From 35813f7ba6e39f389629996ef98907cdb20c9622 Mon Sep 17 00:00:00 2001 From: David Brochart Date: Tue, 23 Apr 2019 13:20:26 +0200 Subject: [PATCH] Fix image link (not showing up on the web) (#3454) --- docs/source/notebooks/SMC2_gaussians.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/notebooks/SMC2_gaussians.ipynb b/docs/source/notebooks/SMC2_gaussians.ipynb index 5f893674c4..b508407e59 100644 --- a/docs/source/notebooks/SMC2_gaussians.ipynb +++ b/docs/source/notebooks/SMC2_gaussians.ipynb @@ -53,7 +53,7 @@ "\n", "The previous paragraph is summarized in the next figure, the first subplot show 5 samples (orange dots) at some particular stage. The second subplots show how this samples are reweighted according to the their posterior density (blue Gaussian curve). The third subplot shows the result of running a certain number of Metropolis steps, starting from the _selected/reweighting_ samples in the second subplots, notice how the two samples with the lower posterior density (smaller circles) are discarded and not used to seed Markov chains.\n", "\n", - "\"SMC \n", + "\"SMC \n", "\n", "So far we have that the SMC sampler is just a bunch of parallel Markov chains, not very impressive, right? Well not that fast. SMC proceed by moving _sequentially_ trough a series of stages, starting from a simple to sample distribution until it get to the posterior distribution. All this intermediate distribution (or _tempered posterior distributions_) are controlled by _tempering_ parameter called $\\beta$. SMC takes this idea from other _tempering_ methods originated from a branch of physics known as _statistical mechanics_. The idea is as follow the number of accessible states a _real physical_ system can reach is controlled by the temperature, if the temperature is the lowest possible ($0$ Kelvin) the system is trapped in a single state, on the contrary if the temperature is $\\infty$ all states are equally accessible! In the _statistical mechanics_ literature $\\beta$ is know as the inverse temperature, the higher the more constrained the system is. Going back to the Bayesian statistics context a _natural_ analogy to these physical systems is given by the following formula:\n", "\n",