andrewgelman.com - Statistical Modeling, Causal Inference, and Social Science -

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Statistical Modeling, Causal Inference, and Social Science -

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IP-Address: 184.168.47.225
Country: United States
Region: Arizona
City: Scottsdale
Latitude: 33.6119
Longitude: -111.8906
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Statistical Modeling, Causal Inference, and Social Science - - andrewgelman.com

The Image http://andrewgelman.com/wp-content/uploads/2018/08/Screen-Shot-2018-08-09-at-11.10.34-PM-1024x894.png have no alt-Tag. Please add a alt-Tag.

The Image http://andrewgelman.com/wp-content/uploads/2018/08/Screen-Shot-2018-08-09-at-11.10.34-PM-1024x894.png have no title-Tag. Please add a title-Tag.

The Image http://s0.wp.com/latex.php?latex=p%28y%7Cx%2C%5Ctheta%29p%28x%7C%5Cphi%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y|x,\theta)p(x|\phi)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%7Cx%2C%5Ctheta%29p%28x%7C%5Cphi%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y|x,\theta)p(x|\phi)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%7Cx%2C%5Ctheta%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y|x,\theta)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%7Cx%2C%5Ctheta%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y|x,\theta)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%7Cx%2C%5Ctheta%29+%3D+%5Cprod_%7Bn%3D1%7D%5EN+p%28y_n%7Cx_n%2C%5Ctheta%29.&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y|x,\theta) = \prod_{n=1}^N p(y_n|x_n,\theta).". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%7Cx%2C%5Ctheta%29+%3D+%5Cprod_%7Bn%3D1%7D%5EN+p%28y_n%7Cx_n%2C%5Ctheta%29.&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y|x,\theta) = \prod_{n=1}^N p(y_n|x_n,\theta).". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y_%7BN%2B1%7D%7Cx_%7BN%2B1%7D%2C%5Ctheta%29.&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y_{N+1}|x_{N+1},\theta).". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y_%7BN%2B1%7D%7Cx_%7BN%2B1%7D%2C%5Ctheta%29.&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y_{N+1}|x_{N+1},\theta).". This is good.

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The Image http://s0.wp.com/latex.php?latex=%5Ctheta&bg=ffffff&fg=000000&s=0 have the title-Tag: "\theta". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Ctheta&bg=ffffff&fg=000000&s=0 have the alt-Tag: "\theta". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Ctheta&bg=ffffff&fg=000000&s=0 have the title-Tag: "\theta". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y_%7BN%2B1%7D%7Cx_%7BN%2B1%7D%2Cx%2Cy%29%3D%5Cint+p%28y_%7BN%2B1%7D%7Cx_%7BN%2B1%7D%2C%5Ctheta%29+p%28%5Ctheta%7Cx%2Cy%29+d%5Ctheta.&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y_{N+1}|x_{N+1},x,y)=\int p(y_{N+1}|x_{N+1},\theta) p(\theta|x,y) d\theta.". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y_%7BN%2B1%7D%7Cx_%7BN%2B1%7D%2Cx%2Cy%29%3D%5Cint+p%28y_%7BN%2B1%7D%7Cx_%7BN%2B1%7D%2C%5Ctheta%29+p%28%5Ctheta%7Cx%2Cy%29+d%5Ctheta.&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y_{N+1}|x_{N+1},x,y)=\int p(y_{N+1}|x_{N+1},\theta) p(\theta|x,y) d\theta.". This is good.

The Image http://s0.wp.com/latex.php?latex=%28y_%7BN%2B1%7D%2C+x_%7BN%2B1%7D%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "(y_{N+1}, x_{N+1})". This is good.

The Image http://s0.wp.com/latex.php?latex=%28y_%7BN%2B1%7D%2C+x_%7BN%2B1%7D%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "(y_{N+1}, x_{N+1})". This is good.

The Image http://s0.wp.com/latex.php?latex=%28y_%7BN%2B1%7D%2C+x_%7BN%2B1%7D%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "(y_{N+1}, x_{N+1})". This is good.

