If one coin toss yields Head, what is the PDF for the probability of a head?
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ margin-bottom:0;
}
$begingroup$
This is not a homework question. I discovered that I am not the only tenant in a highrise that is getting headaches from paint fumes. I talked to one couple in the elevator about the paint fumes. I turns out that they have the same problem. Based on just one observation, I would be dismissed as a quack if I try to convince the property manager that tenants in general are likely to find the paint fumes problematic. However, I was wondering if that one observation allowed one to contruct a PDF of $p$ with a broad spread ($p$ being the proportion of tenants who are troubled by the paint fumes).
probability
asked Apr 20 at 6:55
user2153235user2153235
132
New contributor
user2153235 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
This is not a homework question. I discovered that I am not the only tenant in a highrise that is getting headaches from paint fumes. I talked to one couple in the elevator about the paint fumes. I turns out that they have the same problem. Based on just one observation, I would be dismissed as a quack if I try to convince the property manager that tenants in general are likely to find the paint fumes problematic. However, I was wondering if that one observation allowed one to contruct a PDF of $p$ with a broad spread ($p$ being the proportion of tenants who are troubled by the paint fumes).
probability
asked Apr 20 at 6:55
user2153235user2153235
132
New contributor
user2153235 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
4
$begingroup$
If you get an inspector in to measure the level of toxic fumes, you do not need statistics.
$endgroup$
– Carl
Apr 20 at 7:39
$begingroup$
I wasn't going to present the statistics, it was an intellectual question. The city is in-bed with the large owners of many highrises in the city, and one must be prepared to quit one's job and push full time if due diligence is desired. I'm currently appealing to the property owners desire for attractive premises, and the hurdle right now is to convince them that the observed periods of no ventilation are reliable. Hopefully, a few witnesses will do that.
$endgroup$
– user2153235
yesterday
add a comment |
$begingroup$
This is not a homework question. I discovered that I am not the only tenant in a highrise that is getting headaches from paint fumes. I talked to one couple in the elevator about the paint fumes. I turns out that they have the same problem. Based on just one observation, I would be dismissed as a quack if I try to convince the property manager that tenants in general are likely to find the paint fumes problematic. However, I was wondering if that one observation allowed one to contruct a PDF of $p$ with a broad spread ($p$ being the proportion of tenants who are troubled by the paint fumes).
probability
asked Apr 20 at 6:55
user2153235user2153235
132
New contributor
user2153235 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
This is not a homework question. I discovered that I am not the only tenant in a highrise that is getting headaches from paint fumes. I talked to one couple in the elevator about the paint fumes. I turns out that they have the same problem. Based on just one observation, I would be dismissed as a quack if I try to convince the property manager that tenants in general are likely to find the paint fumes problematic. However, I was wondering if that one observation allowed one to contruct a PDF of $p$ with a broad spread ($p$ being the proportion of tenants who are troubled by the paint fumes).
probability
probability
asked Apr 20 at 6:55
user2153235user2153235
132
New contributor
user2153235 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 20 at 6:55
user2153235user2153235
132
New contributor
user2153235 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 20 at 6:55
user2153235user2153235
132
New contributor
user2153235 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 20 at 6:55
user2153235user2153235
132
asked Apr 20 at 6:55
user2153235user2153235
132
132
New contributor
user2153235 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user2153235 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user2153235 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
4
$begingroup$
If you get an inspector in to measure the level of toxic fumes, you do not need statistics.
$endgroup$
– Carl
Apr 20 at 7:39
$begingroup$
I wasn't going to present the statistics, it was an intellectual question. The city is in-bed with the large owners of many highrises in the city, and one must be prepared to quit one's job and push full time if due diligence is desired. I'm currently appealing to the property owners desire for attractive premises, and the hurdle right now is to convince them that the observed periods of no ventilation are reliable. Hopefully, a few witnesses will do that.
$endgroup$
– user2153235
yesterday
add a comment |
4
$begingroup$
If you get an inspector in to measure the level of toxic fumes, you do not need statistics.
$endgroup$
– Carl
Apr 20 at 7:39
$begingroup$
I wasn't going to present the statistics, it was an intellectual question. The city is in-bed with the large owners of many highrises in the city, and one must be prepared to quit one's job and push full time if due diligence is desired. I'm currently appealing to the property owners desire for attractive premises, and the hurdle right now is to convince them that the observed periods of no ventilation are reliable. Hopefully, a few witnesses will do that.
$endgroup$
– user2153235
yesterday
4
4
$begingroup$
If you get an inspector in to measure the level of toxic fumes, you do not need statistics.
$endgroup$
– Carl
Apr 20 at 7:39
$begingroup$
If you get an inspector in to measure the level of toxic fumes, you do not need statistics.
