scholarly journals multibridge: An R Package To Evaluate Informed Hypotheses in Binomial and Multinomial Models

2021 ◽  
Author(s):  
Alexandra Sarafoglou ◽  
Frederik Aust ◽  
Maarten Marsman ◽  
Eric-Jan Wagenmakers ◽  
Julia M. Haaf
Keyword(s):  
Null Hypothesis ◽  
Multinomial Distribution ◽  
Inequality Constraints ◽  
R Package ◽  
Equality Constraints ◽  
Frequency Data ◽  
Multinomial Models ◽  
Bridge Sampling ◽  
Restricted Parameter Space ◽  
Accurate Comparison

The multibridge R package allows a Bayesian evaluation of informed hypotheses H_r applied to frequency data from an independent binomial or multinomial distribution. multibridge uses bridge sampling to efficiently compute Bayes factors for the following hypotheses concerning the latent category proportions theta: (a) hypotheses that postulate equality constraints (e.g., theta_1 = theta_2 = theta_3); (b) hypotheses that postulate inequality constraints (e.g., theta_1 < theta_2 < theta_3) or (theta_1 > theta_2 > theta_3); (c) hypotheses that postulate mixtures of inequality constraints and equality constraints (e.g., theta_1 < theta_2 = theta_3); and (d) hypotheses that postulate mixtures of (a)--(c) (e.g., theta_1 < theta_2 = theta_3, theta_4). Any informed hypothesis H_r may be compared against the encompassing hypothesis H_e that all category proportions vary freely, or against the null hypothesis H_0 that all category proportions are equal. multibridge facilitates the fast and accurate comparison of large models with many constraints and models for which relatively little posterior mass falls in the restricted parameter space. This paper describes the underlying methodology and illustrates the use of multibridge through fully reproducible examples.

scholarly journals Evaluating Multinomial Order Restrictions with Bridge Sampling

2020 ◽  
Author(s):  
Alexandra Sarafoglou ◽  
Julia M. Haaf ◽  
Alexander Ly ◽  
Quentin Frederik Gronau ◽  
Eric-Jan Wagenmakers ◽  
...  
Keyword(s):  
Parameter Space ◽  
Bayesian Methods ◽  
Inequality Constraints ◽  
Order Restrictions ◽  
Empirical Application ◽  
Bridge Sampling ◽  
Restricted Parameter Space ◽  
Computationally Expensive ◽  
Exact Equality ◽  
Standard Tests

Hypotheses concerning the distribution of multinomial proportions typically entail exact equality constraints that can be evaluated using standard tests. Whenever researchers formulate inequality constrained hypotheses, however, they must rely on sampling-based methods that are relatively inefficient and computationally expensive. To address this problem we developed a bridge sampling routine that allows an efficient evaluation of multinomial inequality constraints. An empirical application showcases that bridge sampling outperforms current Bayesian methods, especially when relatively little posterior mass falls in the restricted parameter space. The method is extended to mixtures between equality and inequality constrained hypotheses.

A weak maximum principle for optimal control problems with mixed constraints under a constant rank condition

2020 ◽  
Vol 37 (3) ◽  
pp. 1021-1047
Author(s):  
Roberto Andreani ◽  
Valeriano Antunes de Oliveira ◽  
Jamielli Tomaz Pereira ◽  
Geraldo Nunes Silva
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Equality Constraints ◽  
Control Problems ◽  
Constant Rank ◽  
Rank Condition ◽  
Weak Maximum Principle

Abstract Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented.

scholarly journals Statistical Reporting Inconsistencies in Experimental Philosophy

2017 ◽  
Author(s):  
Matteo Colombo ◽  
Georgi Duev ◽  
Michele B. Nuijten ◽  
Jan Sprenger
Keyword(s):  
Null Hypothesis ◽  
Experimental Philosophy ◽  
R Package ◽  
Experimental Methods ◽  
Point Of View ◽  
Behavioral Sciences ◽  
Null Hypothesis Significance Testing ◽  
Psychological Science ◽  
Philosophical Questions ◽  
Better Than

Experimental philosophy (x-phi) is a young field of research in the intersection of philosophy and psychology. It aims to make progress on philosophical questions by using experimental methods traditionally associated with the psychological and behavioral sciences, such as null hypothesis significance testing (NHST). Motivated by recent discussions about a methodological crisis in the behavioral sciences, questions have been raised about the methodological standards of x-phi. Here, we focus on one aspect of this question, namely the rate of inconsistencies in statistical reporting. Previous research has examined the extent to which published articles in psychology and other behavioral sciences present statistical inconsistencies in reporting the results of NHST. In this study, we used the R package statcheck to detect statistical inconsistencies in x-phi, and compared rates of inconsistencies in psychology and philosophy. We found that rates of inconsistencies in x-phi are lower than in the psychological and behavioral sciences. From the point of view of statistical reporting consistency, x-phi seems to do no worse, and perhaps even better, than psychological science.

scholarly journals SCOPIT: sample size calculations for single-cell sequencing experiments

2019 ◽  
Vol 20 (1) ◽  
Author(s):  
Alexander Davis ◽  
Ruli Gao ◽  
Nicholas E. Navin
Keyword(s):  
Single Cell ◽  
Web Application ◽  
Multinomial Distribution ◽  
R Package ◽  
Cell Type ◽  
Single Cell Sequencing ◽  
Link Type ◽  
Dna And Rna ◽  
Sample Size Calculations ◽  
Number Of Cells

Abstract Background In single cell DNA and RNA sequencing experiments, the number of cells to sequence must be decided before running an experiment, and afterwards, it is necessary to decide whether sufficient cells were sampled. These questions can be addressed by calculating the probability of sampling at least a defined number of cells from each subpopulation (cell type or cancer clone). Results We developed an interactive web application called SCOPIT (Single-Cell One-sided Probability Interactive Tool), which calculates the required probabilities using a multinomial distribution (www.navinlab.com/SCOPIT). In addition, we created an R package called pmultinom for scripting these calculations. Conclusions Our tool for fast multinomial calculations provide a simple and intuitive procedure for prospectively planning single-cell experiments or retrospectively evaluating if sufficient numbers of cells have been sequenced. The web application can be accessed at navinlab.com/SCOPIT.

