Distributions from any of thirteen standard families may be plotted and many useful summaries computed: mean, mode(s), median, quartiles (or any other quantiles), standard deviation, highest density intervals and probabilities of arbitrary intervals. Furthermore, arbitrary mixtures of distributions from any family can be defined and examined in the same way. Another key feature of First Bayes is that all these plots and summaries are available whenever such distributions arise in First Bayes. This includes prior, posterior and predictive distributions in analysis of one-parameter models, and corresponding one-dimensional marginal distributions in analysis of more complex models.
Analysis of two simple kinds of linear model are also offered. One is the case of one or more normal samples with common but unknown variance (one-way analysis of variance), and the other is simple linear regression. Marginal distributions may be computed (and examined) for arbitrary linear combinations of the location parameters. In the case of regression, scatter and residual plots can be produced.
Predictive distributions are available in a variety of forms for all analyses. For all analyses, the current posterior distribution can be turned into the prior distribution in order to add further data sequentially. Whenever the user makes changes to data or prior distributions, all analyses, distribution summaries and plots are automatically updated.
MSB was originally written in the APL language, and one impetus for writing First Bayes was the fact that powerful Windows-based development tools became available for APL. If you don't enjoy programming, you have probably never used APL. If you do enjoy programming but haven't used APL you are missing a real treat. If you are an APL user, you know what I mean! I discovered APL in 1976, and have been hooked ever since. I have used many other languages, but nothing compares with APL for power and elegance. APL is a joy to program in. But more than that, it provides such a wonderful development environment that complex applications can be built and debugged incredibly quickly.
APL is an interpreted language, and is not compiled. As a result any application written in APL needs an APL interpreter to run it. APL is a complex language and interpreters are not cheap. Another impetus for writing First Bayes was that the new Windows version of APL from Dyalog Ltd allowed applications to be distributed with a free "run-time only" interpreter. This has the advantage of allowing First Bayes to be distributed as a completely self contained package at no charge. The interpreter is Dyalog APL/W version 7.3 for the Windows 3.1/3.11 version of First Bayes, or Dyalog APL/W version 9.0 for Windows 95 or later. Dyalog Ltd continue to improve the interpreter, and the latest versions have lots of new features, so if I ever get round to updating First Bayes I will have some nice things to play with!
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