The Image http://s0.wp.com/latex.php?latex=%28y_%7BN%2B1%7D%2C+x_%7BN%2B1%7D%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "(y_{N+1}, x_{N+1})". This is good.

The Image http://s0.wp.com/latex.php?latex=%28y_%7BN%2B1%7D%2C+x_%7BN%2B1%7D%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "(y_{N+1}, x_{N+1})". This is good.

The Image http://s0.wp.com/latex.php?latex=%28y_%7BN%2B1%7D%2C+x_%7BN%2B1%7D%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "(y_{N+1}, x_{N+1})". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%2Cx%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y,x)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%2Cx%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y,x)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y_%7BN%2B1%7D%2Cx_%7BN%2B1%7D%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y_{N+1},x_{N+1})". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y_%7BN%2B1%7D%2Cx_%7BN%2B1%7D%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y_{N+1},x_{N+1})". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y_%7Bn%7D%7Cx_%7Bn%7D%2Cx_%7B-n%7D%2Cy_%7B-n%7D%29%3D%5Cint+p%28y_%7Bn%7D%7Cx_%7Bn%7D%2C%5Ctheta%29+p%28%5Ctheta%7Cx_%7B-n%7D%2Cy_%7B-n%7D%29+d%5Ctheta.&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y_{n}|x_{n},x_{-n},y_{-n})=\int p(y_{n}|x_{n},\theta) p(\theta|x_{-n},y_{-n}) d\theta.". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y_%7Bn%7D%7Cx_%7Bn%7D%2Cx_%7B-n%7D%2Cy_%7B-n%7D%29%3D%5Cint+p%28y_%7Bn%7D%7Cx_%7Bn%7D%2C%5Ctheta%29+p%28%5Ctheta%7Cx_%7B-n%7D%2Cy_%7B-n%7D%29+d%5Ctheta.&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y_{n}|x_{n},x_{-n},y_{-n})=\int p(y_{n}|x_{n},\theta) p(\theta|x_{-n},y_{-n}) d\theta.". This is good.

The Image http://s0.wp.com/latex.php?latex=x_%7BN%2B1%7D&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x_{N+1}". This is good.

The Image http://s0.wp.com/latex.php?latex=x_%7BN%2B1%7D&bg=ffffff&fg=000000&s=0 have the title-Tag: "x_{N+1}". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%7Cx%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y|x)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%7Cx%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y|x)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28x%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(x)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28x%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(x)". This is good.

The Image http://s0.wp.com/latex.php?latex=x_n&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x_n". This is good.

The Image http://s0.wp.com/latex.php?latex=x_n&bg=ffffff&fg=000000&s=0 have the title-Tag: "x_n". This is good.

The Image http://s0.wp.com/latex.php?latex=y_n&bg=ffffff&fg=000000&s=0 have the alt-Tag: "y_n". This is good.

The Image http://s0.wp.com/latex.php?latex=y_n&bg=ffffff&fg=000000&s=0 have the title-Tag: "y_n". This is good.

The Image http://s0.wp.com/latex.php?latex=y_n&bg=ffffff&fg=000000&s=0 have the alt-Tag: "y_n". This is good.

The Image http://s0.wp.com/latex.php?latex=y_n&bg=ffffff&fg=000000&s=0 have the title-Tag: "y_n". This is good.

The Image http://s0.wp.com/latex.php?latex=%28x_n%2C+y_n%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "(x_n, y_n)". This is good.

The Image http://s0.wp.com/latex.php?latex=%28x_n%2C+y_n%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "(x_n, y_n)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28x%2Cy%7C%5Cphi%2C%5Ctheta%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(x,y|\phi,\theta)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28x%2Cy%7C%5Cphi%2C%5Ctheta%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(x,y|\phi,\theta)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28%5Cphi%2C%5Ctheta%29%3Dp%28%5Cphi%29p%28%5Ctheta%29%2C&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(\phi,\theta)=p(\phi)p(\theta),". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28%5Cphi%2C%5Ctheta%29%3Dp%28%5Cphi%29p%28%5Ctheta%29%2C&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(\phi,\theta)=p(\phi)p(\theta),". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28%5Cphi%2C%5Ctheta%7Cx%2Cy%29%3Dp%28%5Cphi%7Cx%29p%28%5Ctheta%7Cx%2Cy%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(\phi,\theta|x,y)=p(\phi|x)p(\theta|x,y)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28%5Cphi%2C%5Ctheta%7Cx%2Cy%29%3Dp%28%5Cphi%7Cx%29p%28%5Ctheta%7Cx%2Cy%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(\phi,\theta|x,y)=p(\phi|x)p(\theta|x,y)". This is good.

