Cosinor analysis may be carried out on serial-sections of the series for improved model-fit and for tracking changes in rhythm parameters. Noise and drift reduction can also be achieved by folding the series onto a single cycle, which leads to substantial gains in the model-fit but lowers the amplitude. Central values of model parameters are negligibly changed by consideration of the autoregressive nature of residuals.

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Hybrid Evolutionary Algorithm for Rule Set Discovery in Time-Series Data to Forecast and Explain Algal Population Dynamics in Two Lakes Different in Morphometry and Eutrophication

Ecological Informatics ◽

10.1007/3-540-28426-5_17 ◽

2006 ◽

pp. 347-367 ◽

Cited By ~ 7

Author(s):

H. Cao ◽

F. Recknagel ◽

B. Kim ◽

N. Takamura

Keyword(s):

Time Series ◽

Population Dynamics ◽

Evolutionary Algorithm ◽

Time Series Data ◽

Series Data ◽

Algal Population ◽

Hybrid Evolutionary Algorithm ◽

Rule Set

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Simulating tubulin-associated unit transport in an axon: using bootstrapping for estimating confidence intervals of best-fit parameter values obtained from indirect experimental data

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2017.0045 ◽

2017 ◽

Vol 473 (2201) ◽

pp. 20170045 ◽

Cited By ~ 7

Author(s):

I. A. Kuznetsov ◽

A. V. Kuznetsov

Keyword(s):

Experimental Data ◽

Confidence Intervals ◽

Surrogate Data ◽

Model Parameters ◽

Model Predictions ◽

Estimate Parameter ◽

Minimum Number ◽

Percentile Bootstrap ◽

Parameter Values ◽

Best Fit

In this paper, we first develop a model of axonal transport of tubulin-associated unit (tau) protein. We determine the minimum number of parameters necessary to reproduce published experimental results, reducing the number of parameters from 18 in the full model to eight in the simplified model. We then address the following questions: Is it possible to estimate parameter values for this model using the very limited amount of published experimental data? Furthermore, is it possible to estimate confidence intervals for the determined parameters? The idea that is explored in this paper is based on using bootstrapping. Model parameters were estimated by minimizing the objective function that simulates the discrepancy between the model predictions and experimental data. Residuals were then identified by calculating the differences between the experimental data and model predictions. New, surrogate ‘experimental’ data were generated by randomly resampling residuals. By finding sets of best-fit parameters for a large number of surrogate data the histograms for the model parameters were produced. These histograms were then used to estimate confidence intervals for the model parameters, by using the percentile bootstrap. Once the model was calibrated, we applied it to analysing some features of tau transport that are not accessible to current experimental techniques.

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Pemodelan Harga Beras di Pulau Sumatera dengan Menggunakan Model Generalized Space Time ARIMA

Xplore Journal of Statistics ◽

10.29244/xplore.v2i2.105 ◽

2018 ◽

Vol 2 (2) ◽

pp. 49-57

Author(s):

Dwi Yulianti ◽

I Made Sumertajaya ◽

Itasia Dina Sulvianti

Keyword(s):

Time Series ◽

Time Series Data ◽

Moving Average ◽

Space Time ◽

Series Data ◽

Model Parameters ◽

Autoregressive Integrated Moving Average ◽

Sumatra Island ◽

Rice Price ◽

Multiple Variables

Generalized space time autoregressive integrated moving average (GSTARIMA) model is a time series model of multiple variables with spatial and time linkages (space time). GSTARIMA model is an extension of the space time autoregressive integrated moving average (STARIMA) model with the assumption that each location has unique model parameters, thus GSTARIMA model is more flexible than STARIMA model. The purposes of this research are to determine the best model and predict the time series data of rice price on all provincial capitals of Sumatra island using GSTARIMA model. This research used weekly data of rice price on all provincial capitals of Sumatra island from January 2010 to December 2017. The spatial weights used in this research are the inverse distance and queen contiguity. The modeling result shows that the best model is GSTARIMA (1,1,0) with queen contiguity weighted matrix and has the smallest MAPE value of 1.17817 %.

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A Bayesian approach to modeling phytoplankton population dynamics from size distribution time series

PLoS Computational Biology ◽

10.1371/journal.pcbi.1009733 ◽

2022 ◽

Vol 18 (1) ◽

pp. e1009733

Author(s):

Jann Paul Mattern ◽

Kristof Glauninger ◽

Gregory L. Britten ◽

John R. Casey ◽

Sangwon Hyun ◽

...

Keyword(s):

Time Series ◽

Population Dynamics ◽

Size Distribution ◽

Bayesian Approach ◽

Critical Parameters ◽

Microbial Populations ◽

Series Data ◽

Matrix Population Models ◽

Modeling Framework ◽

Phytoplankton Population

The rates of cell growth, division, and carbon loss of microbial populations are key parameters for understanding how organisms interact with their environment and how they contribute to the carbon cycle. However, the invasive nature of current analytical methods has hindered efforts to reliably quantify these parameters. In recent years, size-structured matrix population models (MPMs) have gained popularity for estimating division rates of microbial populations by mechanistically describing changes in microbial cell size distributions over time. Motivated by the mechanistic structure of these models, we employ a Bayesian approach to extend size-structured MPMs to capture additional biological processes describing the dynamics of a marine phytoplankton population over the day-night cycle. Our Bayesian framework is able to take prior scientific knowledge into account and generate biologically interpretable results. Using data from an exponentially growing laboratory culture of the cyanobacterium Prochlorococcus, we isolate respiratory and exudative carbon losses as critical parameters for the modeling of their population dynamics. The results suggest that this modeling framework can provide deeper insights into microbial population dynamics provided by size distribution time-series data.

