Creating a Home Library – Even nowadays almost everything seems to be changed into the virtual form (including books), but there is (still) nothing which can satisfy you more than reading a physical book inside a beautiful and heart calming library. Use the type of bookshelves that stand from the floor to the ceiling, it will save you lots of spaces. Make book’s placement system in order to make it easier to find the books you want to read. In future postings I will introduce Mata code for fitting some further Bayesian models, so I thought that I would create a new library that I will call libbayes. This library will contain all of the Mata functions that I refer to in this blog. When this do file is run, the library is created in the PERSONAL folder, which I have chosen because that directory is searched automatically by Stata when it looks for Mata libraries (type the command -sysdir- to find the location of this folder). As my first project I plan to write a function for fitting a finite mixture of multivariate normal distributions using conjugate priors and a Gibbs sampler.
To create the Gibbs sampler for fitting a mixture of multivariate normal distributions, we will need functions that simulate random values from the Wishart, Multivariate normal, Dirichlet and Categorical distributions, so today I will add those functions to my library. The advantage of calculating the cholesky decomposition outside of the function is that if you want to simulate many values from distributions with the same variance matrix, then you can calculate the cholesky decomposition once and then call rMNormal() as many times as you wish.
A similar reasoning leads us to use cholesky(invsym(R)) as the input to the Wishart function.
The Dirichlet distribution is a generalization of the Beta distribution and provides a simple prior for a set of probabilities that sum to one. The functions in our library will be called by numerous other programs so it is vitally important that we test them to ensure, first, that they are correct and second, that they are robust to misuse.
To check the accuracy of the functions we could write a series of Mata programs that call them but I prefer the interactivity of Stata and so I wrote four short Stata programs that call these Mata functions and I used those for testing.

The Stata program rCat calls rCategorical() to generate n values from a single catergorical distibution with probabilities p (which must sum to one, although this is not checked).
The library itself not only provides a comfortable and private reading spot for you, but also can help organizing your gigantic books collection. Try to find the place with fewer noises, or the place that is far away from your main activity room like living room for instance. Also consider the choice of shelves that mount over the door and window in order to get the spacious feeling of your home library. For convenience, those four samplers are collected together with other Mata code referred to in the book, in a library that I called libmcmc (in Stata a library name needs to begin with lib).
I will start today by showing how the library is created and then I will add some functions for simulating random values from a few standard distributions. Each program is added in turn and then Stata is told to update its index of Mata libraries.
This code can be used in many different ways, for example for density smoothing, clustering or even fitting smooth lines to a scatter plot, it also serves as a convenient stepping stone to introducing non-parametric Bayesian analysis, which can be though of as an extension of finite mixture modelling in which the number of components in the mixture becomes infinite.
What is more, anyone who likes to parameterize in terms of S=invsym(R) can use the same function by calling it with the argument cholesky(S). Drawing random probabilities from a Dirichlet distribution is just a matter of creating a set of appropriately chosen gamma variables and then normalizing them to sum to one.
Robustness usually involves checking the inputs to ensure that dimensions match and constraints are fulfilled, for instance, the scalar parameter of a Wishart distribution should not be less than the dimension of the matrix. Inside the Stata program the probabilities are transferred to Mata using the st_matrix() function and then rCategorical() is called repeatedly and the results are returned as locals.

The software for this blog will not allow me to upload a do file directly, so the link is to a pdf; however, it is simple to copy and paste the code from the pdf into the do file editor. In order to get the sense of conventional library inside your home, read along for the details. Avoid the places like children playroom, television (or living) room, the room that is too near to the road, and the guest room.
Make the lighting as proper as you can by putting a window or good standing lamps in order to get the indirect lighting that is not too bright but still comfortable for reading. If any images that appear on the website are in Violation of Copyright Law or if you own copyrights over any of them and do not agree with it being shown here, please also contact us and We will remove the offending information as soon as possible. Updating the index is only needed the first time that a new library is created because the index is automatically updated at the start of each Stata session, but it does no harm if the index is updated unnecessarily. I tend to be rather lazy with my programming so I have switched matastrict off.
I have deliberately chosen not to include any such checks in these functions because in a Bayesian analysis they might be called hundreds of thousands of times and speed is important.
After the Stata function has been called, the results are tabulated so that we can see that the proportions agree with the probabilities supplied to the function. Had I switched it on, then I would have had to define the type of every structure that I use in the functions.
This approach is not as efficient as creating a calling function in Mata but it is simple to write and simple to use.

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