The Image http://s0.wp.com/latex.php?latex=x_%7BN%2B1%7D&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x_{N+1}". This is good.

The Image http://s0.wp.com/latex.php?latex=x_%7BN%2B1%7D&bg=ffffff&fg=000000&s=0 have the title-Tag: "x_{N+1}". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28x%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(x)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28x%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(x)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28x_%7BN%2B1%7D%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(x_{N+1})". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28x_%7BN%2B1%7D%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(x_{N+1})". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28x%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(x)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28x%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(x)". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28x%2Cy%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(x,y)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28x%2Cy%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(x,y)". This is good.

The Image http://s0.wp.com/latex.php?latex=%28x_n%2Cy_n%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "(x_n,y_n)". This is good.

The Image http://s0.wp.com/latex.php?latex=%28x_n%2Cy_n%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "(x_n,y_n)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%7Cx%2C%5Ctheta%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y|x,\theta)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%7Cx%2C%5Ctheta%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y|x,\theta)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28%5Ctheta%7Cx%2Cy%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(\theta|x,y)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28%5Ctheta%7Cx%2Cy%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(\theta|x,y)". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28%5Ctilde%7By%7D_n%7Cx_n%2Cx%2Cy%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(\tilde{y}_n|x_n,x,y)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28%5Ctilde%7By%7D_n%7Cx_n%2Cx%2Cy%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(\tilde{y}_n|x_n,x,y)". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Ctilde%7By%7D_n&bg=ffffff&fg=000000&s=0 have the alt-Tag: "\tilde{y}_n". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Ctilde%7By%7D_n&bg=ffffff&fg=000000&s=0 have the title-Tag: "\tilde{y}_n". This is good.

The Image http://s0.wp.com/latex.php?latex=x_n&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x_n". This is good.

The Image http://s0.wp.com/latex.php?latex=x_n&bg=ffffff&fg=000000&s=0 have the title-Tag: "x_n". This is good.

The Image http://s0.wp.com/latex.php?latex=x_n&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x_n". This is good.

The Image http://s0.wp.com/latex.php?latex=x_n&bg=ffffff&fg=000000&s=0 have the title-Tag: "x_n". This is good.

The Image http://s0.wp.com/latex.php?latex=x_n&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x_n". This is good.

The Image http://s0.wp.com/latex.php?latex=x_n&bg=ffffff&fg=000000&s=0 have the title-Tag: "x_n". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=1%2C%5Cldots%2CN&bg=ffffff&fg=000000&s=0 have the alt-Tag: "1,\ldots,N". This is good.

The Image http://s0.wp.com/latex.php?latex=1%2C%5Cldots%2CN&bg=ffffff&fg=000000&s=0 have the title-Tag: "1,\ldots,N". This is good.

The Image http://s0.wp.com/latex.php?latex=N%2B1%2C%5Cldots%2CN%2Bm&bg=ffffff&fg=000000&s=0 have the alt-Tag: "N+1,\ldots,N+m". This is good.

The Image http://s0.wp.com/latex.php?latex=N%2B1%2C%5Cldots%2CN%2Bm&bg=ffffff&fg=000000&s=0 have the title-Tag: "N+1,\ldots,N+m". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=y&bg=ffffff&fg=000000&s=0 have the alt-Tag: "y". This is good.

The Image http://s0.wp.com/latex.php?latex=y&bg=ffffff&fg=000000&s=0 have the title-Tag: "y". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Cprod_%7Bn%3D1%7D%5EN+p%28y_n%7Cf_n%2C%5Ctheta%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "\prod_{n=1}^N p(y_n|f_n,\theta)". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Cprod_%7Bn%3D1%7D%5EN+p%28y_n%7Cf_n%2C%5Ctheta%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "\prod_{n=1}^N p(y_n|f_n,\theta)". This is good.

