Questions tagged [numerics]
Also known as Numerical Analysis, Numerics aims to provide methods and algorithms for numerical computations.
159
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Estimating correlation parameter from known value of bivariate normal distribution
I want to estimate the correlation parameter $\rho$ using the following expression taken from this paper (equation 10 on page 17):
$$ \hat{s}^2+\hat{\mu}^2=N_2(N^{-1}(\hat{\mu}),N^{-1}(\hat{\mu}), \...
2
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1
answer
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How to do log subtract (just like logsumexp) with probabilities? [closed]
To subtract a small probability from another, this answer has constraint on log probabilities l1 > l2: Subtracting very small probabilities - How to compute? but I need a function that works for ...
- 201
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1
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What is a numerically stable way to generate an exponential distribution that properly yields very large, low-probability values in Excel and C++?
I have sets of sampled data with the following statistics:
Because the mean is so close to the min, and because of our understanding of the process that generated the samples, we are treating the ...
- 331
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1
answer
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Understanding the advantages of BF16 vs. FP16 in mixed precision training
Brain float (BF16) and 16-bit floating point (FP16) both require 2 bytes of memory, but in contrast to FP16, BF16 allows to represent a much larger numerical range than FP16, so under-/overflows won't ...
- 151
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Numerical quadrature for Pareto distribution
I would like to numerically evaluate an integral of the following type, when evaluating $f(x)$ at any given point is numerically costly:
$$
\int_{x_m}^\infty x^{-\alpha}f(x) \, dx, \quad \alpha >1, ...
- 31
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Gradient descent residual
I've implemented the gradient descent method for finding roots of a system of nonlinear equations and I am wondering how the residual is determined? Is the residual simply the Euclidean norm (2-norm) ...
- 1
5
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2
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157
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Approximating the standard normal density with the logistic density: How to numerically optimize $\infty$-norm?
Let's say that we want to use the logistic distribution as an approximation to the standard normal density. As the location parameter of the logistic distribution is $0$, the scale parameter $s$ is ...
- 31k
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Get samples from a known log density
I have two distributions $p_a$ and $p_b$ and I want to sample from $p_c$, defined via
the log density
$$
\log p_c(x) = (1+w) \log p_a(x) - w \log p_b(x)
$$
or via the desnity
$$
p_c(x) = \frac{ p_a(x)^...
- 111
2
votes
1
answer
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MLE for parametric binomial model
I have a model in which $p_i=f(\theta,Z_i)$, where $Z_i$ are iid latent variables distributed with CDF $F_\theta$, and $d_i\sim B(n_i,p_i)$, where $B$ is the binomial distribution. The likelihood ...
- 211
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Comparison of two models with different number of parameters
I want to compare two models, which has different number of parameters. The first model is Arbitrage free Nelson-Siegel model, which has the following equation:
$y_{t}(\tau )=X_{1,t}+X_{2,t}(\frac{1-e^...
- 111
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Algorithm for Irwin Hall Distribution [closed]
I've been trying to create a function for the Irwin Hall distribution that doesn't face the same issue as the unifed package implementation. Because the function suffers from numerical issues, I ...
- 113
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97
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Numerical Stability when Inverse CDF Sampling from Truncated Density
Let $f(x)$ be the pdf of a random variable that we want to truncate to the interval $[a,b]$ and then sample from it. Let $F(x)$ denote the corresponding cdf. We can use inverse cdf sampling and ...
- 710
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vote
1
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Can (or should) data dominated by two values be treated as categorical?
Problem. I have few data sets containing real values (aka observation and prediction). >85% of data values are oscillating between two values exactly (e.g. 0 or 10), while the rest are real numbers ...
- 31
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A question on computational complexity of a numerical differentiation (equation (5.77)) in Bishop's Pattern Recognition and Machine Learning
In page 249 of Christopher M. Bishop's book "Pattern Recognition and Machine Learning", it is said
Again, the implementation of such algorithms can be checked by using
numerical ...
- 333
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Numerically solving a sparse matrix equation
I want to find the $X$ that solves the matrix equation
$$ AX = B $$
with $A$ and $B$ known - $
A$ and $X$ are rectangular, $A$ is $n \times m $ and $X$ is an $m \times n$, with $m > n$.
(...
