User jjepsuomi

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27

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Derivative of determinant and Mahalanobis distance w.r.t matrix elements

Nov 6 at 11:35 greg 19.6k

0

votes

1

answer

24

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Why is the set $C=\{x\in\mathbb{R}:v(\{x\})\neq 0\}$ countable, where $v$ is a finite measure on $(\mathbb{R}, \mathcal{B}(\mathbb{R}))$

measure-theory

Nov 15 '19 at 10:23 jjepsuomi 7,503

1

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0

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132

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What is the key difference between Stochastic Gradient Descent and Hamiltonian Monte Carlo optimization

optimization stochastic-processes markov-chains monte-carlo gradient-descent

Oct 14 '19 at 7:19 jjepsuomi 7,503

4

votes

2

answers

139

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What is the difference between a response, output, hidden and latent variables in modeling?

statistics mathematical-modeling data-analysis

Oct 28 '19 at 13:14 jjepsuomi 7,503

1

vote

2

answers

66

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Clarifying topological concepts: induced/weak/initial topology and weakly compact

general-topology functional-analysis

Mar 27 '19 at 22:10 Henno Brandsma 183k

1

vote

1

answer

40

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Prove: the inverse of an absolutely continuous operator $A:E_1 \to E_2$ need not be continuous.

functional-analysis

Feb 4 '19 at 10:32 jjepsuomi 7,503

1

4

votes

2

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681

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What is the motivation of defining weak derivative as it is?

measure-theory sobolev-spaces weak-derivatives

Aug 7 '19 at 10:16 David Lingard 605

1

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2

answers

60

views

Gaussian distribution and proportionality

normal-distribution

Oct 24 '18 at 14:06 jjepsuomi 7,503

4

5

votes

1

answer

294

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How to evaluate the integral $\int\mathbf{g}^T\mathbf{v} \exp{(-\frac{1}{2}\mathbf{v}^T \mathbf{A}\mathbf{v})}\,d\mathbf{v}$

integration multiple-integral gaussian-integral

Oct 27 '18 at 14:54 jjepsuomi 7,503

1

vote

1

answer

46

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What does “subset of a topological vector space is compact w.r.t to the weak topology” mean?

general-topology

May 1 '18 at 7:33 Kavi Rama Murthy 239k

1

vote

1

answer

75

views

Why does $E_g\left[-\frac{(x-\mu)^2}{2\sigma^2}\right] = -\sigma^2_0+\frac{(\mu-\mu_0)^2}{\sigma^2}$

normal-distribution expectation approximation

Feb 23 '18 at 10:15 jjepsuomi 7,503

1

vote

0

answers

51

views

The large-sample distribution of the likelihood ratio for testing composite hypotheses

statistics notation

Feb 15 '18 at 17:36 jjepsuomi 7,503

4

votes

1

answer

394

views

Understanding Leibniz's Formula for $\pi/4$, geometric proof

geometry triangles area

Jan 22 '18 at 12:46 Community♦ 1

1

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3

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134

views

How to calculate $\int \frac{1}{1+\exp(-r\sin(tx))}\,dx$

integration

Jan 19 '18 at 7:46 Claude Leibovici 178k

2

votes

1

answer

214

views

Asymptotic equivalence of Akaike Information Criterion and cross-validation?

probability statistics mathematical-modeling information-theory

Sep 8 '18 at 17:32 zipzapboing 142

0

votes

1

answer

114

views

Understanding the derivation of automatic relevance determination

probability statistics bayesian

Jan 8 '18 at 23:16 Community♦ 1

2

0

votes

1

answer

160

views

Why does $\int(\theta-\hat{\theta})\exp\left\{-\frac{n}{2}(\theta-\hat{\theta})^TJ(\hat{\theta})(\theta-\hat{\theta})\right\}\,d\theta=0$?

statistics bayesian fisher-information

Nov 2 '17 at 13:16 Gabriel Romon 30k

2

votes

2

answers

807

views

Is it always okay to drop higher order terms out in Taylor approximation?

functional-analysis statistics taylor-expansion approximation

Nov 6 '17 at 18:48 Ryan Warnick 1,536

2

votes

1

answer

50

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On the functional form of Kullback-Leibler information

statistics information-theory

Oct 26 '17 at 19:17 Lucio 842

0

votes

1

answer

119

views

What does notation $\delta_x(dy)$ mean?

measure-theory notation markov-chains dirac-delta

Oct 16 '17 at 13:46 FGJones 453

1

vote

1

answer

232

views

Why does $\log p(\mu, \log \sigma | y)=\text{constant} -n\log\sigma-\frac{1}{2\sigma^2}\left((n-1)s^2+n(\overline{y}-\mu)^2\right)$?

