Questions tagged [particle-filter]
Particle filters (or sequential Monte Carlo) is a form of genetic simulation algorithm used for filtering problems in signal analysis and time series analysis.
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Is it possible to use Particle Marginal Metropolis Hastings to estimate the transition matrix and input?
A state space model is defined as:
$$x_{t+1} = A_tx_t + B_tu_t$$
$$y_{t+1} = H_tx_{t+1}$$
So my question is: is it possible to use Particle Marginal Metropolis Hastings to estimate the transition ...
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Metropolis-Hastings algorithm doesn't converge to the global minimum
I calculated the total root mean squared error of 24 parameters that are estimated with metropolis hastings, I ran the algorithm for 100.000 iterations, and as the chain forward it reached a global ...
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Particle Marginal Metropolis Hastings - How to multiply the proposal distribution by the distribution of x?
When we are using particle marginal metropolis hastings, we will approximate the distribution of x with particle filter, in this pdf written below says:
In such situations it
is natural to suggest ...
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Setting up a particle filter for a deterministic system with stochastic, time-discrete observations
I have a deterministic process $x(t)>0$ for $0 < t < T$, governed by an ODE for which I want to do parameter inference in a Bayesian sense. The process is hidden but I have $n$ stochastic ...
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Determine the parameters of a particle filter that best fit observations
I am wondering is there any established framework to optimize the parameter $\lambda$ of a particle filter such that $p(O|\lambda)$ is maximized, where $O$ is the observation sequence. For HMM and ...
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Some Problems in Auxiliary Particle Filter
recently I am studying PF. And I am stuck in APF for a few days, though I derived many times. Here is my question:
I followed the framework of this paper. The APF is defined in Algorithm 1:
The ...
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Inferring a random walk from noisy "images"
I'm interested in the following inference / filtering problem in a hidden Markov model setting. Suppose we have a simple random walk $x_t\in\mathbb{Z}$ and observations are "images" ...
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Why do we want to minimise the variance of our importance weights in SIS with respect to the proposal distribution
Is there a clear and precise explanation of why minimising the variance of the weights in SIS with respect to a proposal ensures that the samples generated from the empirical distribution induced by ...
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What is the point of the re-sampling step in a particle filter?
My general understanding of particle filters is that you represent your state as a collection of discrete particles which you then transform using your state propagation equation.
What I don't ...
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Bayesian evidence with Sequential Monte Carlo and an unnormalized likelihood function: a contradiction?
There is a contradiction in my understanding of Sequential Monte Carlo for estimating Bayesian evidence for model comparison:
Marginal likelihood (aka normalizing constant, aka Bayesian evidence) ...
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Slice sampling in Particle Gibbs with Ancestral Sampling
Bear with me as I am not from statistical background. My question is about the implementation of PGAS algorithm as given in Lindsten et. al 2014 concerning sampling in state-space models. The two ...
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ABC, make tolerance threshold $\epsilon$ adaptive
Briefly the Approximate Bayesian Computation instead of using the exact likelihood function $L(\theta;x)$ tries to approximate this function with the use of the observed summary statistics $s(x_{obs})$...
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Sampling from transition model in particle filter
I am reading the foundational paper about Bayesian bootstrap particle filter (Gordon, Salmond, Smith, 1993) and they are solving the following discrete time estimation problem: $x_k\in R^n$ , $$f_k:\...
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Computing mean of filtering and smoothing distributions from a particle filter
Suppose I have a model with latent states $x_1, x_2, \ldots x_T$ and observations $y_1, y_2, \ldots y_T$. I run a sequential monte carlo algorithm to give me the following approximation to $p(x_{1:T} |...
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Setting the observation likelihood threshold for outlier detection if you know know the percentage of outliers
Let's assume I have a sensor that gives me measurements $z$ and I know that $50\%$ of the measurements I read are outliers (more than 3 standard deviations away from the real measurement distribution)....
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