shehryaramin
New member
- Joined
- Jan 20, 2018
- Messages
- 2
[FONT="]I am not very sure if I am able to pose the question properly, but I am having a lot of problem trying to justify a joint distribution derived from the marginals.[/FONT]
[FONT="]I am given that:[/FONT]
[FONT="](y[/FONT]t+1[FONT="] | x[/FONT]t+1[FONT="], θ) ~ N (x[/FONT]t+1[FONT="], σ[/FONT]2[FONT="])[/FONT]
[FONT="](x[/FONT]t+1[FONT="] | x[/FONT]t[FONT="], θ) ~ N (x[/FONT]t+1[FONT="], σ[/FONT]2[FONT="])[/FONT]
[FONT="](y[/FONT]t+1[FONT="] | x[/FONT]t[FONT="], θ) ~ N (x[/FONT]t[FONT="], σ[/FONT]2[FONT="] + τ[/FONT]2[FONT="])[/FONT]
[FONT="](Basically θ represents the parameters sigma and tau) [/FONT]
[FONT="]Then how can we derive (x[/FONT]t+1[FONT="] | y[/FONT]t+1[FONT="], x[/FONT]t[FONT="], θ)?[/FONT]
[FONT="]The answer is: [/FONT]
[FONT="](x[/FONT]t+1[FONT="] | y[/FONT]t+1[FONT="], x[/FONT]t[FONT="], θ) ~ N (µ, w[/FONT]2[FONT="]), [/FONT]
[FONT="]µ = w[/FONT]2[FONT="](σ[/FONT]-2[FONT="]y[/FONT]t+1[FONT="] + τ[/FONT]-2[FONT="]x[/FONT]t[FONT="]) and w[/FONT]-2[FONT="] = σ[/FONT]-2[FONT="]+ τ[/FONT]-2
[FONT="]but I don’t know how to calculate it. Any help will be much appreciated.[/FONT]
[FONT="]I am given that:[/FONT]
[FONT="](y[/FONT]t+1[FONT="] | x[/FONT]t+1[FONT="], θ) ~ N (x[/FONT]t+1[FONT="], σ[/FONT]2[FONT="])[/FONT]
[FONT="](x[/FONT]t+1[FONT="] | x[/FONT]t[FONT="], θ) ~ N (x[/FONT]t+1[FONT="], σ[/FONT]2[FONT="])[/FONT]
[FONT="](y[/FONT]t+1[FONT="] | x[/FONT]t[FONT="], θ) ~ N (x[/FONT]t[FONT="], σ[/FONT]2[FONT="] + τ[/FONT]2[FONT="])[/FONT]
[FONT="](Basically θ represents the parameters sigma and tau) [/FONT]
[FONT="]Then how can we derive (x[/FONT]t+1[FONT="] | y[/FONT]t+1[FONT="], x[/FONT]t[FONT="], θ)?[/FONT]
[FONT="]The answer is: [/FONT]
[FONT="](x[/FONT]t+1[FONT="] | y[/FONT]t+1[FONT="], x[/FONT]t[FONT="], θ) ~ N (µ, w[/FONT]2[FONT="]), [/FONT]
[FONT="]µ = w[/FONT]2[FONT="](σ[/FONT]-2[FONT="]y[/FONT]t+1[FONT="] + τ[/FONT]-2[FONT="]x[/FONT]t[FONT="]) and w[/FONT]-2[FONT="] = σ[/FONT]-2[FONT="]+ τ[/FONT]-2
[FONT="]but I don’t know how to calculate it. Any help will be much appreciated.[/FONT]