Questions tagged [analytical]

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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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0answers
8 views

Definition of closed-form analytical solution [duplicate]

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 ...
0
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1answer
20 views

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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2answers
63 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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0answers
21 views

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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0answers
52 views

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 ...
1
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1answer
52 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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0answers
21 views

Expectation of a normal variable conditioned by function of the energy (chi-square)

As $x\sim\mathcal N \left(\mu, \Sigma\right)$, and $R$ is a suitable sized matrix, of rank 1, it is well known that $x^TRx\sim\chi^2_1\left(\lambda\right)$, i.e. it is distributed as a non central chi-...
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0answers
64 views

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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1answer
50 views

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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1answer
224 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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1answer
74 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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1answer
121 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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2answers
34 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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1answer
80 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 ...
2
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1answer
276 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 ...
1
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1answer
72 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. ...