scholarly journals Introduction to Bayesian Statistical Inference

2021 ◽  
pp. 1-13
Author(s):  
Georgios P. Karagiannis
Keyword(s):  
Statistical Analysis ◽  
Statistical Inference ◽  
Prior Information ◽  
Predictive Inference ◽  
Conjugate Priors ◽  
Bayesian Paradigm ◽  
Credible Sets ◽  
Supplementary Material ◽  
Basic Concepts ◽  
Point Estimators

AbstractWe present basic concepts of Bayesian statistical inference. We briefly introduce the Bayesian paradigm. We present the conjugate priors; a computational convenient way to quantify prior information for tractable Bayesian statistical analysis. We present tools for parametric and predictive inference, and particularly the design of point estimators, credible sets, and hypothesis tests. These concepts are presented in running examples. Supplementary material is available from GitHub.

scholarly journals Principles of Statistical Inference: Likelihood and the Bayesian Paradigm

2010 ◽  
Vol 16 ◽  
pp. 1-18 ◽  
Author(s):  
Steve C. Wang
Keyword(s):  
Maximum Likelihood ◽  
Statistical Inference ◽  
Bayesian Approach ◽  
Subjective Probability ◽  
Prior Information ◽  
Maximum Likelihood Estimators ◽  
Likelihood Ratio Tests ◽  
Bayesian Paradigm ◽  
Point Estimators ◽  
The Bayesian Approach

We review two foundations of statistical inference, the theory of likelihood and the Bayesian paradigm. We begin by applying principles of likelihood to generate point estimators (maximum likelihood estimators) and hypothesis tests (likelihood ratio tests). We then describe the Bayesian approach, focusing on two controversial aspects: the use of prior information and subjective probability. We illustrate these analyses using simple examples.

scholarly journals An Assessment of the Effects of Prior Distributions on the Bayesian Predictive Inference

2016 ◽  
Vol 5 (5) ◽  
pp. 31
Author(s):  
Azizur Rahman ◽  
Junbin Gao ◽  
Catherine D'Este ◽  
Syed Ejaz Ahmed
Keyword(s):  
Statistical Analysis ◽  
Linear Regression ◽  
Regression Models ◽  
Prior Information ◽  
Predictive Inference ◽  
Shape Parameters ◽  
Linear Regression Models ◽  
Prior Distributions ◽  
Noninformative Prior ◽  
Observable Data

Predictive inference is one of the oldest methods of statistical analysis and it is based on observable data. Prior information plays an important role in the Bayesian methodology. Researchers in this field are often subjective to exercise noninformative prior. This study tests the effects of a range of prior distributions on the Bayesian predictive inference for different modelling situations such as linear regression models under normal and Student-t errors. Findings reveal that different choice of priors not only provide different prediction distributions of the future response(s)  but also change the location and/or scale or shape parameters of the prediction distributions.

scholarly journals Bayesian sample size re-estimation using power priors

2018 ◽  
Vol 28 (6) ◽  
pp. 1664-1675 ◽  
Author(s):  
TB Brakenhoff ◽  
KCB Roes ◽  
S Nikolakopoulos
Keyword(s):  
Sample Size ◽  
Prior Information ◽  
Controlled Trial ◽  
Small Populations ◽  
Small Pilot Study ◽  
Randomized Controlled ◽  
Bayesian Paradigm ◽  
Operational Characteristics ◽  
True Variance ◽  
Bayesian Sample Size

The sample size of a randomized controlled trial is typically chosen in order for frequentist operational characteristics to be retained. For normally distributed outcomes, an assumption for the variance needs to be made which is usually based on limited prior information. Especially in the case of small populations, the prior information might consist of only one small pilot study. A Bayesian approach formalizes the aggregation of prior information on the variance with newly collected data. The uncertainty surrounding prior estimates can be appropriately modelled by means of prior distributions. Furthermore, within the Bayesian paradigm, quantities such as the probability of a conclusive trial are directly calculated. However, if the postulated prior is not in accordance with the true variance, such calculations are not trustworthy. In this work we adapt previously suggested methodology to facilitate sample size re-estimation. In addition, we suggest the employment of power priors in order for operational characteristics to be controlled.

scholarly journals COVID-19 In United States: Statistical Analysis and Inferences From the Empirical Data

2021 ◽  
Author(s):  
Nivedita Rethnakar
Keyword(s):  
United States ◽  
Statistical Analysis ◽  
Statistical Inference ◽  
Empirical Data ◽  
Respiratory Diseases ◽  
Temporal Dynamics ◽  
The United States ◽  
Mortality Statistics ◽  
Race Ethnicity ◽  
The Impact

Abstract This paper investigates the mortality statistics of the COVID-19 pandemic from the United States perspective. Using empirical data analysis and statistical inference tools, we bring out several exciting and important aspects of the pandemic, otherwise hidden. Specific patterns seen in demo- graphics such as race/ethnicity and age are discussed both qualitatively and quantitatively. We also study the role played by factors such as population density. Connections between COVID-19 and other respiratory diseases are also covered in detail. The temporal dynamics of the COVID-19 outbreak and the impact of vaccines in controlling the pandemic are also looked at with suf- ficient rigor. It is hoped that statistical inference such as the ones gathered in this paper would be helpful for better scientific understanding, policy prepa- ration and thus adequately preparing, should a similar situation arise in the future.

