Using Particle Filters to Analyse the Credibility in Model Predictions

2015 ◽  
Vol 807 ◽  
pp. 218-225
Author(s):  
Peter Lewis Green
Keyword(s):  
Bayesian Approach ◽  
Particle Filters ◽  
Parameter Estimates ◽  
Model Predictions ◽  
Bayesian Tracking ◽  
Time Invariant

Models are often used to make predictions far from the region where they were trained and validated. In this paper attempts are made to analyse the credibility that can be placed in such predictions. The proposed approach involves treating a model’s parameters as time-variant (even if it is believed that this is not the case), before utilising Bayesian tracking techniques to realise parameter estimates. An example is used to demonstrate that, relative to a Bayesian approach where the parameters are assumed to be time-invariant, treating the parameters as time-variant can reveal important flaws in the model and raise questions about its ability to make credible predictions.

Theoretical investigation into the dissolved oxygen levels in follicular fluid of the developing human follicle using mathematical modelling

2008 ◽  
Vol 20 (3) ◽  
pp. 408 ◽  
Author(s):  
Gabe P. Redding ◽  
John E. Bronlund ◽  
Alan L. Hart
Keyword(s):  
Dissolved Oxygen ◽  
Mathematical Modelling ◽  
Follicular Fluid ◽  
Ovarian Follicle ◽  
Quantitative Description ◽  
Parameter Estimates ◽  
Published Data ◽  
Human Follicular Fluid ◽  
Oxygen Levels ◽  
Model Predictions

Oxygen levels in the follicle are likely to be critical to follicle development. However, a quantitative description of oxygen levels in the follicle is lacking. Mathematical modelling was used to predict the dissolved oxygen levels in the follicular fluid of the developing human follicle. The model predictions showed that follicular fluid dissolved oxygen levels are highly variable among follicles, due to the unique geometry of individual follicles. More generally, predictions showed that oxygen levels in follicular fluid increase rapidly during the initial early antral stages of follicle growth before peaking in the later early antral phase. Follicular fluid dissolved oxygen levels then decline through to the beginning of the pre-ovulatory phase, from which they increase through to ovulation. Based on the best available parameter estimates, the model predictions suggest that the mean dissolved oxygen levels in human follicular fluid during the late antral and pre-ovulatory phases range between 11 and 51 mmHg (~1.5–6.7 vol%). These predictions suggest that the human ovarian follicle is a low-oxygen environment that is often challenged by hypoxia, and are in agreement with only some published data on follicular fluid oxygen levels. Predictions are discussed in relation to follicle health and oocyte culture.

scholarly journals Quantitative investigations of different vaccination policies for the control of congenital rubella syndrome (CRS) in the United Kingdom

1986 ◽  
Vol 96 (2) ◽  
pp. 305-333 ◽  
Author(s):  
R. M. Anderson ◽  
B. T. Grenfell
Keyword(s):  
Young Male ◽  
Parameter Estimates ◽  
Male And Female ◽  
Teenage Girls ◽  
Congenital Rubella ◽  
The United Kingdom ◽  
Age Related ◽  
Model Predictions ◽  
Female Children

SUMMARYThe paper examines predictions of the impact of various one-, two- and three-stage vaccination policies on the incidence of congenital rubella syndrome (CRS) in the United Kingdom with the aid of a mathematical model of the transmission dynamics of rubella virus. Parameter estimates for the model are derived from either serological data or case notifications, and special attention is given to the significance of age-related changes in the rate of exposure to rubella infection and heterogeneous mixing between age groups. Where possible, model predictions are compared with observed epidemiological trends.The principal conclusion of the analyses is that benefit is to be gained in the UK, both in the short and long term, by the introduction of a multiple-stage vaccination policy involving high levels of vaccination coverage of young male and female children (at around two years of age) and teenage girls (between the ages of 10–15 years), plus continued surveillance and vaccination of adult women in the child-bearing age classes. Model predictions suggest that to reduce the incidence of CRS in future years, below the level generated by a continuation of the current UK policy (the vaccination of teenage girls), would require high rates of vaccination > 60%) of both boys and girls at around two years of age. Numerical studies also suggest that uniform vaccination coverage levels of greater than 80–85% of young male and female children could, in the long term (40 years or more), eradicate rubella virus from the population. The robustness of these conclusions with respect to the accuracy of parameter estimates and various assumptions concerning the pattern of age-related change in exposure to infections and ‘who acquires infection from whom’ is discussed.

scholarly journals A Bayesian Approach to Estimating Reciprocal Effects with the Bivariate STARTS Model using Markov Chain Monte Carlo

2021 ◽  
Author(s):  
Oliver Lüdtke ◽  
Alexander Robitzsch ◽  
Esther Ulitzsch
Keyword(s):  
Bayesian Approach ◽  
Prior Distribution ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Reciprocal Effects ◽  
Ml Estimation ◽  
Model Parameterization ◽  
Lagged Effects ◽  
The Bayesian Approach ◽  
Over Time

The bivariate Stable Trait, AutoRegressive Trait, and State (STARTS) model provides a general approach for estimating reciprocal effects between constructs over time. However, previous research has shown that this model is difficult to estimate using the maximum likelihood (ML) method (e.g., nonconvergence). In this article, we introduce a Bayesian approach for estimating the bivariate STARTS model and implement it in the software Stan. We discuss issues of model parameterization and show how appropriate prior distributions for model parameters can be selected. Specifically, we propose the four-parameter beta distribution as a flexible prior distribution for the autoregressive and cross-lagged effects. Using a simulation study, we show that the proposed Bayesian approach provides more accurate estimates than ML estimation in challenging data constellations. An example is presented to illustrate how the Bayesian approach can be used to stabilize the parameter estimates of the bivariate STARTS model.

