What is the difference between an accuracy measure and an error metric?Difference between forecasting accuracy and forecasting error?Evaluating relative accuracy/error for continuous value prediction (and assessing relative average difference/error)The relationship between trading profitibility and forecasting accuracyWhat is the best way to remember the difference between sensitivity, specificity, precision, accuracy, and recall?What is the difference between oob (out of bag) error and (1 - accuracy) in RandomForest?Forecast accuracy metric that involves prediction intervalsWhy not using the R squared to measure forecast accuracy?What is the difference between accuracy and precision?Difference between forecasting accuracy and forecasting error?difference between accuracy and Rand index (R)Difference between Mean/average accuracy and Overall accuracy
How does the +1 Keen Composite Longbow (+2 Str) work?
Warped chessboard
What is metrics.roc_curve and metrics.auc measuring when I'm comparing binary data with probability estimates?
Why "strap-on" boosters, and how do other people say it?
Best practice for printing and evaluating formulas with the minimal coding
How do you cope with rejection?
Was Tyrion always a poor strategist?
How do we explain the use of a software on a math paper?
US F1 Visa grace period attending a conference
Managing heat dissipation in a magic wand
Are CTRL+C and <esc> the same?
Expand a hexagon
Does science define life as "beginning at conception"?
Filter a file list against an integer array?
Why was Houston selected as the location for the Manned Spacecraft Center?
How to become an Editorial board member?
Is there a realtime, uncut video of Saturn V ignition through tower clear?
Why is there no current between two capacitors connected in series?
How to draw with Tikz a chord parallel to AC that passes through a point?
What are the domains of the multiplication and unit morphisms of a monoid object?
Story about encounter with hostile aliens
Salesforce bug enabled "Modify All"
Does a windmilling propeller create more drag than a stopped propeller in an engine out scenario?
Do most Taxis give Receipts in London?
What is the difference between an accuracy measure and an error metric?
Difference between forecasting accuracy and forecasting error?Evaluating relative accuracy/error for continuous value prediction (and assessing relative average difference/error)The relationship between trading profitibility and forecasting accuracyWhat is the best way to remember the difference between sensitivity, specificity, precision, accuracy, and recall?What is the difference between oob (out of bag) error and (1 - accuracy) in RandomForest?Forecast accuracy metric that involves prediction intervalsWhy not using the R squared to measure forecast accuracy?What is the difference between accuracy and precision?Difference between forecasting accuracy and forecasting error?difference between accuracy and Rand index (R)Difference between Mean/average accuracy and Overall accuracy
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
The two concepts are distinct in measure theory. Nonetheless, moving out from measure theory, the two terms are often used interchangeably. To most forecasters, especially forecast practitioners, they both refer to functions of forecast errors, e.g., MBE, MAE, or RMSE.
I am hoping somebody could elaborate on the potential harms and pitfalls when the two terms are mixed up.
A measure $mu$ on a set $X$ is a mapping $mu:mathcalArightarrow[0,infty]$ defined on a $sigma$-algebra $mathcalA$ that satisfies non-negativity, null empty set, and $sigma$-additivity, that is $mu(A) ge 0 ,, forall ,, A in mathcalA$, $mu( emptyset)=0$, and $mu( sqcup_j in mathbbN A_j) = sum_j in mathbbN mu(A_j)$, where symbol $sqcup$ denotes disjoint union. On the other hand, a metric is a distance measure $d:Xtimes X rightarrow [0,infty]$ that satisfies definiteness, symmetry, and triangle inequality, that is $d(x,y) = 0$ iff $x = y$, $d(x,y) = d(y,x)$, and $d(x,y)le d(x,z) + d(z,y)$, $forall$ $x,y,zin X$.
