# Questions tagged [analytical]

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21 views

### 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 ...
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 ...
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\\ ...
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 ...
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 ...
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 ...
52 views

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 ...
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 ...
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 ...
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 ...
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 ...
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. ...
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 ...