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Polynomial Chaos Based Solution to Inverse Problems in Petroleum Reservoir Engineering

Volume 5: Multiphase Flow ◽

10.1115/ajkfluids2019-5291 ◽

2019 ◽

Author(s):

Sufia Khatoon ◽

Jyoti Phirani ◽

Supreet Singh Bahga

Keyword(s):

Bayesian Inference ◽

History Matching ◽

Polynomial Chaos ◽

Reservoir Engineering ◽

Model Parameters ◽

Petroleum Reservoir ◽

Model Predictions ◽

Production History ◽

Porosity And Permeability ◽

Computationally Expensive

Abstract In reservoir simulations, model parameters such as porosity and permeability are often uncertain and therefore better estimates of these parameters are obtained by matching the simulation predictions with the production history. Bayesian inference provides a convenient way of estimating parameters of a mathematical model, starting from a probable range of parameter values and knowing the production history. Bayesian inference techniques for history matching require computationally expensive Monte Carlo simulations, which limit their use in petroleum reservoir engineering. To overcome this limitation, we perform accelerated Bayesian inference based history matching by employing polynomial chaos (PC) expansions to represent random variables and stochastic processes. As a substitute to computationally expensive Monte Carlo simulations, we use a stochastic technique based on PC expansions for propagation of uncertainty from model parameters to model predictions. The PC expansions of the stochastic variables are obtained using relatively few deterministic simulations, which are then used to calculate the probability density of the model predictions. These results are used along with the measured data to obtain a better estimate (posterior distribution) of the model parameters using the Bayes rule. We demonstrate this method for history matching using an example case of SPE1CASE2 problem of SPEs Comparative Solution Projects. We estimate the porosity and permeability of the reservoir from limited and noisy production data.

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Improved supervised learning methods for EoR parameters reconstruction

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz2429 ◽

2019 ◽

Vol 490 (1) ◽

pp. 371-384 ◽

Cited By ~ 3

Author(s):

Aristide Doussot ◽

Evan Eames ◽

Benoit Semelin

Keyword(s):

Neural Network ◽

Neural Networks ◽

Bayesian Inference ◽

Maximum Likelihood ◽

Supervised Learning ◽

Confidence Level ◽

Thermal Noise ◽

Model Parameters ◽

Learning Methods ◽

Parameter Values

ABSTRACT Within the next few years, the Square Kilometre Array (SKA) or one of its pathfinders will hopefully detect the 21-cm signal fluctuations from the Epoch of Reionization (EoR). Then, the goal will be to accurately constrain the underlying astrophysical parameters. Currently, this is mainly done with Bayesian inference. Recently, neural networks have been trained to perform inverse modelling and, ideally, predict the maximum-likelihood values of the model parameters. We build on these by improving the accuracy of the predictions using several supervised learning methods: neural networks, kernel regressions, or ridge regressions. Based on a large training set of 21-cm power spectra, we compare the performances of these methods. When using a noise-free signal generated by the model itself as input, we improve on previous neural network accuracy by one order of magnitude and, using a local ridge kernel regression, we gain another factor of a few. We then reach an accuracy level on the reconstruction of the maximum-likelihood parameter values of a few per cents compared the 1σ confidence level due to SKA thermal noise (as estimated with Bayesian inference). For an input signal affected by an SKA-like thermal noise but constrained to yield the same maximum-likelihood parameter values as the noise-free signal, our neural network exhibits an error within half of the 1σ confidence level due to the SKA thermal noise. This accuracy improves to 10$\, {\rm per\, cent}$ of the 1σ level when using the local ridge kernel. We are thus reaching a performance level where supervised learning methods are a viable alternative to determine the maximum-likelihood parameters values.

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Random order autoregressive time series model with structural break

Model Assisted Statistics and Applications ◽

10.3233/mas-200490 ◽

2020 ◽

Vol 15 (3) ◽

pp. 225-237

Author(s):

Saurabh Kumar ◽

Jitendra Kumar ◽

Vikas Kumar Sharma ◽

Varun Agiwal

Keyword(s):

Time Series ◽

Structural Breaks ◽

Time Series Data ◽

Structural Break ◽

Random Order ◽

Real Data ◽

Series Data ◽

Model Parameters ◽

Multiple Time ◽

Multiple Time Points

This paper deals with the problem of modelling time series data with structural breaks occur at multiple time points that may result in varying order of the model at every structural break. A flexible and generalized class of Autoregressive (AR) models with multiple structural breaks is proposed for modelling in such situations. Estimation of model parameters are discussed in both classical and Bayesian frameworks. Since the joint posterior of the parameters is not analytically tractable, we employ a Markov Chain Monte Carlo method, Gibbs sampling to simulate posterior sample. To verify the order change, a hypotheses test is constructed using posterior probability and compared with that of without breaks. The methodologies proposed here are illustrated by means of simulation study and a real data analysis.

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