The Image http://s0.wp.com/latex.php?latex=f&bg=ffffff&fg=000000&s=0 have the alt-Tag: "f". This is good.

The Image http://s0.wp.com/latex.php?latex=f&bg=ffffff&fg=000000&s=0 have the title-Tag: "f". This is good.

The Image http://s0.wp.com/latex.php?latex=f&bg=ffffff&fg=000000&s=0 have the alt-Tag: "f". This is good.

The Image http://s0.wp.com/latex.php?latex=f&bg=ffffff&fg=000000&s=0 have the title-Tag: "f". This is good.

The Image http://s0.wp.com/latex.php?latex=%28y_n-f_n%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "(y_n-f_n)". This is good.

The Image http://s0.wp.com/latex.php?latex=%28y_n-f_n%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "(y_n-f_n)". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=m&bg=ffffff&fg=000000&s=0 have the alt-Tag: "m". This is good.

The Image http://s0.wp.com/latex.php?latex=m&bg=ffffff&fg=000000&s=0 have the title-Tag: "m". This is good.

The Image http://s0.wp.com/latex.php?latex=f_n&bg=ffffff&fg=000000&s=0 have the alt-Tag: "f_n". This is good.

The Image http://s0.wp.com/latex.php?latex=f_n&bg=ffffff&fg=000000&s=0 have the title-Tag: "f_n". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Ctheta&bg=ffffff&fg=000000&s=0 have the alt-Tag: "\theta". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Ctheta&bg=ffffff&fg=000000&s=0 have the title-Tag: "\theta". This is good.

The Image http://s0.wp.com/latex.php?latex=m&bg=ffffff&fg=000000&s=0 have the alt-Tag: "m". This is good.

The Image http://s0.wp.com/latex.php?latex=m&bg=ffffff&fg=000000&s=0 have the title-Tag: "m". This is good.

The Image http://s0.wp.com/latex.php?latex=1%2C%5Cldots%2CN&bg=ffffff&fg=000000&s=0 have the alt-Tag: "1,\ldots,N". This is good.

The Image http://s0.wp.com/latex.php?latex=1%2C%5Cldots%2CN&bg=ffffff&fg=000000&s=0 have the title-Tag: "1,\ldots,N". This is good.

The Image http://s0.wp.com/latex.php?latex=M&bg=ffffff&fg=000000&s=0 have the alt-Tag: "M". This is good.

The Image http://s0.wp.com/latex.php?latex=M&bg=ffffff&fg=000000&s=0 have the title-Tag: "M". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Cprod_%7Bm%3D1%7D%5EM+%5Cleft%5B+%5Cprod_%7Bn%3D1%7D%5EN+p%28y_%7Bmn%7D%7Cx_%7Bmn%7D%2C%5Ctheta_m%29+p%28%5Ctheta_m%7C%5Cpsi%29++%5Cright%5D+p%28%5Cpsi%29%2C&bg=ffffff&fg=000000&s=0 have the alt-Tag: "\prod_{m=1}^M \left[ \prod_{n=1}^N p(y_{mn}|x_{mn},\theta_m) p(\theta_m|\psi) \right] p(\psi),". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Cprod_%7Bm%3D1%7D%5EM+%5Cleft%5B+%5Cprod_%7Bn%3D1%7D%5EN+p%28y_%7Bmn%7D%7Cx_%7Bmn%7D%2C%5Ctheta_m%29+p%28%5Ctheta_m%7C%5Cpsi%29++%5Cright%5D+p%28%5Cpsi%29%2C&bg=ffffff&fg=000000&s=0 have the title-Tag: "\prod_{m=1}^M \left[ \prod_{n=1}^N p(y_{mn}|x_{mn},\theta_m) p(\theta_m|\psi) \right] p(\psi),". This is good.

The Image http://s0.wp.com/latex.php?latex=y&bg=ffffff&fg=000000&s=0 have the alt-Tag: "y". This is good.

