A natural prior probability distribution derived from the propositional calculus

1994 ◽  
Vol 70 (3) ◽  
pp. 243-285 ◽  
Author(s):  
J.B. Paris ◽  
A. Vencovská ◽  
G.M. Wilmers
Keyword(s):  
Probability Distribution ◽  
Prior Probability ◽  
Propositional Calculus ◽  
Prior Probability Distribution

scholarly journals A Bayesian Inference Method Using Monte Carlo Sampling for Estimating the Number of Communities in Bipartite Networks

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Guo-Zheng Wang ◽  
Li Xiong ◽  
Hu-Chen Liu
Keyword(s):  
Monte Carlo ◽  
Bayesian Inference ◽  
Probability Distribution ◽  
Community Detection ◽  
Degree Distribution ◽  
Prior Probability ◽  
Bipartite Networks ◽  
Inference Method ◽  
Prior Probability Distribution ◽  
Bayesian Inference Method

Community detection is an important analysis task for complex networks, including bipartite networks, which consist of nodes of two types and edges connecting only nodes of different types. Many community detection methods take the number of communities in the networks as a fixed known quantity; however, it is impossible to give such information in advance in real-world networks. In our paper, we propose a projection-free Bayesian inference method to determine the number of pure-type communities in bipartite networks. This paper makes the following contributions: (1) we present the first principle derivation of a practical method, using the degree-corrected bipartite stochastic block model that is able to deal with networks with broad degree distributions, for estimating the number of pure-type communities of bipartite networks; (2) a prior probability distribution is proposed over the partition of a bipartite network; (3) we design a Monte Carlo algorithm incorporated with our proposed method and prior probability distribution. We give a demonstration of our algorithm on synthetic bipartite networks including an easy case with a homogeneous degree distribution and a difficult case with a heterogeneous degree distribution. The results show that the algorithm gives the correct number of communities of synthetic networks in most cases and outperforms the projection method especially in the networks with heterogeneous degree distributions.

Implicitly localized MCMC sampler to cope with nonlocal/nonlinear data constraints in large-size inverse problems

2020 ◽  
Author(s):  
Jean-Michel Brankart
Keyword(s):  
Probability Distribution ◽  
Inverse Problems ◽  
Large Scale ◽  
Prior Probability ◽  
Practical Applications ◽  
Posterior Probability Distribution ◽  
Prior Probability Distribution ◽  
Large Size ◽  
Non Gaussian ◽  
Nonlocal Nonlinear

<p>Many practical applications involve the resolution of large-size inverse problems, without providing more than a moderate-size sample to describe the prior probability distribution. In this situation, additional information must be supplied to augment the effective dimension of the available sample, for instance using a covariance localization approach. In this study, it is suggested that covariance localization can be efficiently applied to an approximate variant of the Metropolis/Hastings algorithm, by modulating the ensemble members by the large-scale patterns of other members. Modulation is used to design a (global) proposal probability distribution (i) that can be sampled at a very low cost, (ii) that automatically accounts for a localized prior covariance, and (iii) that leads to an efficient sampler for the augmented prior probability distribution or for the posterior probability distribution. The resulting algorithm is applied to an academic example, illustrating (i) the effectiveness of covariance localization, (ii) the ability of the method to deal with nonlocal/nonlinear observation operators and non-Gaussian observation errors, (iii) the reliability, resolution and optimality of the updated ensemble, using probabilistic scores appropriate to a non-Gaussian posterior distribution, and (iv) the scalability of the algorithm as a function of the size of the problem. The codes are openly available from github.com/brankart/ensdam.</p>

Prior probabilities and thermal characteristics of heat engines

Open Physics ◽  
2012 ◽  
Vol 10 (3) ◽  
Author(s):  
Preety Aneja ◽  
Ramandeep Johal
Keyword(s):  
Probability Distribution ◽  
Bayesian Approach ◽  
Prior Information ◽  
Prior Probability ◽  
Thermal Characteristics ◽  
Complete Information ◽  
Otto Cycle ◽  
Prior Probabilities ◽  
Prior Probability Distribution ◽  
Heat Engines

AbstractThe thermal characteristics of a heat cycle are studied from a Bayesian approach. In this approach, we assign a certain prior probability distribution to an uncertain parameter of the system. Based on that prior, we study the expected behaviour of the system and it has been found that even in the absence of complete information, we obtain thermodynamic-like behaviour of the system. Two models of heat cycles, the quantum Otto cycle and the classical Otto cycle are studied from this perspective. Various expressions for thermal efficiences can be obtained with a generalised prior of the form Π(x) ∝ 1/x b. The predicted thermodynamic behaviour suggests a connection between prior information about the system and thermodynamic features of the system.

scholarly journals Numeral terms and the predictive potential of Bayesian updating

