Bayesian Inference, Model Selection and Likelihood Estimation using Fast Rejection Sampling: The Conway-Maxwell-Poisson Distribution

Abstract In epidemiological modelling, the instantaneous reproduction number, Rt, is important to understand the transmission dynamics of infectious diseases. Current Rt estimates often suffer from problems such as lagging, averaging and uncertainties demoting the usefulness of Rt. To address these problems, we propose a new method in the framework of sequential Bayesian inference where a Data Assimilation approach is taken for Rt estimation, resulting in the state-of-the-art ‘DARt’ system for Rt estimation. With DARt, the problem of time misalignment caused by lagging observations is tackled by incorporating observation delays into the joint inference of infections and Rt; the drawback of averaging is improved by instantaneous updating upon new observations and a model selection mechanism capturing abrupt changes caused by interventions; the uncertainty is quantified and reduced by employing Bayesian smoothing. We validate the performance of DARt through simulations and demonstrate its power in revealing the transmission dynamics of COVID-19.

Download Full-text

Supplemental Material for A Bayesian Inference Model for Metamemory

Psychological Review ◽

10.1037/rev0000270.supp ◽

2021 ◽

Keyword(s):

Bayesian Inference ◽

Inference Model

Download Full-text

Estimating Rainfall Design Values for the City of Oslo, Norway—Comparison of Methods and Quantification of Uncertainty

Water ◽

10.3390/w12061735 ◽

2020 ◽

Vol 12 (6) ◽

pp. 1735 ◽

Cited By ~ 1

Author(s):

Julia Lutz ◽

Lars Grinde ◽

Anita Verpe Dyrrdal

Keyword(s):

Bayesian Inference ◽

Goodness Of Fit ◽

Bayesian Method ◽

Gumbel Distribution ◽

Likelihood Estimation ◽

Current Method ◽

Credible Interval ◽

Computational Method ◽

Goodness Of Fit Tests ◽

Idf Curves

Due to its location, its old sewage system, and the channelling of rivers, Oslo is highly exposed to urban flooding. Thus, it is crucial to provide relevant and reliable information on extreme precipitation in the planning and design of infrastructure. Intensity-Duration-Frequency (IDF) curves are a frequently used tool for that purpose. However, the computational method for IDF curves in Norway was established over 45 years ago, and has not been further developed since. In our study, we show that the current method of fitting a Gumbel distribution to the highest precipitation events is not able to reflect the return values for the long return periods. Instead, we introduce the fitting of a Generalised Extreme Value (GEV) distribution for annual maximum precipitation in two different ways, using (a) a modified Maximum Likelihood estimation and (b) Bayesian inference. The comparison of the two methods for 14 stations in and around Oslo reveals that the estimated median return values are very similar, but the Bayesian method provides upper credible interval boundaries that are considerably higher. Two different goodness-of-fit tests favour the Bayesian method; thus, we suggest using the Bayesian inference for estimating IDF curves for the Oslo area.

Download Full-text

Fast leave-one-out methods for inference, model selection, and diagnostic checking

The Stata Journal Promoting communications on statistics and Stata ◽

10.1177/1536867x20976312 ◽

2020 ◽

Vol 20 (4) ◽

pp. 785-804

Author(s):

Federico Belotti ◽

Franco Peracchi

Keyword(s):

Model Selection ◽

Full Advantage ◽

Cross Validation ◽

Computing Time ◽

Substantial Reduction ◽

Inference Model ◽

Diagnostic Measures ◽

Diagnostic Checking ◽

Linear Estimators ◽

Leave One Out

In this article, we describe jackknife2, a new prefix command for jackknifing linear estimators. It takes full advantage of the available leave-one-out formula, thereby allowing for substantial reduction in computing time. Of special note is that jackknife2 allows the user to compute cross-validation and diagnostic measures that are currently not available after ivregress 2sls, xtreg, and xtivregress.

Download Full-text

River water quality modelling and simulation based on Markov Chain Monte Carlo computation and Bayesian inference model

African Journal of Science Technology Innovation and Development ◽

10.1080/20421338.2019.1692460 ◽

2020 ◽

Vol 12 (6) ◽

pp. 771-785 ◽

Cited By ~ 1

Author(s):

Mrunmayee Manjari Sahoo ◽

Kanhu Charan Patra

Keyword(s):

Water Quality ◽

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Bayesian Inference ◽

Water Quality Modelling ◽

Inference Model ◽

Monte Carlo Computation ◽

Simulation Based ◽

River Water Quality Modelling

Download Full-text

Bayesian Inference and Testing Any Hypothesis You Can Specify

Advances in Methods and Practices in Psychological Science ◽

10.1177/2515245918773087 ◽

2018 ◽

Vol 1 (2) ◽

pp. 281-295 ◽

Cited By ~ 6

Author(s):

Alexander Etz ◽

Julia M. Haaf ◽

Jeffrey N. Rouder ◽

Joachim Vandekerckhove

Keyword(s):

Bayesian Inference ◽

Model Selection ◽

Hypothesis Testing ◽

Likelihood Ratio ◽

Special Form ◽

Null Hypothesis ◽

Bayes Factor ◽

Alternative Hypotheses ◽

Competing Models

Hypothesis testing is a special form of model selection. Once a pair of competing models is fully defined, their definition immediately leads to a measure of how strongly each model supports the data. The ratio of their support is often called the likelihood ratio or the Bayes factor. Critical in the model-selection endeavor is the specification of the models. In the case of hypothesis testing, it is of the greatest importance that the researcher specify exactly what is meant by a “null” hypothesis as well as the alternative to which it is contrasted, and that these are suitable instantiations of theoretical positions. Here, we provide an overview of different instantiations of null and alternative hypotheses that can be useful in practice, but in all cases the inferential procedure is based on the same underlying method of likelihood comparison. An associated app can be found at https://osf.io/mvp53/ . This article is the work of the authors and is reformatted from the original, which was published under a CC-By Attribution 4.0 International license and is available at https://psyarxiv.com/wmf3r/ .

Download Full-text

Impact of the Uncertainties of the RAOs of a Semisubmersible Platform on the Performance of a Motion-Based Wave Inference Method

Volume 7A: Ocean Engineering ◽

10.1115/omae2019-96670 ◽

2019 ◽

Author(s):

J. Mas-Soler ◽

Pedro C. de Mello ◽

Eduardo A. Tannuri ◽

Alexandre N. Simos ◽

A. Souto-Iglesias

Keyword(s):

Bayesian Inference ◽

Transfer Functions ◽

Inference Model ◽

Sea State ◽

Statistical Errors ◽

Regularization Parameters ◽

Ill Posed ◽

State Estimations ◽

The Impact ◽

Mathematical Process

Abstract Motion based wave inference allows the estimation of the directional sea spectrum from the measured motions of a vessel. Solving the resulting inverse problem is challenging as it is often ill-posed; as a matter of fact, statistical errors of the estimated platform response functions (RAOs) may lead to misleading estimations of the sea states as many noise values are severely amplified in the mathematical process. Hence, in order to obtain reliable estimations of the sea conditions some hypothesis must be included by means of regularization parameters. This work discusses how these errors affect the regularization parameters and the accuracy of the sea state estimations. For this purpose, a statistical quantification of the errors associated to the estimated transfer functions has been included in an expanded Bayesian inference approach. Then, the resulting statistical inference model has been verified by means of a comparison between the outputs of this approach and those obtained without considering the statistical errors in the Bayesian inference. The assessment of the impact on the accuracy of the estimations is based on the results of a dedicated model-scale experimental campaign, which includes more than 150 different test conditions.

Download Full-text