Suppose y=131 U2 U3 3/41 ~ N, (μ, σ214) where μ=[ μ1 μ1 μ1 142]1. Find...
Bayesian updating Suppose that we have the model y|μ ~ N(μ, τ-1) where τ > 0 is known and μ is an unknown parameter (iii) Suppose that we have a prior μ ~ N(a, b-1) where b > 0, Show that the prior distribution π(A) verifies r(11) x exp (iv) Show that the posterior π(μ|y) verifies (v) which distribution is π(μ|y)?
Bayesian updating Suppose that we have the model y|μ ~ N(μ, τ-1) where τ > 0 is known and...
Bayesian updating Suppose that we have the model y|μ ~ N(μ, τ-1) where τ > 0 is known and μ is an unknown parameter (vi) Suppose that ( of y with a -ab1. Suppose that you observe a realization Compute the posterior distribution value of 1. π(μ|1) and explain how it relates to π(μ). vii) Suppose now that you observe a second realization of y with a value of -1. Update the posterior π(p11) to incorporate this new information.
Bayesian...
Bayesian updating Suppose that we have the model y|μ ~ N(μ, τ-1) where τ > 0 is known and μ is an unknown parameter (vi) Suppose that ( of y with a -ab1. Suppose that you observe a realization Compute the posterior distribution value of 1. π(μ|1) and explain how it relates to π(μ). vii) Suppose now that you observe a second realization of y with a value of -1. Update the posterior π(p11) to incorporate this new information.
Bayesian...
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1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for R3. Then express x as a linear 3 4 combination of the u's. u -3 U2 = 0 ,u3 5 6 -2 2 -1 (10 points) Suppose a vector y is orthogonal to vectors u and v. Prove that y is orthogonal to the vector 4u - 3v. 10. (2 points each) True or False: ( ) Eigenvalues must be nonzero scalars. ( )...
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...
Consider the following differential equation. Assume that all eigenvalues are real y" + λy 0, y(0) 0, y(n) + y'(n) 0 (a) Determine the form of the eigenfunctions n(x)-cos μηχ, where u2- O φ n(x)-1-μ tan(A), where-u2-λ 0 φ n(x)-sin μηχ, where μ2-λ O φ n(x)-1-μ cot(A), where-μ2-λ O φη(x) = 1-μ cot(A), where μ = λ Determine the determinantal equation satisfied by the nonzero eigenvalues O μη satisfies cot v/μ -V μ nn satisfies tan v/λπ-- νλ O An...
(1 point) 0 Given v 3 find the linear combination for v in the subspace W spanned by 0 0 3 3 and 114 , u2 = , из- 4 4 Note that ul , u2 , u3 and 14 are orthogonal. u1+ 7 U2 ll4
(1 point) 0 Given v 3 find the linear combination for v in the subspace W spanned by 0 0 3 3 and 114 , u2 = , из- 4 4 Note that ul...
5. Let y|μ ~ N(μ, φ), where φ is known. There is no reliable prior information about the mean other than that it is expected to be a positive quantity. Therefore, use the improper prior distribution: p(p)-1 if (0,x) and 0 otherwise. Suppose we observe one y. Then, find the posterior mean of p. (obtain an explicit expression)
Bayesian updating Suppose that we have the model y|μ ~ N(μ, τ-1) where τ > 0 is known and μ is an unknown parameter (i) Write down the conditional probability density function of y given μ (ii) Show that rw1p) amp(剖-rr)
Bayesian updating Suppose that we have the model y|μ ~ N(μ, τ-1) where τ > 0 is known and μ is an unknown parameter (i) Write down the conditional probability density function of y given μ (ii) Show that...
Bayesian updating Suppose that we have the model y|μ ~ N(μ, τ-1) where τ > 0 is known and μ is an unknown parameter (i) Write down the conditional probability density function of y given μ (ii) Show that rw1p) amp(剖-rr)
Bayesian updating Suppose that we have the model y|μ ~ N(μ, τ-1) where τ > 0 is known and μ is an unknown parameter (i) Write down the conditional probability density function of y given μ (ii) Show that...