Fdtxjr

What are the out-of-universe reasons for the references to Toby Maguire-era Spider-Man in ITSV

Can melee weapons be used to deliver Contact Poisons?

Trademark violation for app?

Should I use a zero-interest credit card for a large one-time purchase?

Fantasy story; one type of magic grows in power with use, but the more powerful they are, they more they are drawn to travel to their source

Is it ethical to give a final exam after the professor has quit before teaching the remaining chapters of the course?

Why do the resolve message appear first?

How to Make a Beautiful Stacked 3D Plot

Has negative voting ever been officially implemented in elections, or seriously proposed, or even studied?

Is there any way for the UK Prime Minister to make a motion directly dependent on Government confidence?

Closed form of recurrent arithmetic series summation

How do pianists reach extremely loud dynamics?

How to tell that you are a giant?

An adverb for when you're not exaggerating

Is it cost-effective to upgrade an old-ish Giant Escape R3 commuter bike with entry-level branded parts (wheels, drivetrain)?

What is homebrew?

What is the escape velocity of a neutron particle (not neutron star)

Is there a kind of relay only consumes power when switching?

Do I really need recursive chmod to restrict access to a folder?

How to react to hostile behavior from a senior developer?

How could we fake a moon landing now?

How to down pick a chord with skipped strings?

Is it common practice to audition new musicians 1-2-1 before rehearsing with the entire band?

Dating a Former Employee

Bayesian classification question

0

$begingroup$

$x^n=(x_1,...,x_n)$ i.id. $fin: mathcalF=
N(mathbfmu_j,Omega):j=1,2$, the prior is $pi(1)=pi(2)=1/2$, with0-1 loss. The gola is to classify $x^n$ as a whole to one of the distribution in $mathcalF$.

i)Find the Bayesian classification rule.

ii)Show that the overall Bayesian classification error is
$$e(brevedelta)=1-Phi(sqrtnD),$$with $$D=fracsqrt(mu_2-mu_1)^TOmega^-1(mu_2-mu_1)2$$
where $Phi(·)$ is the distribution function of N(0,1).

---

I am only able to specify the decision as

$$
brevedelta= left{ beginarrayrcl
1
& f(x|1)/f(x|2)ge1 \ 0 & otherwise
endarrayright.
$$

$$f(x|1)/f(x|2)=exp(-frac12(-2x^TOmega^-1(mu_1-mu_2)+mu_1^TOmega^-1mu_1-mu_2^TOmega^-1mu_2))ge1$$

And the terms inside exp( ) should be greater than 0 but I don't know how to simplify the expression and I don't know how to solve for ii).

bayesian

share|cite|improve this question

asked Mar 27 at 3:34

Chloe ZhouChloe Zhou

969

$endgroup$

add a comment | 

0

$begingroup$

$x^n=(x_1,...,x_n)$ i.id. $fin: mathcalF=
N(mathbfmu_j,Omega):j=1,2$, the prior is $pi(1)=pi(2)=1/2$, with0-1 loss. The gola is to classify $x^n$ as a whole to one of the distribution in $mathcalF$.

i)Find the Bayesian classification rule.

ii)Show that the overall Bayesian classification error is
$$e(brevedelta)=1-Phi(sqrtnD),$$with $$D=fracsqrt(mu_2-mu_1)^TOmega^-1(mu_2-mu_1)2$$
where $Phi(·)$ is the distribution function of N(0,1).

---

I am only able to specify the decision as

$$
brevedelta= left{ beginarrayrcl
1
& f(x|1)/f(x|2)ge1 \ 0 & otherwise
endarrayright.
$$

$$f(x|1)/f(x|2)=exp(-frac12(-2x^TOmega^-1(mu_1-mu_2)+mu_1^TOmega^-1mu_1-mu_2^TOmega^-1mu_2))ge1$$

And the terms inside exp( ) should be greater than 0 but I don't know how to simplify the expression and I don't know how to solve for ii).

bayesian

share|cite|improve this question

asked Mar 27 at 3:34

Chloe ZhouChloe Zhou

969

$endgroup$

add a comment | 

$begingroup$

$x^n=(x_1,...,x_n)$ i.id. $fin: mathcalF=
N(mathbfmu_j,Omega):j=1,2$, the prior is $pi(1)=pi(2)=1/2$, with0-1 loss. The gola is to classify $x^n$ as a whole to one of the distribution in $mathcalF$.

i)Find the Bayesian classification rule.

ii)Show that the overall Bayesian classification error is
$$e(brevedelta)=1-Phi(sqrtnD),$$with $$D=fracsqrt(mu_2-mu_1)^TOmega^-1(mu_2-mu_1)2$$
where $Phi(·)$ is the distribution function of N(0,1).

---

I am only able to specify the decision as

$$
brevedelta= left{ beginarrayrcl
1
& f(x|1)/f(x|2)ge1 \ 0 & otherwise
endarrayright.
$$

$$f(x|1)/f(x|2)=exp(-frac12(-2x^TOmega^-1(mu_1-mu_2)+mu_1^TOmega^-1mu_1-mu_2^TOmega^-1mu_2))ge1$$

And the terms inside exp( ) should be greater than 0 but I don't know how to simplify the expression and I don't know how to solve for ii).

bayesian

share|cite|improve this question

asked Mar 27 at 3:34

Chloe ZhouChloe Zhou

969

$endgroup$

share|cite|improve this question

asked Mar 27 at 3:34

Chloe ZhouChloe Zhou

969

share|cite|improve this question

asked Mar 27 at 3:34

Chloe ZhouChloe Zhou

969

asked Mar 27 at 3:34

Chloe ZhouChloe Zhou

969

asked Mar 27 at 3:34

Chloe ZhouChloe Zhou

969