Inference for the difference of two independent normal means has been widely studied in staitstical literature. In this paper, we consider the case that the variances are unknown but with a known relationship between ...Inference for the difference of two independent normal means has been widely studied in staitstical literature. In this paper, we consider the case that the variances are unknown but with a known relationship between them. This situation arises frequently in practice, for example, when two instruments report averaged responses of the same object based on a different number of replicates, the ratio of the variances of the response is then known, and is the ratio of the number of replicates going into each response. A likelihood based method is proposed. Simulation results show that the proposed method is very accurate even when the sample sizes are small. Moreover, the proposed method can be extended to the case that the ratio of the variances is unknown.展开更多
Prediction of the progression of an infectious disease outbreak is important for planning and coordinating a response.Differential equations are often used to model an epidemic outbreak's behaviour but are challen...Prediction of the progression of an infectious disease outbreak is important for planning and coordinating a response.Differential equations are often used to model an epidemic outbreak's behaviour but are challenging to parameterise.Furthermore,these models can suffer from misspecification,which biases predictions and parameter estimates.Stochastic models can help with misspecification but are even more expensive to simulate and perform inference with.Here,we develop an explicitly likelihood-based variation of the generalised profiling method as a tool for prediction and inference under model mis-specification.Our approach allows us to carry out identifiability analysis and uncertainty quantification using profile likelihood-based methods without the need for marginalisation.We provide justification for this approach by introducing a new interpretation of the model approximation component as a stochastic constraint.This preserves the rationale for using profiling rather than integration to remove nuisance parameters while also providing a link back to stochastic models.We applied an initial version of this method during an outbreak of measles in Samoa in 2019e2020 and found that it achieved relatively fast,accurate predictions.Here we present the most recent version of our method and its application to this measles outbreak,along with additional validation.展开更多
文摘Inference for the difference of two independent normal means has been widely studied in staitstical literature. In this paper, we consider the case that the variances are unknown but with a known relationship between them. This situation arises frequently in practice, for example, when two instruments report averaged responses of the same object based on a different number of replicates, the ratio of the variances of the response is then known, and is the ratio of the number of replicates going into each response. A likelihood based method is proposed. Simulation results show that the proposed method is very accurate even when the sample sizes are small. Moreover, the proposed method can be extended to the case that the ratio of the variances is unknown.
文摘Prediction of the progression of an infectious disease outbreak is important for planning and coordinating a response.Differential equations are often used to model an epidemic outbreak's behaviour but are challenging to parameterise.Furthermore,these models can suffer from misspecification,which biases predictions and parameter estimates.Stochastic models can help with misspecification but are even more expensive to simulate and perform inference with.Here,we develop an explicitly likelihood-based variation of the generalised profiling method as a tool for prediction and inference under model mis-specification.Our approach allows us to carry out identifiability analysis and uncertainty quantification using profile likelihood-based methods without the need for marginalisation.We provide justification for this approach by introducing a new interpretation of the model approximation component as a stochastic constraint.This preserves the rationale for using profiling rather than integration to remove nuisance parameters while also providing a link back to stochastic models.We applied an initial version of this method during an outbreak of measles in Samoa in 2019e2020 and found that it achieved relatively fast,accurate predictions.Here we present the most recent version of our method and its application to this measles outbreak,along with additional validation.