The Image http://s0.wp.com/latex.php?latex=y&bg=ffffff&fg=000000&s=0 have the title-Tag: "y". This is good.

The Image http://s0.wp.com/latex.php?latex=y_%7Bmn%7D&bg=ffffff&fg=000000&s=0 have the alt-Tag: "y_{mn}". This is good.

The Image http://s0.wp.com/latex.php?latex=y_%7Bmn%7D&bg=ffffff&fg=000000&s=0 have the title-Tag: "y_{mn}". This is good.

The Image http://s0.wp.com/latex.php?latex=j&bg=ffffff&fg=000000&s=0 have the alt-Tag: "j". This is good.

The Image http://s0.wp.com/latex.php?latex=j&bg=ffffff&fg=000000&s=0 have the title-Tag: "j". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Ctheta_m&bg=ffffff&fg=000000&s=0 have the alt-Tag: "\theta_m". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Ctheta_m&bg=ffffff&fg=000000&s=0 have the title-Tag: "\theta_m". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%2Cx%29%3D+%5Cprod_%7Bm%3D1%7D%5EM+%5Cleft%5B+%5Cprod_%7Bn%3D1%7D%5EN+p%28y_%7Bmn%7D%7Cx_%7Bmn%7D%2C%5Ctheta_m%29p%28%5Ctheta_m%7C%5Cpsi%29+%5Cright%5D+p%28%5Cpsi%29+%5Cprod_%7Bm%3D1%7D%5EM+%5Cleft%5B+%5Cprod_%7Bn%3D1%7D%5EN+p%28x_%7Bmn%7D%7C%5Cphi_m%29p%28%5Cphi_m%7C%5Cvarphi%29+%5Cright%5D+p%28%5Cvarphi%29.&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y,x)= \prod_{m=1}^M \left[ \prod_{n=1}^N p(y_{mn}|x_{mn},\theta_m)p(\theta_m|\psi) \right] p(\psi) \prod_{m=1}^M \left[ \prod_{n=1}^N p(x_{mn}|\phi_m)p(\phi_m|\varphi) \right] p(\varphi).". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%2Cx%29%3D+%5Cprod_%7Bm%3D1%7D%5EM+%5Cleft%5B+%5Cprod_%7Bn%3D1%7D%5EN+p%28y_%7Bmn%7D%7Cx_%7Bmn%7D%2C%5Ctheta_m%29p%28%5Ctheta_m%7C%5Cpsi%29+%5Cright%5D+p%28%5Cpsi%29+%5Cprod_%7Bm%3D1%7D%5EM+%5Cleft%5B+%5Cprod_%7Bn%3D1%7D%5EN+p%28x_%7Bmn%7D%7C%5Cphi_m%29p%28%5Cphi_m%7C%5Cvarphi%29+%5Cright%5D+p%28%5Cvarphi%29.&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y,x)= \prod_{m=1}^M \left[ \prod_{n=1}^N p(y_{mn}|x_{mn},\theta_m)p(\theta_m|\psi) \right] p(\psi) \prod_{m=1}^M \left[ \prod_{n=1}^N p(x_{mn}|\phi_m)p(\phi_m|\varphi) \right] p(\varphi).". This is good.

The Image http://s0.wp.com/latex.php?latex=y_%7BM%2B1%2Cn%7D&bg=ffffff&fg=000000&s=0 have the alt-Tag: "y_{M+1,n}". This is good.

The Image http://s0.wp.com/latex.php?latex=y_%7BM%2B1%2Cn%7D&bg=ffffff&fg=000000&s=0 have the title-Tag: "y_{M+1,n}". This is good.

The Image http://s0.wp.com/latex.php?latex=M%2B1&bg=ffffff&fg=000000&s=0 have the alt-Tag: "M+1". This is good.

The Image http://s0.wp.com/latex.php?latex=M%2B1&bg=ffffff&fg=000000&s=0 have the title-Tag: "M+1". This is good.

The Image http://s0.wp.com/latex.php?latex=x_%7Bmn%7D&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x_{mn}". This is good.