I am not so sure when to use the word "measure," and when to use "metric."
forecasting accuracy measure-theory
edited May 14 at 9:22
Scortchi♦
23.7k756187
asked May 14 at 6:56
seryangdseryangd
233
$endgroup$
add a comment |
$begingroup$
The two concepts are distinct in measure theory. Nonetheless, moving out from measure theory, the two terms are often used interchangeably. To most forecasters, especially forecast practitioners, they both refer to functions of forecast errors, e.g., MBE, MAE, or RMSE.
I am hoping somebody could elaborate on the potential harms and pitfalls when the two terms are mixed up.
A measure $mu$ on a set $X$ is a mapping $mu:mathcalArightarrow[0,infty]$ defined on a $sigma$-algebra $mathcalA$ that satisfies non-negativity, null empty set, and $sigma$-additivity, that is $mu(A) ge 0 ,, forall ,, A in mathcalA$, $mu( emptyset)=0$, and $mu( sqcup_j in mathbbN A_j) = sum_j in mathbbN mu(A_j)$, where symbol $sqcup$ denotes disjoint union. On the other hand, a metric is a distance measure $d:Xtimes X rightarrow [0,infty]$ that satisfies definiteness, symmetry, and triangle inequality, that is $d(x,y) = 0$ iff $x = y$, $d(x,y) = d(y,x)$, and $d(x,y)le d(x,z) + d(z,y)$, $forall$ $x,y,zin X$.
I am not so sure when to use the word "measure," and when to use "metric."
forecasting accuracy measure-theory
edited May 14 at 9:22
Scortchi♦
23.7k756187
asked May 14 at 6:56
seryangdseryangd
233
$endgroup$
add a comment |
$begingroup$
The two concepts are distinct in measure theory. Nonetheless, moving out from measure theory, the two terms are often used interchangeably. To most forecasters, especially forecast practitioners, they both refer to functions of forecast errors, e.g., MBE, MAE, or RMSE.
I am hoping somebody could elaborate on the potential harms and pitfalls when the two terms are mixed up.
A measure $mu$ on a set $X$ is a mapping $mu:mathcalArightarrow[0,infty]$ defined on a $sigma$-algebra $mathcalA$ that satisfies non-negativity, null empty set, and $sigma$-additivity, that is $mu(A) ge 0 ,, forall ,, A in mathcalA$, $mu( emptyset)=0$, and $mu( sqcup_j in mathbbN A_j) = sum_j in mathbbN mu(A_j)$, where symbol $sqcup$ denotes disjoint union. On the other hand, a metric is a distance measure $d:Xtimes X rightarrow [0,infty]$ that satisfies definiteness, symmetry, and triangle inequality, that is $d(x,y) = 0$ iff $x = y$, $d(x,y) = d(y,x)$, and $d(x,y)le d(x,z) + d(z,y)$, $forall$ $x,y,zin X$.
I am not so sure when to use the word "measure," and when to use "metric."
forecasting accuracy measure-theory
edited May 14 at 9:22
Scortchi♦
23.7k756187
asked May 14 at 6:56
seryangdseryangd
233
$endgroup$
The two concepts are distinct in measure theory. Nonetheless, moving out from measure theory, the two terms are often used interchangeably. To most forecasters, especially forecast practitioners, they both refer to functions of forecast errors, e.g., MBE, MAE, or RMSE.
I am hoping somebody could elaborate on the potential harms and pitfalls when the two terms are mixed up.
A measure $mu$ on a set $X$ is a mapping $mu:mathcalArightarrow[0,infty]$ defined on a $sigma$-algebra $mathcalA$ that satisfies non-negativity, null empty set, and $sigma$-additivity, that is $mu(A) ge 0 ,, forall ,, A in mathcalA$, $mu( emptyset)=0$, and $mu( sqcup_j in mathbbN A_j) = sum_j in mathbbN mu(A_j)$, where symbol $sqcup$ denotes disjoint union. On the other hand, a metric is a distance measure $d:Xtimes X rightarrow [0,infty]$ that satisfies definiteness, symmetry, and triangle inequality, that is $d(x,y) = 0$ iff $x = y$, $d(x,y) = d(y,x)$, and $d(x,y)le d(x,z) + d(z,y)$, $forall$ $x,y,zin X$.
