Questions tagged [analytical]

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The probability/cumulative density function for inequality of two random variables

I have two random variables X and Y which came from different inverse gaussian (IG) ...
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Analytic structure of the Dirichlet L functions with the Hurwitz zeta function

I am getting confused about how to get results from below by using the Hurwitz zeta function. Really don't know how to do it. "The Dirichlet L functions for non-principal Dirichlet characters are ...
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1 answer
20 views

Data analytics basics for a organization

I have no knowledge on data analytics, just trying to start. I also have no idea which tools to use, so here is my question, If I have to build a data analytics for an organization which shows trends ...
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1 vote
0 answers
17 views

HOW to determine $S$ in $SEIR$ epidemiology model

With the contact rate parameters for a $SEIR$ model as follows: $$ \begin{aligned} \beta &= 0.139\\ \gamma &= \frac{1}{10.4}\\ \sigma &= 0.1\\ R_0 &= 1.4456\\ N &= 3,787,000\\ I(0) ...
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4 votes
1 answer
79 views

Can the horseshoe prior be expressed analytically?

My question is about the horseshoe prior, described by Carvalho et al. It is specified as: $$ \beta_i|\lambda_i,\tau\sim\mathcal N(0,\tau^2\lambda_i^2)\\ \lambda_i\sim\mathcal C^+(0,1) $$ I have read ...
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3 votes
1 answer
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Generating an analytical copula for an example problem

I am currently doing research that requires me to understand dependence modeling. As a first step, I am reading An Introduction to Copulas. I am, stuck on the first example problem which I have re-...
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1 answer
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Analytically derive standard deviation of parent normal distribution (with known mean) from moments of the truncated normal distribution

Given $\sigma_t$ and $\mu_t$ of a truncated normal distribution, as well as $\mu_p$ of the parent normal distribution, I would like to analytically compute the standard deviation $\sigma_p$ of the ...
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2 votes
1 answer
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Are EM and MCMC closed-form analytical solution

I came across the concept of closed-form analytical solution while learning MCMC and got a bit confused. At this point, my understanding is that the problem does not have closed-form solution if it ...
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Does there exist an analytical solution to the log-likelihood minimisation for a Gaussian model with linear variance?

I'm trying to model some data using the following distribution: \begin{align} r &\sim \mathcal{N}(\mu, \sigma^2) \nonumber\\ \mu &= m_0 + m_1 d \nonumber\\ \sigma^2 &= s_0+s_1 d\nonumber\\ ...
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5 votes
2 answers
97 views

Two dependent uniformly distributed continuous variables and Bayes' theorem: a billiard table exercise

I am trying to solve the following exercise from Judea Pearl's Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. 2.2. A billiard table has unit length, measured from ...
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How can I use transformation properties to obtain the distribution of $h(\mathbf{s})$?

Let that $\mathbf{s}=(s_1,s_2) \sim Unif(S)$, where $S$ is some spatial area. Suppose $y=h(\mathbf{s})=1-[exp(exp(\beta_0+\beta_1(\mathbf{s}-\mathbf{x})^T(\mathbf{s}-\mathbf{x})))]^{-1}$. We have that ...
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1 vote
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Circular variance of a mixture of Von Mises distributions

Does anyone know if there is an analytical solution for the (circular) variance of a mixture of Von Mises distributions that all have equal (circular) mean? Simulation results suggest that the ...
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1 vote
1 answer
66 views

Analytical solution for optimization problem

Is there an analytical solution for the following optimization problem: $b, y \in \mathbb{R}^n$ (vectors), $b^* = \arg min_{b \in \mathbb{R}^n} f(b)$, where $f(b) = ||b-y||_{2}^{2} + \varphi ||b||_{...
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Why are analytical solutions possible for some optimization problems but not possible for others?

For example, an analytical solution is possible for linear regression (i.e. the normal equations) but it is not possible for logistic regression but logistic regression can be optimized with gradient ...
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1 answer
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Difference between forecasting model, forecasting method and forecasting function

I am new to the field of Business Analytics. Can anyone distinguish between forecasting model, forecasting method and forecasting function? According to the book forecasting function is is an equation ...
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1 vote
1 answer
635 views

How was statistics performed before computers?

What was the general approach to performing statistics before calculations were fully computerised (i.e. before both calculation and memory were managed by computer)? I understand the question could ...
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3 votes
1 answer
138 views

Are analytical derivatives unambiguously superior to numerical derivatives in GMM?

I am estimating a non-linear GMM model. In both Stata and R, you need to specify the moment equations and the instruments, but there is no need need to provide analytical derivatives for the estimator ...
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2 votes
1 answer
138 views

Analytical probability of acceptance for MCMC

When we do MCMC algorithm we search for a tradeoff between probability of acceptance for each step and typical size of steps undertaken during each iteration of the sampling algorithm. Are there any ...
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1 vote
2 answers
38 views

How to choose the best duration time for a survey

To analyse the traffic of passengers using an elevator of 8 floors with one main entrance, I need to register the number of passengers entering and quiting the elevator and also the waiting time. ...
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1 vote
1 answer
98 views

Is there a valid way to merge sampled/panel data with exhaustive usage data?

We have an existing study of media consumption which is online and offline. Online study: To measure consumption online, we use log data from web accesses and various other sources. We have reliable ...
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2 votes
1 answer
340 views

How to calculate the expectation of a "ceiling" normal distribution besides Monte Carlo?

Let's say I have a random variable B transformed from a standard normal distribution. When the value is larger than 1, it is set to be 0. Is there an analytical way to get the expectation of random ...
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  • 147
1 vote
1 answer
122 views

Known univariate unimodal analytical convolution with gaussian

I have data that are distributed with an unknown distribution. The data are from one continuous variable and unimodal. The shape looks like a gaussian, but it is asymmetric and with more long tails. ...
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