# Mode: The Mode(s) of a Vector In LaplacesDemon: Complete Environment for Bayesian Inference

## Description

The mode is a measure of central tendency. It is the value that occurs most frequently, or in a continuous probability distribution, it is the value with the most density. A distribution may have no modes (such as with a constant, or in a uniform distribution when no value occurs more frequently than any other), or one or more modes.

## Usage

 ```1 2 3 4 5 6 7``` ```is.amodal(x, min.size=0.1) is.bimodal(x, min.size=0.1) is.multimodal(x, min.size=0.1) is.trimodal(x, min.size=0.1) is.unimodal(x, min.size=0.1) Mode(x) Modes(x, min.size=0.1) ```

## Arguments

 `x` This is a vector in which a mode (or modes) will be sought. `min.size` This is the minimum size that can be considered a mode, where size means the proportion of the distribution between areas of increasing kernel density estimates.

## Details

The `is.amodal` function is a logical test of whether or not `x` has a mode. If `x` has a mode, then `TRUE` is returned, otherwise `FALSE`.

The `is.bimodal` function is a logical test of whether or not `x` has two modes. If `x` has two modes, then `TRUE` is returned, otherwise `FALSE`.

The `is.multimodal` function is a logical test of whether or not `x` has multiple modes. If `x` has multiple modes, then `TRUE` is returned, otherwise `FALSE`.

The `is.trimodal` function is a logical test of whether or not `x` has three modes. If `x` has three modes, then `TRUE` is returned, otherwise `FALSE`.

The `is.unimodal` function is a logical test of whether or not `x` has one mode. If `x` has one mode, then `TRUE` is returned, otherwise `FALSE`.

The `Mode` function returns the most frequent value when `x` is discrete. If `x` is a constant, then it is considered amodal, and `NA` is returned. If multiple modes exist, this function returns only the mode with the highest density, or if two or more modes have the same density, then it returns the first mode found. Otherwise, the `Mode` function returns the value of `x` associated with the highest kernel density estimate, or the first one found if multiple modes have the same density.

The `Modes` function is a simple, deterministic function that differences the kernel density of `x` and reports a number of modes equal to half the number of changes in direction, although the `min.size` function can be used to reduce the number of modes returned, and defaults to 0.1, eliminating modes that do not have at least 10% of the distributional area. The `Modes` function returns a list with three components: `modes`, `modes.dens`, and `size`. The elements in each component are ordered according to the decreasing density of the modes. The `modes` component is a vector of the values of `x` associated with the modes. The `modes.dens` component is a vector of the kernel density estimates at the modes. The `size` component is a vector of the proportion of area underneath each mode.

The `IterativeQuadrature`, `LaplaceApproximation`, and `VariationalBayes` functions characterize the marginal posterior distributions by posterior modes (means) and variance. A related topic is MAP or maximum a posteriori estimation.

Otherwise, the results of Bayesian inference tend to report the posterior mean or median, along with probability intervals (see `p.interval` and `LPL.interval`), rather than posterior modes. In many types of models, such as mixture models, the posterior may be multimodal. In such a case, the usual recommendation is to choose the highest mode if feasible and possible. However, the highest mode may be uncharacteristic of the majority of the posterior.

## Author(s)

Statisticat, LLC. [email protected]

`IterativeQuadrature`, `LaplaceApproximation`, `LaplacesDemon`, `LPL.interval`, `p.interval`, and `VariationalBayes`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```library(LaplacesDemon) ### Below are distributions with different numbers of modes. x <- c(1,1) #Amodal x <- c(1,2,2,2,3) #Unimodal x <- c(1,2) #Bimodal x <- c(1,3,3,3,3,4,4,4,4,4) #min.size affects the answer x <- c(1,1,3,3,3,3,4,4,4,4,4) #Trimodal ### And for each of the above, the functions below may be applied. Mode(x) Modes(x) is.amodal(x) is.bimodal(x) is.multimodal(x) is.trimodal(x) is.unimodal(x) ```