I am not so sure when to use the word "measure," and when to use "metric."
forecasting accuracy measure-theory
forecasting accuracy measure-theory
edited May 14 at 9:22
Scortchi♦
23.7k756187
asked May 14 at 6:56
seryangdseryangd
233
edited May 14 at 9:22
Scortchi♦
23.7k756187
asked May 14 at 6:56
seryangdseryangd
233
edited May 14 at 9:22
Scortchi♦
23.7k756187
edited May 14 at 9:22
Scortchi♦
23.7k756187
edited May 14 at 9:22
Scortchi♦
23.7k756187
23.7k756187
asked May 14 at 6:56
seryangdseryangd
233
asked May 14 at 6:56
seryangdseryangd
233
asked May 14 at 6:56
seryangdseryangd
233
233
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I do not think that there is a lot of potential confusion stemming from the difference between "errors" and "accuracy", as long as people explain what measure they are using. If they note that they are using the MAPE, they can discuss "lower error" and "higher accuracy", and everyone will know which way the MAPE moved. Similarly if they prefer working with "accuracy" and define it as 1-MAPE. As you write, both terms are used in the forecasting community, and I haven't noted any particular confusion in the 13+ years I have been active there.
Difference between forecasting accuracy and forecasting error? may be useful, or possibly earlier threads in which I have pontificated about forecast error or accuracy, or even a couple of popular articles I have written on forecast accuracy measurement, e.g., Kolassa & Schütz (2007) and Kolassa (2008) and Kolassa (2009) and Kolassa & Martin (2011), also Kolassa (2016) and a forthcoming commentary on the M4 competition.
"Accuracy measure" uses the word "measure" in its everyday sense, not in the mathematical measure theoretical way. Similarly, "error metric" uses "metric" in its everyday sense, not in the sense of a metric on a mathematical set.
edited May 14 at 9:23
Scortchi♦
23.7k756187
answered May 14 at 8:03
Stephan KolassaStephan Kolassa
50.7k8103189
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "65"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f408233%2fwhat-is-the-difference-between-an-accuracy-measure-and-an-error-metric%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I do not think that there is a lot of potential confusion stemming from the difference between "errors" and "accuracy", as long as people explain what measure they are using. If they note that they are using the MAPE, they can discuss "lower error" and "higher accuracy", and everyone will know which way the MAPE moved. Similarly if they prefer working with "accuracy" and define it as 1-MAPE. As you write, both terms are used in the forecasting community, and I haven't noted any particular confusion in the 13+ years I have been active there.
Difference between forecasting accuracy and forecasting error? may be useful, or possibly earlier threads in which I have pontificated about forecast error or accuracy, or even a couple of popular articles I have written on forecast accuracy measurement, e.g., Kolassa & Schütz (2007) and Kolassa (2008) and Kolassa (2009) and Kolassa & Martin (2011), also Kolassa (2016) and a forthcoming commentary on the M4 competition.
"Accuracy measure" uses the word "measure" in its everyday sense, not in the mathematical measure theoretical way. Similarly, "error metric" uses "metric" in its everyday sense, not in the sense of a metric on a mathematical set.
edited May 14 at 9:23
Scortchi♦
23.7k756187
answered May 14 at 8:03
Stephan KolassaStephan Kolassa
50.7k8103189
$endgroup$
add a comment |
$begingroup$
I do not think that there is a lot of potential confusion stemming from the difference between "errors" and "accuracy", as long as people explain what measure they are using. If they note that they are using the MAPE, they can discuss "lower error" and "higher accuracy", and everyone will know which way the MAPE moved. Similarly if they prefer working with "accuracy" and define it as 1-MAPE. As you write, both terms are used in the forecasting community, and I haven't noted any particular confusion in the 13+ years I have been active there.
