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# incrmse

> Compute the [mean squared error][mean-squared-error] (MSE) incrementally.

<section class="intro">

The [mean squared error][mean-squared-error] is defined as

<!-- <equation class="equation" label="eq:mean_squared_error" align="center" raw="\operatorname{MSE} = \frac{1}{n} \sum_{i=0}^{n-1} (y_i - x_i)^2" alt="Equation for the mean squared error."> -->

<div class="equation" align="center" data-raw-text="\operatorname{MSE} = \frac{1}{n} \sum_{i=0}^{n-1} (y_i - x_i)^2" data-equation="eq:mean_squared_error">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/f5d4f0cac0a117ba1e0c70706a2fb284f69e7291/lib/node_modules/@stdlib/stats/incr/mse/docs/img/equation_mean_squared_error.svg" alt="Equation for the mean squared error.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrmse = require( '@stdlib/stats/incr/mse' );
```

#### incrmse()

Returns an accumulator `function` which incrementally computes the [mean squared error][mean-squared-error].

```javascript
var accumulator = incrmse();
```

#### accumulator( \[x, y] )

If provided input values `x` and `y`, the accumulator function returns an updated [mean squared error][mean-squared-error]. If not provided input values `x` and `y`, the accumulator function returns the current [mean squared error][mean-squared-error].

```javascript
var accumulator = incrmse();

var m = accumulator( 2.0, 3.0 );
// returns 1.0

m = accumulator( -1.0, -4.0 );
// returns 5.0

m = accumulator( -3.0, 5.0 );
// returns ~24.67

m = accumulator();
// returns ~24.67
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `NaN` for **all** future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrmse = require( '@stdlib/stats/incr/mse' );

var accumulator;
var v1;
var v2;
var i;

// Initialize an accumulator:
accumulator = incrmse();

// For each simulated datum, update the mean squared error...
for ( i = 0; i < 100; i++ ) {
    v1 = ( randu()*100.0 ) - 50.0;
    v2 = ( randu()*100.0 ) - 50.0;
    accumulator( v1, v2 );
}
console.log( accumulator() );
```

</section>

<!-- /.examples -->

<section class="links">

[mean-squared-error]: https://en.wikipedia.org/wiki/Mean_squared_error

</section>

<!-- /.links -->
