density_table

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The Density Table

Discussion

The density table is used to identify densities. It has the following columns:

density_id

This column has type integer and is the primary key for this table. Its initial value is zero, and it increments by one for each row.

density_name

This column has type text . This column is unique; i.e., each name can only appear ones in this table. All of the density_id values that appear in the prior and data tables must appear in the density table. Below is a list of the possible density names with a link to the corresponding meaning:

uniform

Uniform

binomial

Binomial . This density is special because it can only be used in the data table. The data table meas_std must be null and the sample_size must not be null.

Binomial Notation

\(n\)

sample_size in the data table

\(k\)

counts in a binomial sample (need not be an integer)

\(y=k/n\)

meas_value in the data table

\(\mu\)

average integrand is model mean for y.

\(\sqrt{\mu / n}\)

approximation used for meas_value standard deviation

gaussian

Gaussian

cen_gaussian

Censored Gaussian

log_gaussian

Log-Gaussian

cen_log_gaussian

Censored Log-Gaussian

laplace

Laplace

cen_laplace

Censored Laplace

log_laplace

Log-Laplace

cen_log_laplace

Censored Log-Laplace

students

Student’s-t

log_students

Log-Student’s-t

Notation

Linear

We refer to the following densities as linear: gaussian , cen_gaussian , laplace , cen_laplace , students .

Censored

We refer to the following densities as censored: cen_gaussian , cen_log_gaussian , cen_laplace , cen_log_laplace .

Log Scaled

We refer to the following densities as log scaled: log_gaussian , cen_log_laplace , log_laplace , log_students .

Nonsmooth

We refer to the following densities as nonsmooth: laplace , cen_laplace , log_laplace .

Example

The file density_table.py contains an example density table.