On extreme stable laws and some applications

1971 ◽  
Vol 8 (4) ◽  
pp. 794-801 ◽  
Author(s):  
Morris L. Eaton ◽  
Carl Morris ◽  
Herman Rubin
Keyword(s):  
Likelihood Ratio Test ◽  
Generating Functions ◽  
Null Hypothesis ◽  
Multinomial Distribution ◽  
Moment Generating Function ◽  
Stable Laws ◽  
Ratio Test ◽  
Moment Sequence ◽  
Decreasing Failure Rate ◽  
Statistical Results

SummaryIt is shown that the extreme stable laws have one-sided moment generating functions with interesting mathematical forms. The fact that one of these forms, zcz, is a moment generating function is used to establish two interesting statistical results; first, that rr is a moment sequence for a density with decreasing failure rate, and secondly, that the likelihood ratio test for testing a simple null hypothesis in a multinomial distribution is admissible and Bayes.

scholarly journals Asymptotic variability of (multilevel) multirater kappa coefficients

2018 ◽  
Vol 28 (10-11) ◽  
pp. 3012-3026 ◽  
Author(s):  
Sophie Vanbelle
Keyword(s):  
Confidence Intervals ◽  
Data Structures ◽  
Standard Error ◽  
Null Hypothesis ◽  
Matrix Algebra ◽  
R Package ◽  
Multilevel Data ◽  
Simple Matrix ◽  
Asymptotic Variability

Agreement studies are of paramount importance in various scientific domains. When several observers classify objects on categorical scales, agreement can be quantified through multirater kappa coefficients. In most statistical packages, the standard error of these coefficients is only available under the null hypothesis that the coefficient is equal to zero, preventing the construction of confidence intervals in the general case. The aim of this paper is triple. First, simple analytic formulae for the standard error of multirater kappa coefficients will be given in the general case. Second, these formulae will be extended to the case of multilevel data structures. The formulae are based on simple matrix algebra and are implemented in the R package “multiagree”. Third, guidelines on the choice between the different mulitrater kappa coefficients will be provided.

scholarly journals TropFishR : an R package for fisheries analysis with length‐frequency data

2017 ◽  
Vol 8 (11) ◽  
pp. 1520-1527 ◽  
Author(s):  
Tobias Karl Mildenberger ◽  
Marc Hollis Taylor ◽  
Matthias Wolff
Keyword(s):  
R Package ◽  
Frequency Data ◽  
Length Frequency ◽  
Length Frequency Data

Modification of Nonlinear Equality Constraints in Nonlinear Problems

1974 ◽  
Vol 96 (1) ◽  
pp. 138-144
Author(s):  
R. J. Polo ◽  
V. A. Sposito ◽  
T. T. Lee
Keyword(s):  
Nonlinear Programming ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Nonlinear Problems ◽  
Unconstrained Minimization ◽  
Equality Constraints ◽  
Feasible Region ◽  
Mathematical Methods ◽  
Minimization Technique ◽  
Nonlinear Equality

This paper presents a technique for solving nonlinear programming problems with nonconvex feasible regions. The procedure expands the feasible region by replacing nonlinear equality constraints by appropriate inequality constraints. The expansion is used to solve two structural optimization problems using the sequential unconstrained-minimization technique of Fiacco and McCormick. The solutions are compared with solutions obtained by classical mathematical methods.

Testing informative hypotheses in SEM increases power: An illustration contrasting classical hypothesis testing with a parametric bootstrap approach

2011 ◽  
Vol 35 (2) ◽  
pp. 180-190 ◽  
Author(s):  
Rens van de Schoot ◽  
Dagmar Strohmeier
Keyword(s):  
Hypothesis Testing ◽  
Simulation Study ◽  
Null Hypothesis ◽  
Inequality Constraints ◽  
Parametric Bootstrap ◽  
Direct Test ◽  
Bootstrap Procedure ◽  
Null Hypothesis Testing ◽  
Bootstrap Approach ◽  
Classical Hypothesis

In the present paper, the application of a parametric bootstrap procedure, as described by van de Schoot, Hoijtink, and Deković (2010), will be applied to demonstrate that a direct test of an informative hypothesis offers more informative results compared to testing traditional null hypotheses against catch-all rivals. Also, more power can be gained when informative hypotheses are tested directly. In this paper we will (a) compare the results of traditional analyses with the results of this novel methodology; (b) introduce applied researchers to the parametric bootstrap procedure for the evaluation of informative hypotheses; and (c) provide the results of a simulation study to demonstrate power gains when using inequality constraints. We argue that researchers should directly evaluate inequality-constrained hypotheses if there is a strong theory about the ordering of relevant parameters. In this way, researchers can make use of all knowledge available from previous investigations, while also learning more from their data compared to traditional null-hypothesis testing.

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