Classical Statistical Inference

2014 ◽  
Author(s):  
Željko Ivezi ◽  
Andrew J. Connolly ◽  
Jacob T. VanderPlas ◽  
Alexander Gray ◽  
Željko Ivezi ◽  
...  
Keyword(s):  
Machine Learning ◽  
Statistical Inference ◽  
Point Estimation ◽  
Point Of View ◽  
Confidence Estimation ◽  
Scientific Communities ◽  
Bayesian Techniques ◽  
Bayesian Paradigm ◽  
Frequentist Paradigm ◽  
Classical Point

This chapter introduces the main concepts of statistical inference, or drawing conclusions from data. There are three main types of inference: point estimation, confidence estimation, and hypothesis testing. There are two major statistical paradigms which address the statistical inference questions: the classical, or frequentist paradigm, and the Bayesian paradigm. While most of statistics and machine learning is based on the classical paradigm, Bayesian techniques are being embraced by the statistical and scientific communities at an ever-increasing pace. The chapter begins with a short comparison of classical and Bayesian paradigms, and then discusses the three main types of statistical inference from the classical point of view.

The Implementation of Statistical Inference to Study the Bending Strength of Sustainable Hybrid Sandwich Panel Composite

2011 ◽  
Vol 250-253 ◽  
pp. 956-961
Author(s):  
Jauhar Fajrin ◽  
Zhu Ge Yan ◽  
Frank Bullen ◽  
Hao Wang
Keyword(s):  
Statistical Analysis ◽  
Statistical Inference ◽  
Intermediate Layer ◽  
Sandwich Panel ◽  
Bending Strength ◽  
Sandwich Panels ◽  
T Test ◽  
Bending Stress ◽  
Comparative Statistical Analysis

The study reported here involves the evaluation of the ultimate bending stress (bending strength) of hybrid sandwich panels using a simple comparative statistical analysis. Four sets of beam were tested with each set consisting of modified beams (MB) and unmodified beam (UB) samples. A total of 42 beam samples were tested using 3 point bending followed by statistical inference analysis using a t-test. The results show that the introduction of an intermediate layer has a significant effect on increasing the bending strength of the new hybrid sandwich panel composite.

The Problem of Multiple Inference in Psychiatric Research

1985 ◽  
Vol 19 (3) ◽  
pp. 265-274 ◽  
Author(s):  
Wayne Hall ◽  
Kevin Bird
Keyword(s):  
Statistical Analysis ◽  
Statistical Inference ◽  
Multivariate Statistical Analysis ◽  
Research Study ◽  
Psychiatric Research ◽  
Exploratory Research ◽  
Multivariate Statistical ◽  
Advantages And Disadvantages ◽  
Multivariate Study ◽  
Study Designs

This paper deals with the problem of multiple inference in psychiatric research, an issue which arises whenever a researcher has to make more than one statistical inference in a single research study. It frequently arises in psychiatric research because of multivariate study designs, with subjects being measured on more than one dependent variable with the intention of studying differences between groups in mean scores. The disadvantages of the commonly adopted strategy of using multiple univariate tests (e.g. multiple t-tests) are outlined. Two broad strategies — Bonferroni-adjusted univariate tests and multivariate statistical analysis — are introduced. Their advantages and disadvantages are discussed in terms of their usefulness in confirmatory and exploratory research in psychiatry.

Approximations to hard-core models and their application to statistical analysis

1982 ◽  
Vol 19 (A) ◽  
pp. 281-292 ◽  
Author(s):  
Mark Westcott
Keyword(s):  
Statistical Analysis ◽  
Statistical Inference ◽  
Lower Bounds ◽  
Hard Core ◽  
Distribution Functions ◽  
Core Model ◽  
Upper And Lower Bounds ◽  
Nearest Neighbour ◽  
Hard Core Model

This paper derives upper and lower bounds to the distribution functions of nearest-neighbour and minimum nearest-neighbour distances between N points generated by a hard-core model on the surface of a sphere. The use of these bounds in statistical inference is discussed.

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