scholarly journals Changes in Size and Interpretation of Parameter Estimates in Within-Person Models in the Presence of Time-Invariant and Time-Varying Covariates

2021 ◽  
Vol 12 ◽  
Author(s):  
Marcus Mund ◽  
Matthew D. Johnson ◽  
Steffen Nestler
Keyword(s):  
Parameter Estimates ◽  
Methodological Research ◽  
Panel Model ◽  
Random Intercept ◽  
Curve Model ◽  
Latent Curve ◽  
Research Questions ◽  
Time Invariant ◽  
Time Varying Covariates ◽  
Reciprocal Associations

For several decades, cross-lagged panel models (CLPM) have been the dominant statistical model in relationship research for investigating reciprocal associations between two (or more) constructs over time. However, recent methodological research has questioned the frequent usage of the CLPM because, amongst other things, the model commingles within-person associations with between-person associations, while most developmental research questions pertain to within-person processes. Furthermore, the model presumes that there are no third variables that confound the relationships between the longitudinally assessed variables. Therefore, the usage of alternative models such as the Random-Intercept Cross-Lagged Panel Model (RI-CLPM) or the Latent Curve Model with Structured Residuals (LCM-SR) has been suggested. These models separate between-person from within-person variation and they also control for time constant covariates. However, there might also be third variables that are not stable but rather change across time and that can confound the relationships between the variables studied in these models. In the present article, we explain the differences between the two types of confounders and investigate how they affect the parameter estimates of within-person models such as the RI-CLPM and the LCM-SR.

scholarly journals On calculation of recursive M- and GM-estimates in LQG control systems

2008 ◽  
Vol 48 ◽  
Author(s):  
Rimantas Pupeikis
Keyword(s):  
Maximum Likelihood ◽  
Linear Time ◽  
Parametric Identification ◽  
Parameter Estimates ◽  
Linear Quadratic ◽  
Unknown Parameters ◽  
Linear Time Invariant ◽  
Identification Approach ◽  
Recursive Techniques ◽  
Time Invariant

The aim of the given paper is development of a parametric identification approach for a closedloop system when the parameters of a discrete-time linear time-invariant (LTI) dynamic system as well as that of LQG (Linear Quadratic Gaussian) controller are not known and ought to be calculated. The recursive techniques based on an the maximum likelihood(M) and generalized maximum likelihood(GM) estimator algorithms are applied here in the calculation of the system as well as noise filter parameters. Afterwards, the recursive parameter estimates are used in each current iteration to determine unknown parameters of the LQG-controller, too. The results of numerical simulation by computer are discussed.

Incorporating Prior Knowledge into the Analysis of Conjoint Studies

1995 ◽  
Vol 32 (2) ◽  
pp. 152-162 ◽  
Author(s):  
Greg M. Allenby ◽  
Neeraj Arora ◽  
James L. Ginter
Keyword(s):  
Prior Knowledge ◽  
Bayesian Approach ◽  
Prior Information ◽  
Predictive Performance ◽  
Face Validity ◽  
Parameter Estimates ◽  
Product Attribute ◽  
Specific Product ◽  
Ordinal Information ◽  
Attribute Levels

The authors use conjoint analysis to provide interval-level estimates of part-worths allowing tradeoffs among attribute levels to be examined. Researchers often possess prior information about the part-worths, such as the order and range restrictions of product attribute levels. It is known, for example, that consumers would rather pay less for a specific product given that all other product attribute levels are unchanged. The authors present a Bayesian approach to incorporate prior ordinal information about these part-worths into the analysis of conjoint studies. Their method results in parameter estimates with greater face validity and predictive performance than estimates that do not utilize prior information or those that use traditional methods such as LINMAP. Unlike existing methods, the authors’ methods apply to both rating and choice-based conjoint studies.

scholarly journals Ooid growth: Uniqueness of time-invariant, smooth shapes in 2D

2019 ◽  
Vol 31 (1) ◽  
pp. 172-182 ◽  
Author(s):  
ANDRÁS A. SIPOS
Keyword(s):  
Physical Environment ◽  
Invariant Solution ◽  
Smooth Convex ◽  
Bijective Mapping ◽  
Planar Curves ◽  
Convex Curves ◽  
Model Predictions ◽  
Geometric Equation ◽  
Time Invariant ◽  
Compact Shape

Evolution of planar curves under a nonlocal geometric equation is investigated. It models the simultaneous contraction and growth of carbonate particles called ooids in geosciences. Using classical ODE results and a bijective mapping, we demonstrate that the steady parameters associated with the physical environment determine a unique, time-invariant, compact shape among smooth, convex curves embedded in ℝ2. It is also revealed that any time-invariant solution possesses D2 symmetry. The model predictions remarkably agree with ooid shapes observed in nature.

scholarly journals Parameter estimates of general failure rate model: A Bayesian approach

2019 ◽  
Vol 351 ◽  
pp. 317-330 ◽  
Author(s):  
Asok K. Nanda ◽  
Sudhansu S. Maiti ◽  
Chanchal Kundu ◽  
Amarjit Kundu
Keyword(s):  
Failure Rate ◽  
Bayesian Approach ◽  
Parameter Estimates ◽  
Rate Model
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