This program implements the analyses discussed in the following paper.

Al Labadi, L., Evans, M. and Liang, Q. (2022) ROC analyses based on measuring evidence using the relative belief ratio. Entropy 2022, 24(12), 1710; doi.org/10.3390/e24121710.

Some software and a website have been created to implement the methods of the paper and can be accessed here.

The software can be downloaded and installed on a local machine. Link to GitHub repository

These analyses are described in the following manuscript.

Prior Elicitation and Relative Belief Inferences for Linear Models

** 1. Multivariate Normal Code **

This code implements relative belief inferences for a multivariate normal with unknown mean vector and variance matrix. The online version of the program can be accessed here.

The following describes the indiviual parts of the program. These can be downloaded and run sequentially. User can read in data from a csv file (see examples below) or input this manually.

Part 0: Data Input and Sufficient Statistics Computations

Part 1: Elicitation of the Prior - user provides inputs for the elicitation

Part 2: Sampling from the prior - generates a sample of size Nprior (specified by the user) from the prior

Part 3: Sampling from the Importance Sampler for Posterior Calculations - generates a sample of size Npostimp (specified by user) from the importance sampler

Part 4: SIR Algorithm to Approximately Sample from the Posterior - generates an approximate sample from the posterior of size Npost (specified by the user), this is not essential for any of the other calculations

Part 5: Calculating the Prior Density, Posterior Density and Relative Belief Ratio for the Parameter of Interest psi - approximates the prior, posterior and relative belief ratio of psi (user may need to add code to specify psi) and user needs to specify the number of cells used for the density estimation (numcells) and the amount of smoothing (mprior) for the prior and (mpost) for the posterior

Part 6. Inferences for psi - determines the relative belief estimate of psi, its plausible region and posterior content as well as provides a hypothesis assessment of H_0 : psi=psi_0

- 0. Data Input and Sufficient Statistics Computations
- 1. Eliciting the Prior
- 2. Sampling from the Prior
- 3. Sampling from the Importance Distribution
- 4. SIR sample
- 5. Densities and Relative Belief Ratio for psi
- 6. Inferences for psi

- Y_example.csv - file containing the data (here a sample of 50 from a 5-dimensional normal)
- prior_elicit_example.csv (quantities used to determine the prior on the means and variances where a uniform prior is used on the correlation matrix).

The software can be downloaded and installed on a local machine. Link to GitHub repository