| 1 | \form#0:$A=\frac{df}{dx}|_{x0,u0}$ |
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| 2 | \form#1:$A=\frac{d}{dx}f(x,u)|_{x0,u0}$ |
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| 3 | \form#2:$A=\frac{d}{du}f(x,u)|_{x0,u0}$ |
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| 4 | \form#3:$x \sim epdf(rv)$ |
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| 5 | \form#4:\[ f(x|a,b) = \prod f(x_i|a_i,b_i) \] |
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| 6 | \form#5:\[M = L'DL\] |
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| 7 | \form#6:\[ x_t = A x_{t-1} + B u_t + Q^{1/2} e_t \] |
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| 8 | \form#7:\[ y_t = C x_{t-1} + C u_t + Q^{1/2} w_t. \] |
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| 9 | \form#8:\[ f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) \] |
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| 10 | \form#9:$x^{(i)}, i=1..n$ |
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| 11 | \form#10:$x \sim epdf(rv|cond)$ |
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| 12 | \form#11:$\alpha=k$ |
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| 13 | \form#12:$\beta=k/\mu$ |
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| 14 | \form#13:$\mu/\sqrt(k)$ |
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| 15 | \form#14:$\mu$ |
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| 16 | \form#15:$\alpha$ |
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| 17 | \form#16:$\beta$ |
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| 18 | \form#17:\[ \left[\begin{array}{cc} R^{0.5}\\ P_{t|t-1}^{0.5}C' & P_{t|t-1}^{0.5}CA'\\ & Q^{0.5}\end{array}\right]<\mathrm{orth.oper.}>=\left[\begin{array}{cc} R_{y}^{0.5} & KA'\\ & P_{t+1|t}^{0.5}\\ \\\end{array}\right]\] |
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| 19 | \form#18:\[ \mu = \mu_{t-1} ^{l} p^{1-l}\] |
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| 20 | \form#19:$A=Ch' Ch$ |
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| 21 | \form#20:$Ch$ |
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| 22 | \form#21:$L$ |
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| 23 | \form#22:$D$ |
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| 24 | \form#23:$V = V + w v v'$ |
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| 25 | \form#24:$C$ |
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| 26 | \form#25:$V = C*V*C'$ |
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| 27 | \form#26:$V = C'*V*C$ |
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| 28 | \form#27:$V$ |
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| 29 | \form#28:$x$ |
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| 30 | \form#29:$x= v'*V*v$ |
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| 31 | \form#30:$x= v'*inv(V)*v$ |
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| 32 | \form#31:$U$ |
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| 33 | \form#32:$A'D0 A$ |
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| 34 | \form#33:$L'DL$ |
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| 35 | \form#34:$A'*diag(D)*A = self.L'*diag(self.D)*self.L$ |
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| 36 | \form#35:$f(x)$ |
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| 37 | \form#36:$f(rv|rvc,data)$ |
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| 38 | \form#37:$x=$ |
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| 39 | \form#38:$t$ |
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| 40 | \form#39:$t+1$ |
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| 41 | \form#40:$mu=A*rvc$ |
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| 42 | \form#41:$k$ |
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| 43 | \form#42:$p$ |
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| 44 | \form#43:$l$ |
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| 45 | \form#44:$w$ |
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| 46 | \form#45:$f(x) = a$ |
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| 47 | \form#46:$f(x) = Ax+B$ |
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| 48 | \form#47:$f(x,u)$ |
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| 49 | \form#48:$f(x,u) = Ax+Bu$ |
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| 50 | \form#49:$f(x0,u0)$ |
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| 51 | \form#50:$u$ |
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| 52 | \form#51:$[\theta r]$ |
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| 53 | \form#52:$\psi=\psi(y_{1:t},u_{1:t})$ |
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| 54 | \form#53:$u_t$ |
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| 55 | \form#54:$e_t$ |
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| 56 | \form#55:$\theta_t,r_t$ |
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| 57 | \form#56:$\in <0,1>$ |
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| 58 | \form#57:$\theta,r$ |
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| 59 | \form#58:$dt = [y_t psi_t] $ |
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| 60 | \form#59:$epdf(rv)$ |
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| 61 | \form#60:$\mathcal{I}$ |
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| 62 | \form#61:\[ y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t \] |
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| 63 | \form#62:\[ e_t \sim \mathcal{N}(0,1). \] |
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| 64 | \form#63:\[ f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1. \] |
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| 65 | \form#64:$f_i(x)$ |
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| 66 | \form#65:$\omega$ |
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| 67 | \form#66:\[ f(y_t|\psi_t, \Theta) = \sum_{i=1}^{n} w_i f(y_t|\psi_t, \theta_i) \] |
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| 68 | \form#67:$\psi$ |
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| 69 | \form#68:$w=[w_1,\ldots,w_n]$ |
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| 70 | \form#69:$\theta_i$ |
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| 71 | \form#70:$\Theta$ |
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| 72 | \form#71:$\Theta = [\theta_1,\ldots,\theta_n,w]$ |
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| 73 | \form#72:$p\times$ |
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| 74 | \form#73:$n$ |
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| 75 | \form#74:\[ f(x|\beta) = \frac{\Gamma[\gamma]}{\prod_{i=1}^{n}\Gamma(\beta_i)} \prod_{i=1}^{n}x_i^(\beta_i-1) \] |
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| 76 | \form#75:$\gamma=\sum_i beta_i$ |
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| 77 | \form#76:\[ f(x|\beta) = \frac{\Gamma[\gamma]}{\prod_{i=1}^{n}\Gamma(\beta_i)} \prod_{i=1}^{n}x_i^{\beta_i-1} \] |
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| 78 | \form#77:$\gamma=\sum_i \beta_i$ |
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