$endgroup$
– Carl
Apr 20 at 7:39
$begingroup$
I wasn't going to present the statistics, it was an intellectual question. The city is in-bed with the large owners of many highrises in the city, and one must be prepared to quit one's job and push full time if due diligence is desired. I'm currently appealing to the property owners desire for attractive premises, and the hurdle right now is to convince them that the observed periods of no ventilation are reliable. Hopefully, a few witnesses will do that.
$endgroup$
– user2153235
yesterday
$begingroup$
I wasn't going to present the statistics, it was an intellectual question. The city is in-bed with the large owners of many highrises in the city, and one must be prepared to quit one's job and push full time if due diligence is desired. I'm currently appealing to the property owners desire for attractive premises, and the hurdle right now is to convince them that the observed periods of no ventilation are reliable. Hopefully, a few witnesses will do that.
$endgroup$
– user2153235
yesterday
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Independent of paint fumes, the question can be thought of figuring out if a coin is biased or not, based on one (or more if you prefer) toss. One logical way to make inference is using Bayesian framework, but we need priors. Just as in example in here, assuming a non-informative prior, i.e. uniform distribution, which is the same with beta distribution with $alpha=1,beta=1$, the outcome of the experiment can be incorporated into the PDF estimation, yo come up with a posterior. The posterior is again Beta distributed, with $alpha=alpha_0+s$, $beta=beta_0+f$, where $alpha_0,beta_0$ represent your initial belief, i.e. prior, and $s$ number of positive outcomes, and $f$ number of negative outcomes after $n$ trials. In your case, $n=1,f=0,s=1$. And, when you select the non-informative prior, i.e. $alpha_0=1,beta_0=1$, you end up with a Beta distribution for $p$ with $alpha=2,beta=1$:
answered Apr 20 at 8:13
gunesgunes
8,0411418
$endgroup$
1
$begingroup$
Thanks gunes. I was hoping that it would be a canned equation instead of Bayesian analysis, but you made it both. I tried to crack the Bayesian nut multiple times in the past half decade, but never got my head around it. Reading things like Bayesian inference, Think Bayes, and How to measure anything (Chapt.10). Your answer inspired me to try the last one again. Together with your example, I am getting a foothold.
$endgroup$
– user2153235
yesterday
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
});
}
});
user2153235 is a new contributor. Be nice, and check out our Code of Conduct.
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%2f404088%2fif-one-coin-toss-yields-head-what-is-the-pdf-for-the-probability-of-a-head%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
$begingroup$
Independent of paint fumes, the question can be thought of figuring out if a coin is biased or not, based on one (or more if you prefer) toss. One logical way to make inference is using Bayesian framework, but we need priors. Just as in example in here, assuming a non-informative prior, i.e. uniform distribution, which is the same with beta distribution with $alpha=1,beta=1$, the outcome of the experiment can be incorporated into the PDF estimation, yo come up with a posterior. The posterior is again Beta distributed, with $alpha=alpha_0+s$, $beta=beta_0+f$, where $alpha_0,beta_0$ represent your initial belief, i.e. prior, and $s$ number of positive outcomes, and $f$ number of negative outcomes after $n$ trials. In your case, $n=1,f=0,s=1$. And, when you select the non-informative prior, i.e. $alpha_0=1,beta_0=1$, you end up with a Beta distribution for $p$ with $alpha=2,beta=1$:
answered Apr 20 at 8:13
gunesgunes
8,0411418
$endgroup$
1
$begingroup$
Thanks gunes. I was hoping that it would be a canned equation instead of Bayesian analysis, but you made it both. I tried to crack the Bayesian nut multiple times in the past half decade, but never got my head around it. Reading things like Bayesian inference, Think Bayes, and How to measure anything (Chapt.10). Your answer inspired me to try the last one again. Together with your example, I am getting a foothold.
$endgroup$
– user2153235
yesterday
add a comment |
$begingroup$
Independent of paint fumes, the question can be thought of figuring out if a coin is biased or not, based on one (or more if you prefer) toss. One logical way to make inference is using Bayesian framework, but we need priors. Just as in example in here, assuming a non-informative prior, i.e. uniform distribution, which is the same with beta distribution with $alpha=1,beta=1$, the outcome of the experiment can be incorporated into the PDF estimation, yo come up with a posterior. The posterior is again Beta distributed, with $alpha=alpha_0+s$, $beta=beta_0+f$, where $alpha_0,beta_0$ represent your initial belief, i.e. prior, and $s$ number of positive outcomes, and $f$ number of negative outcomes after $n$ trials. In your case, $n=1,f=0,s=1$. And, when you select the non-informative prior, i.e. $alpha_0=1,beta_0=1$, you end up with a Beta distribution for $p$ with $alpha=2,beta=1$:
answered Apr 20 at 8:13
gunesgunes
8,0411418
$endgroup$
1
$begingroup$
Thanks gunes. I was hoping that it would be a canned equation instead of Bayesian analysis, but you made it both. I tried to crack the Bayesian nut multiple times in the past half decade, but never got my head around it. Reading things like Bayesian inference, Think Bayes, and How to measure anything (Chapt.10). Your answer inspired me to try the last one again. Together with your example, I am getting a foothold.