Difference between forecasting accuracy and forecasting error? may be useful, or possibly earlier threads in which I have pontificated about forecast error or accuracy, or even a couple of popular articles I have written on forecast accuracy measurement, e.g., Kolassa & Schütz (2007) and Kolassa (2008) and Kolassa (2009) and Kolassa & Martin (2011), also Kolassa (2016) and a forthcoming commentary on the M4 competition.
"Accuracy measure" uses the word "measure" in its everyday sense, not in the mathematical measure theoretical way. Similarly, "error metric" uses "metric" in its everyday sense, not in the sense of a metric on a mathematical set.
edited May 14 at 9:23
Scortchi♦
23.7k756187
answered May 14 at 8:03
Stephan KolassaStephan Kolassa
50.7k8103189
$endgroup$
add a comment |
$begingroup$
I do not think that there is a lot of potential confusion stemming from the difference between "errors" and "accuracy", as long as people explain what measure they are using. If they note that they are using the MAPE, they can discuss "lower error" and "higher accuracy", and everyone will know which way the MAPE moved. Similarly if they prefer working with "accuracy" and define it as 1-MAPE. As you write, both terms are used in the forecasting community, and I haven't noted any particular confusion in the 13+ years I have been active there.
Difference between forecasting accuracy and forecasting error? may be useful, or possibly earlier threads in which I have pontificated about forecast error or accuracy, or even a couple of popular articles I have written on forecast accuracy measurement, e.g., Kolassa & Schütz (2007) and Kolassa (2008) and Kolassa (2009) and Kolassa & Martin (2011), also Kolassa (2016) and a forthcoming commentary on the M4 competition.
"Accuracy measure" uses the word "measure" in its everyday sense, not in the mathematical measure theoretical way. Similarly, "error metric" uses "metric" in its everyday sense, not in the sense of a metric on a mathematical set.
edited May 14 at 9:23
Scortchi♦
23.7k756187
answered May 14 at 8:03
Stephan KolassaStephan Kolassa
50.7k8103189
$endgroup$
I do not think that there is a lot of potential confusion stemming from the difference between "errors" and "accuracy", as long as people explain what measure they are using. If they note that they are using the MAPE, they can discuss "lower error" and "higher accuracy", and everyone will know which way the MAPE moved. Similarly if they prefer working with "accuracy" and define it as 1-MAPE. As you write, both terms are used in the forecasting community, and I haven't noted any particular confusion in the 13+ years I have been active there.
Difference between forecasting accuracy and forecasting error? may be useful, or possibly earlier threads in which I have pontificated about forecast error or accuracy, or even a couple of popular articles I have written on forecast accuracy measurement, e.g., Kolassa & Schütz (2007) and Kolassa (2008) and Kolassa (2009) and Kolassa & Martin (2011), also Kolassa (2016) and a forthcoming commentary on the M4 competition.
"Accuracy measure" uses the word "measure" in its everyday sense, not in the mathematical measure theoretical way. Similarly, "error metric" uses "metric" in its everyday sense, not in the sense of a metric on a mathematical set.
edited May 14 at 9:23
Scortchi♦
23.7k756187
answered May 14 at 8:03
Stephan KolassaStephan Kolassa
50.7k8103189
edited May 14 at 9:23
Scortchi♦
23.7k756187
edited May 14 at 9:23
Scortchi♦
23.7k756187
edited May 14 at 9:23
Scortchi♦
23.7k756187
23.7k756187
answered May 14 at 8:03
Stephan KolassaStephan Kolassa
50.7k8103189
answered May 14 at 8:03
Stephan KolassaStephan Kolassa
50.7k8103189
answered May 14 at 8:03
Stephan KolassaStephan Kolassa
50.7k8103189
50.7k8103189
add a comment |
add a comment |
Thanks for contributing an answer to Cross Validated!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f408233%2fwhat-is-the-difference-between-an-accuracy-measure-and-an-error-metric%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
