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.

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.

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.

scholarly journals Increasing the time resolution of single-molecule experiments with Bayesian inference

2017 ◽  
Author(s):  
Colin D. Kinz-Thompson ◽  
Ruben L. Gonzalez
Keyword(s):  
Bayesian Inference ◽  
Single Molecule ◽  
Time Resolution ◽  
Rate Constants ◽  
Computational Approach ◽  
Biomolecular Systems ◽  
Time Resolved ◽  
The Given ◽  
Kinetics Of ◽  
Resolution Data

AbstractMany time-resolved, single-molecule biophysics experiments seek to characterize the kinetics of biomolecular systems exhibiting dynamics that challenge the time resolution of the given technique. Here we present a general, computational approach to this problem that employs Bayesian inference to learn the underlying dynamics of such systems, even when they are much faster than the time resolution of the experimental technique being used. By accurately and precisely inferring rate constants, our Bayesian Inference for the Analysis of Sub-temporal-resolution Data (BIASD) approach effectively enables the experimenter to super-resolve the poorly resolved dynamics that are present in their data.

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.

Direct Optimization of Multi-Degree-of-Freedom Mechanisms for Near Time Optimal Motions Along Specified Paths

1991 ◽  
Author(s):  
Satish Sundar ◽  
Zvi Shiller
Keyword(s):  
Design Method ◽  
Close Correlation ◽  
Optimization Methods ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Direct Optimization ◽  
Fitting Procedure ◽  
Time Optimal ◽  
Approximate Cost ◽  
The Given

Abstract A design method for selecting system parameters of multi-degree-of-freedom mechanisms for near minimum time motions along specified paths is presented. The time optimization problem is approximated by a simple curve fitting procedure that fits, what we call, the acceleration lines to the given path. The approximate cost function is explicit in the design parameters, facilitating the formulation of the design problem as a constrained optimization. Examples for optimizing the dimensions of a five-bar planar mechanism demonstrate close correlation between the approximate and the exact solutions and better computational efficiency than the previous unconstrained optimization methods.

Bayesian Inference of Information Theoretic Metrics of Anonymity

2014 ◽  
Vol 989-994 ◽  
pp. 4680-4683
Author(s):  
Han Ru Pei ◽  
Zhi Jian Wang ◽  
Yu Wang
Keyword(s):  
Bayesian Inference ◽  
Probability Distribution ◽  
Inference Method ◽  
Information Theoretic ◽  
System Parameters ◽  
Bayesian Inference Method

Information theoretic metrics is popular theory to measure anonymity. However the difficulty in getting the probability distribution of subjects hampers its practical usage. In this paper we propose a Bayesian inference method to tackle this problem. Our method makes it possible to compare the anonymity of different anonymous systems. We use this method to analyze Threshold Mix and point out different system parameters which do and do not have influence on anonymity.

Application of Design Axioms to Marine Design Problems

2000 ◽  
Author(s):  
Y. S. Yang ◽  
B. S. Jang ◽  
Y. S. Song ◽  
Y. S. Yeon ◽  
S. H. Do
Keyword(s):  
Structural Design ◽  
Probabilistic Approach ◽  
Design Stage ◽  
Design Parameters ◽  
Independence Axiom ◽  
Preliminary Design ◽  
Functional Requirements ◽  
Mapping Procedure ◽  
Information Axiom ◽  
The Given

Abstract The Design Axioms proposed by N. P. Suh consist of Independence Axiom and Information Axiom. The Independence Axiom assists a designer in generating good design alternatives by considering the relations between the functions and the physical product using a hierarchical mapping procedure. The Information Axiom, which is related to the probability of achieving the given functional requirements, can be used as a criterion for the selection of the best solution among the proposed alternatives in the conceptual or preliminary design stage. In the early stages of marine design, especially ship design, there exists a lot of uncertainty because of the size and complexity of a marine vehicle. The uncertainty often leads to a probabilistic approach rather than a deterministic approach. The ship designs are mostly routine design to change an existing design case a little. In this paper, the availability of the Design Axioms in this marine design field will be investigated through three examples. In the conceptual design of a thruster, the Independence Axiom will be proven to be useful in examining the independence of functional requirements at each level of the decomposition process. In main engine selection example, the Information Axiom will be used for selecting the best solution among the given alternatives by estimating their respective information contents under the uncertain and ambiguous condition. In the structural design, some difficulties arise in maintaining the independence of functional requirements in general because the number of design parameters is greater than that of functional requirements. Therefore, there is much trouble in generalizing the application of the Design Axioms for the structural design, especially for the preliminary design where the principal design parameters of a design object have to be determined after its shape fixed. This paper will try a generalized approach to the similarity-based design where it is important to select which parameters should be changed and in what order they should be changed. How to make use of the Design Axioms will be showed in a barge design example. However, a lot of research is needed for the generalized application of the Design Axioms for the structural design.

Correlations among some clay parameters — the multivariate distribution

2014 ◽  
Vol 51 (6) ◽  
pp. 686-704 ◽  
Author(s):  
Jianye Ching ◽  
Kok-Kwang Phoon
Keyword(s):  
Probability Distribution ◽  
Joint Distribution ◽  
Site Investigation ◽  
Liquid Limit ◽  
Design Parameters ◽  
Probability Models ◽  
Wide Range ◽  
Multivariate Probability ◽  
Data Points ◽  
Multivariate Probability Distribution

This paper constructs a 10-dimensional multivariate probability distribution covering 10 clay parameters. The parameters are the liquid limit, plasticity index (PI), liquidity index, effective vertical stress, undrained shear strength, sensitivity, and three piezocone test parameters. A CLAY/10/7490 database is compiled in a companion paper for this purpose. The database consists of 7490 data points from 251 studies. The number of data points associated with each study varies from 1 to 419 with an average 30 data points per study. The clay properties cover a wide range of overconsolidation ratios (but mostly 1∼10), a wide range of sensitivity (St) (sites with St = 1∼tens or hundreds are fairly typical), and a wide range of PI (but mostly 8∼100). The constructed multivariate probability distribution can be used as a prior distribution to derive the joint distribution of design parameters based on limited but site-specific field data. Note that the entire joint distribution of the 10 clay parameters is derived, not marginal distributions or simply means and coefficients of variation. These multiple design parameters can be updated from multiple field measurements, which is more useful than updating one design parameter using one field measurement that is typical in current practice. This paper also demonstrates that it is practical to build multivariate probability models by combining available bivariate models, which are prevalent in the geotechnical engineering correlation literature. The proposed approach circumvents the need to collect multivariate data, which are rarely found in typical site investigation programs.

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