The Image http://s0.wp.com/latex.php?latex=x_%7Bmn%7D&bg=ffffff&fg=000000&s=0 have the title-Tag: "x_{mn}". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Cprod_%7Bm%3D1%7D%5EM+%5Cleft%5B+%5Cprod_%7Bn%3D1%7D%5EN+p%28y_%7Bmn%7D%7Cx_%7Bmn%7D%2C%5Ctheta_m%29+%5Cright%5D+p%28%5Ctheta_1%2C%5Cldots%2C%5Ctheta_M%7C%5Cpsi%29p%28%5Cpsi%29%2C&bg=ffffff&fg=000000&s=0 have the alt-Tag: "\prod_{m=1}^M \left[ \prod_{n=1}^N p(y_{mn}|x_{mn},\theta_m) \right] p(\theta_1,\ldots,\theta_M|\psi)p(\psi),". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Cprod_%7Bm%3D1%7D%5EM+%5Cleft%5B+%5Cprod_%7Bn%3D1%7D%5EN+p%28y_%7Bmn%7D%7Cx_%7Bmn%7D%2C%5Ctheta_m%29+%5Cright%5D+p%28%5Ctheta_1%2C%5Cldots%2C%5Ctheta_M%7C%5Cpsi%29p%28%5Cpsi%29%2C&bg=ffffff&fg=000000&s=0 have the title-Tag: "\prod_{m=1}^M \left[ \prod_{n=1}^N p(y_{mn}|x_{mn},\theta_m) \right] p(\theta_1,\ldots,\theta_M|\psi)p(\psi),". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Cphi&bg=ffffff&fg=000000&s=0 have the alt-Tag: "\phi". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Cphi&bg=ffffff&fg=000000&s=0 have the title-Tag: "\phi". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%2Cx%29%3D+%5Cprod_%7Bm%3D1%7D%5EM+%5Cleft%5B+%5Cprod_%7Bn%3D1%7D%5EN+p%28y_%7Bmn%7D%7Cx_%7Bmn%7D%2C%5Ctheta_m%29+%5Cright%5D+p%28%5Ctheta_1%2C%5Cldots%2C%5Ctheta_M%7C%5Cpsi%29p%28%5Cpsi%29+%5Cprod_%7Bm%3D1%7D%5EM+%5Cleft%5B+%5Cprod_%7Bn%3D1%7D%5EN+p%28x_%7Bmn%7D%7C%5Cphi_j%29+%5Cright%5D+p%28%5Cphi_1%2C%5Cldots%2C%5Cphi_M%7C%5Cvarphi%29p%28%5Cvarphi%29.&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y,x)= \prod_{m=1}^M \left[ \prod_{n=1}^N p(y_{mn}|x_{mn},\theta_m) \right] p(\theta_1,\ldots,\theta_M|\psi)p(\psi) \prod_{m=1}^M \left[ \prod_{n=1}^N p(x_{mn}|\phi_j) \right] p(\phi_1,\ldots,\phi_M|\varphi)p(\varphi).". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y%2Cx%29%3D+%5Cprod_%7Bm%3D1%7D%5EM+%5Cleft%5B+%5Cprod_%7Bn%3D1%7D%5EN+p%28y_%7Bmn%7D%7Cx_%7Bmn%7D%2C%5Ctheta_m%29+%5Cright%5D+p%28%5Ctheta_1%2C%5Cldots%2C%5Ctheta_M%7C%5Cpsi%29p%28%5Cpsi%29+%5Cprod_%7Bm%3D1%7D%5EM+%5Cleft%5B+%5Cprod_%7Bn%3D1%7D%5EN+p%28x_%7Bmn%7D%7C%5Cphi_j%29+%5Cright%5D+p%28%5Cphi_1%2C%5Cldots%2C%5Cphi_M%7C%5Cvarphi%29p%28%5Cvarphi%29.&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y,x)= \prod_{m=1}^M \left[ \prod_{n=1}^N p(y_{mn}|x_{mn},\theta_m) \right] p(\theta_1,\ldots,\theta_M|\psi)p(\psi) \prod_{m=1}^M \left[ \prod_{n=1}^N p(x_{mn}|\phi_j) \right] p(\phi_1,\ldots,\phi_M|\varphi)p(\varphi).". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0 have the title-Tag: "x". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y_%7Bmn%7D%7Cx_%7Bmn%7D%2C%5Ctheta_m%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y_{mn}|x_{mn},\theta_m)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y_%7Bmn%7D%7Cx_%7Bmn%7D%2C%5Ctheta_m%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y_{mn}|x_{mn},\theta_m)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28%5Ctheta_1%2C%5Cldots%2C%5Ctheta_M%7C%5Cpsi%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(\theta_1,\ldots,\theta_M|\psi)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28%5Ctheta_1%2C%5Cldots%2C%5Ctheta_M%7C%5Cpsi%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(\theta_1,\ldots,\theta_M|\psi)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y_%7Bmn%7D%7Cx_%7Bmn%7D%2C%5Ctheta_m%29&bg=ffffff&fg=000000&s=0 have the alt-Tag: "p(y_{mn}|x_{mn},\theta_m)". This is good.