bayesian log-likelihood

Oct 1 '17 at 18:03 Nadiels 2,498

0

votes

2

answers

120

views

Evaluating marginal likelihood with Gaussian likelihood and prior

integration bayesian

Sep 17 '17 at 11:15 jjepsuomi 7,503

1

vote

1

answer

22

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Calculating credible region for odds ratio

probability bayesian confidence-interval change-of-variable

Sep 16 '17 at 12:43 Ant 20k

1

4

votes

1

answer

173

views

Pencil and paper example of fitting normal distribution to data with MCMC

statistics normal-distribution markov-chains monte-carlo

Sep 14 '17 at 15:30 Community♦ 1

1

vote

1

answer

617

views

Likelihood function of coin toss in three cases

probability

Sep 9 '17 at 13:11 quasi 50.4k

2

votes

2

answers

46

views

Proving $P\left(\mu \not \to 0\right)=P\left(\bigcup_{N=1}^\infty\bigcap_{m=1}^\infty\bigcup_{n>m}\left|\mu\right| \geq \frac1N\right)$

convergence-divergence random-walk

Sep 5 '17 at 13:15 Community♦ 1

3

votes

3

answers

104

views

How to prove $\displaystyle{\sum_{n=m+1}^\infty} \frac{1}{n^2}\leq \frac1m$

sequences-and-series

Sep 4 '17 at 17:13 JohnColtraneisJC 1,871

1

2

votes

1

answer

59

views

Proving ${\lim_{n\rightarrow \infty}} E\left[\left|\frac{X_n}{n}-E[Y_1]\right|\right]=0$

probability-theory law-of-large-numbers

Aug 30 '17 at 14:27 Jack 44.7k

3

votes

1

answer

63

views

Proving $E\left[\left|\frac1n\sum_{m=1}^n Y_m-Y_m1_{[0,R)}(|Y_m|)\right|\right]\leq E\left[|Y_1|, \,|Y_1|\geq R\right]$

probability definite-integrals expectation

Aug 30 '17 at 13:22 jjepsuomi 7,503

1

vote

1

answer

129

views

Proving The Weak Law of Large Numbers

expectation law-of-large-numbers

Jul 29 '17 at 12:17 jjepsuomi 7,503

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259 Questions

Derivative of determinant and Mahalanobis distance w.r.t matrix elements

Why is the set $C=\{x\in\mathbb{R}:v(\{x\})\neq 0\}$ countable, where $v$ is a finite measure on $(\mathbb{R}, \mathcal{B}(\mathbb{R}))$

What is the key difference between Stochastic Gradient Descent and Hamiltonian Monte Carlo optimization

What is the difference between a response, output, hidden and latent variables in modeling?

Clarifying topological concepts: induced/weak/initial topology and weakly compact

Prove: the inverse of an absolutely continuous operator $A:E_1 \to E_2$ need not be continuous.

What is the motivation of defining weak derivative as it is?

Gaussian distribution and proportionality

How to evaluate the integral $\int\mathbf{g}^T\mathbf{v} \exp{(-\frac{1}{2}\mathbf{v}^T \mathbf{A}\mathbf{v})}\,d\mathbf{v}$

What does “subset of a topological vector space is compact w.r.t to the weak topology” mean?

Why does $E_g\left[-\frac{(x-\mu)^2}{2\sigma^2}\right] = -\sigma^2_0+\frac{(\mu-\mu_0)^2}{\sigma^2}$

The large-sample distribution of the likelihood ratio for testing composite hypotheses

Understanding Leibniz's Formula for $\pi/4$, geometric proof

How to calculate $\int \frac{1}{1+\exp(-r\sin(tx))}\,dx$

Asymptotic equivalence of Akaike Information Criterion and cross-validation?

Understanding the derivation of automatic relevance determination

Why does $\int(\theta-\hat{\theta})\exp\left\{-\frac{n}{2}(\theta-\hat{\theta})^TJ(\hat{\theta})(\theta-\hat{\theta})\right\}\,d\theta=0$?

Is it always okay to drop higher order terms out in Taylor approximation?

On the functional form of Kullback-Leibler information

What does notation $\delta_x(dy)$ mean?

Why does $\log p(\mu, \log \sigma | y)=\text{constant} -n\log\sigma-\frac{1}{2\sigma^2}\left((n-1)s^2+n(\overline{y}-\mu)^2\right)$?

Evaluating marginal likelihood with Gaussian likelihood and prior

Calculating credible region for odds ratio

Pencil and paper example of fitting normal distribution to data with MCMC

Likelihood function of coin toss in three cases

Proving $P\left(\mu \not \to 0\right)=P\left(\bigcup_{N=1}^\infty\bigcap_{m=1}^\infty\bigcup_{n>m}\left|\mu\right| \geq \frac1N\right)$

How to prove $\displaystyle{\sum_{n=m+1}^\infty} \frac{1}{n^2}\leq \frac1m$

Proving ${\lim_{n\rightarrow \infty}} E\left[\left|\frac{X_n}{n}-E[Y_1]\right|\right]=0$

Proving $E\left[\left|\frac1n\sum_{m=1}^n Y_m-Y_m1_{[0,R)}(|Y_m|)\right|\right]\leq E\left[|Y_1|, \,|Y_1|\geq R\right]$

Proving The Weak Law of Large Numbers