# 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 ...
60 views

### 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 ...
160 views

### 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 ...
126 views

### 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 ...
1 vote
122 views

### 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 ...
31 views

### 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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1 vote
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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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### Monte Carlo probability approximation vs Histogram

I am trying to learn the sequential Monte Carlo method (particle filter) in data assimilation. In this method, the aim is to approximate the CDF of the target variable having a random sample of the ...
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### Particle Filter for structural credit risk model

Kwon (2012)* proposes a structural credit risk model where the asset value process and the noise are estimated based on the observed equity prices: $S$ - equity prices $V$ - value of the assets $Z$ - ...
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1 vote
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### Modelling Ball Movement using Delayed Measurements with Known Latency

I am a hobby programmer currently developing an algorithm to combine measurements of a dynamically moving ball position (and velocity) from multiple robots. Each robot measure and calculate the ...
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### Simplying Bayes Theorem expression: SIS particle filter posteriori

In the book Beyond the Kalman Filter: Particle Filters for Tracking Applications on page 39 the weight update equation for the particle filter is derived. The derivations begins by introducing the ...
1 vote
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### Calculating the observation density

In the context of link. For a state space model $$x_{k+1} = f(x_{k}, u_k, w_k)$$ $$y_k = H x_k + v_k$$ where the measurement function is assumed linear and Gaussian and the state transition is ...
370 views

### Particle filter: Evaluating Optimal importance density

NOTE I posted this in the math stack exchange but I realized this may be the more appropriate place, old post here. I'm not sure if I should delete one of them so I just linked them in both? I am ...