The Image http://s0.wp.com/latex.php?latex=p%28y_%7Bmn%7D%7Cx_%7Bmn%7D%2C%5Ctheta_m%29&bg=ffffff&fg=000000&s=0 have the title-Tag: "p(y_{mn}|x_{mn},\theta_m)". This is good.

The Image http://s0.wp.com/latex.php?latex=y_%7BN%2B1%7D&bg=ffffff&fg=000000&s=0 have the alt-Tag: "y_{N+1}". This is good.

The Image http://s0.wp.com/latex.php?latex=y_%7BN%2B1%7D&bg=ffffff&fg=000000&s=0 have the title-Tag: "y_{N+1}". This is good.

The Image http://s0.wp.com/latex.php?latex=x_%7BN%2B1%7D&bg=ffffff&fg=000000&s=0 have the alt-Tag: "x_{N+1}". This is good.

The Image http://s0.wp.com/latex.php?latex=x_%7BN%2B1%7D&bg=ffffff&fg=000000&s=0 have the title-Tag: "x_{N+1}". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Chat%7B%5Ctheta%7D&bg=ffffff&fg=000000&s=0 have the alt-Tag: "\hat{\theta}". This is good.

The Image http://s0.wp.com/latex.php?latex=%5Chat%7B%5Ctheta%7D&bg=ffffff&fg=000000&s=0 have the title-Tag: "\hat{\theta}". This is good.

The Image http://s0.wp.com/latex.php?latex=m&bg=ffffff&fg=000000&s=0 have the alt-Tag: "m". This is good.

The Image http://s0.wp.com/latex.php?latex=m&bg=ffffff&fg=000000&s=0 have the title-Tag: "m". This is good.

The Image http://andrewgelman.com/wp-content/uploads/2018/01/Screen-Shot-2018-01-28-at-9.22.26-PM-1024x869.png have no alt-Tag. Please add a alt-Tag.

The Image http://andrewgelman.com/wp-content/uploads/2018/01/Screen-Shot-2018-01-28-at-9.22.26-PM-1024x869.png have no title-Tag. Please add a title-Tag.

The Image http://andrewgelman.com/wp-content/uploads/2018/01/Screen-Shot-2018-01-28-at-9.46.07-PM-1024x723.png have no alt-Tag. Please add a alt-Tag.

The Image http://andrewgelman.com/wp-content/uploads/2018/01/Screen-Shot-2018-01-28-at-9.46.07-PM-1024x723.png have no title-Tag. Please add a title-Tag.

The Image http://andrewgelman.com/wp-content/uploads/2018/08/Screen-Shot-2018-08-02-at-1.53.47-PM-1024x580.png have no alt-Tag. Please add a alt-Tag.

The Image http://andrewgelman.com/wp-content/uploads/2018/08/Screen-Shot-2018-08-02-at-1.53.47-PM-1024x580.png have no title-Tag. Please add a title-Tag.

The Image http://andrewgelman.com/wp-content/uploads/2018/08/gpu-cholesky-timing.png have the alt-Tag: "Plot of GPU timing". This is good.

The Image http://andrewgelman.com/wp-content/uploads/2018/08/gpu-cholesky-timing.png have no title-Tag. Please add a title-Tag.