$endgroup$
– user2153235
yesterday
add a comment |
$begingroup$
Independent of paint fumes, the question can be thought of figuring out if a coin is biased or not, based on one (or more if you prefer) toss. One logical way to make inference is using Bayesian framework, but we need priors. Just as in example in here, assuming a non-informative prior, i.e. uniform distribution, which is the same with beta distribution with $alpha=1,beta=1$, the outcome of the experiment can be incorporated into the PDF estimation, yo come up with a posterior. The posterior is again Beta distributed, with $alpha=alpha_0+s$, $beta=beta_0+f$, where $alpha_0,beta_0$ represent your initial belief, i.e. prior, and $s$ number of positive outcomes, and $f$ number of negative outcomes after $n$ trials. In your case, $n=1,f=0,s=1$. And, when you select the non-informative prior, i.e. $alpha_0=1,beta_0=1$, you end up with a Beta distribution for $p$ with $alpha=2,beta=1$:
answered Apr 20 at 8:13
gunesgunes
8,0411418
$endgroup$
Independent of paint fumes, the question can be thought of figuring out if a coin is biased or not, based on one (or more if you prefer) toss. One logical way to make inference is using Bayesian framework, but we need priors. Just as in example in here, assuming a non-informative prior, i.e. uniform distribution, which is the same with beta distribution with $alpha=1,beta=1$, the outcome of the experiment can be incorporated into the PDF estimation, yo come up with a posterior. The posterior is again Beta distributed, with $alpha=alpha_0+s$, $beta=beta_0+f$, where $alpha_0,beta_0$ represent your initial belief, i.e. prior, and $s$ number of positive outcomes, and $f$ number of negative outcomes after $n$ trials. In your case, $n=1,f=0,s=1$. And, when you select the non-informative prior, i.e. $alpha_0=1,beta_0=1$, you end up with a Beta distribution for $p$ with $alpha=2,beta=1$:
answered Apr 20 at 8:13
gunesgunes
8,0411418
answered Apr 20 at 8:13
gunesgunes
8,0411418
answered Apr 20 at 8:13
gunesgunes
8,0411418
answered Apr 20 at 8:13
gunesgunes
8,0411418
8,0411418
1
$begingroup$
Thanks gunes. I was hoping that it would be a canned equation instead of Bayesian analysis, but you made it both. I tried to crack the Bayesian nut multiple times in the past half decade, but never got my head around it. Reading things like Bayesian inference, Think Bayes, and How to measure anything (Chapt.10). Your answer inspired me to try the last one again. Together with your example, I am getting a foothold.
$endgroup$
– user2153235
yesterday
add a comment |
1
$begingroup$
Thanks gunes. I was hoping that it would be a canned equation instead of Bayesian analysis, but you made it both. I tried to crack the Bayesian nut multiple times in the past half decade, but never got my head around it. Reading things like Bayesian inference, Think Bayes, and How to measure anything (Chapt.10). Your answer inspired me to try the last one again. Together with your example, I am getting a foothold.
$endgroup$
– user2153235
yesterday
1
1
$begingroup$
Thanks gunes. I was hoping that it would be a canned equation instead of Bayesian analysis, but you made it both. I tried to crack the Bayesian nut multiple times in the past half decade, but never got my head around it. Reading things like Bayesian inference, Think Bayes, and How to measure anything (Chapt.10). Your answer inspired me to try the last one again. Together with your example, I am getting a foothold.
$endgroup$
– user2153235
yesterday
$begingroup$
Thanks gunes. I was hoping that it would be a canned equation instead of Bayesian analysis, but you made it both. I tried to crack the Bayesian nut multiple times in the past half decade, but never got my head around it. Reading things like Bayesian inference, Think Bayes, and How to measure anything (Chapt.10). Your answer inspired me to try the last one again. Together with your example, I am getting a foothold.
$endgroup$
– user2153235
yesterday
add a comment |
user2153235 is a new contributor. Be nice, and check out our Code of Conduct.
user2153235 is a new contributor. Be nice, and check out our Code of Conduct.
user2153235 is a new contributor. Be nice, and check out our Code of Conduct.
user2153235 is a new contributor. Be nice, and check out our Code of Conduct.
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%2f404088%2fif-one-coin-toss-yields-head-what-is-the-pdf-for-the-probability-of-a-head%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
4
$begingroup$
If you get an inspector in to measure the level of toxic fumes, you do not need statistics.
$endgroup$
– Carl
Apr 20 at 7:39
$begingroup$
I wasn't going to present the statistics, it was an intellectual question. The city is in-bed with the large owners of many highrises in the city, and one must be prepared to quit one's job and push full time if due diligence is desired. I'm currently appealing to the property owners desire for attractive premises, and the hurdle right now is to convince them that the observed periods of no ventilation are reliable. Hopefully, a few witnesses will do that.
$endgroup$
– user2153235
yesterday