2021 ◽  
Vol 18 (3) ◽  
pp. 359-390
Author(s):  
Izabela Skoczeń ◽  
Aleksander Smywiński-Pohl
Keyword(s):  
Probability Distribution ◽  
Predictive Power ◽  
Prior Probability ◽  
Empirical Support ◽  
Bayesian Updating ◽  
Modeling Language ◽  
Human Reasoning ◽  
Descriptive Model ◽  
Language Understanding ◽  
Prior Probability Distribution

Abstract In the experiment described in the paper Noah Goodman & Andreas Stuhlmüller. 2013. Knowledge and im-plicature: Modeling language understanding as social cognition. Topics in Cognitive Science 5(1). 173–184, empirical support was provided for the predictive power of the Rational Speech Act (RSA) model concerning the interpretation of utterances employing numerals in uncertainty contexts. The RSA predicts a Bayesian interdependence between beliefs about the probability distribution of the occurrence of an event prior to receiving information and the updated probability distribution after receiving information. In this paper we analyze whether the RSA is a descriptive or a normative model. We present the results of two analogous experiments carried out in Polish. The first experiment does not replicate the original empirical results. We find that this is due to different answers on the prior probability distribution. However, the model predicts the different results on the basis of different collected priors: Bayesian updating predicts human reasoning. By contrast, the second experiment, where the answers on the prior probability distribution are as predicted, is a replication of the original results. In light of these results we conclude that the RSA is a robust, descriptive model, however, the experimental assumptions pertaining to the experimental setting adopted by Goodman and Stuhlmüller are normative.

scholarly journals Bayesian estimation of the seroprevalence of antibodies to SARS-CoV-2

JAMIA Open ◽  
2020 ◽  
Author(s):  
Qunfeng Dong ◽  
Xiang Gao
Keyword(s):  
Probability Distribution ◽  
Large Scale ◽  
Prior Probability ◽  
Probability Distributions ◽  
Single Point ◽  
Point Estimates ◽  
Specificity And Sensitivity ◽  
Large Scale Dataset ◽  
The Us ◽  
Antibody Tests

Abstract Accurate estimations of the seroprevalence of antibodies to severe acute respiratory syndrome coronavirus 2 need to properly consider the specificity and sensitivity of the antibody tests. In addition, prior knowledge of the extent of viral infection in a population may also be important for adjusting the estimation of seroprevalence. For this purpose, we have developed a Bayesian approach that can incorporate the variabilities of specificity and sensitivity of the antibody tests, as well as the prior probability distribution of seroprevalence. We have demonstrated the utility of our approach by applying it to a recently published large-scale dataset from the US CDC, with our results providing entire probability distributions of seroprevalence instead of single-point estimates. Our Bayesian code is freely available at https://github.com/qunfengdong/AntibodyTest.

Bayesian Inference for the Demand of Engineering Products

2012 ◽  
Author(s):  
Ali E. Abbas ◽  
George A. Hazelrigg ◽  
Mahmood Alkindi
Keyword(s):  
Bayesian Inference ◽  
Probability Distribution ◽  
Expected Utility ◽  
Prior Probability ◽  
Consumer Preferences ◽  
Demand Estimation ◽  
Market Analysis ◽  
Design Parameters ◽  
The Given ◽  
Multiple Units

Within the context of a profit making firm, the job of a design engineer is to choose design parameters and product attributes that maximize the expected utility of profit. To do this effectively, the engineer needs to have an estimate of the demand for the product as a function of its price and its attributes. The firm may conduct a survey to elicit consumer preferences for the product at a given price and would like to update their belief about demand given the survey data. The purpose of this paper is to present a Bayesian methodology for demand estimation that meets this need. The estimation process begins with a prior probability distribution of demand at a given price. Using Bayesian analysis, we show how to update demand for the product given various pieces of information such as market analysis, polls and a variety of other methods. We also discuss situations where consumers can demand multiple units of the product at the given price.

The Author Problem: Bayesian Inference with Two Hypotheses

2019 ◽  
pp. 48-60
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Bayesian Inference ◽  
Probability Distribution ◽  
Posterior Probability ◽  
Prior Probability ◽  
Alternative Hypothesis ◽  
Alexander Hamilton ◽  
James Madison ◽  
Federalist Papers ◽  
The Federalist ◽  
The Federalist Papers

The “Author Problem” provides a concrete example of Bayesian inference. This chapter draws on work by Frederick Mosteller and David Wallace, who used Bayesian inference to assign authorship for unsigned Federalist Papers. The Federalist Papers were a collection of papers known to be written during the American Revolution. However, some papers were unsigned by the author, resulting in disputed authorship. The chapter provides a very basic Bayesian analysis of the unsigned “Paper 54,” which was written by Alexander Hamilton or James Madison. The example illustrates the principles of Bayesian inference for two competing hypotheses, including the concepts of alternative hypothesis, prior probability distribution, posterior probability distribution, prior probability of a hypothesis, likelihood of the observed data, and posterior probability of a hypothesis.

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