typo fixes.

Author: yebai

docs/_posts/2020-05-04-Imperial-Report13-analysis.md

@@ -7,7 +7,7 @@ draft: true
 
 The Turing.jl team is currently exploring cooperation with other researchers in an attempt to help with the ongoing SARS-CoV-2 crisis. As preparation for this and to get our feet wet, we decided to perform a replication study of the [Imperial Report 13](https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-13-europe-npi-impact/), which attempts to estimate the real number of infections and impact of non-pharmaceutical interventions on COVID-19. We believe the results and analysis of our study are relevant for the public, and for other researchers who are actively working on epidemiological models. To that end, our implementation and results are available [here](https://github.com/cambridge-mlg/Covid19).
 
-In summary, we replicated the Imperial COVID-19 model using Turing.jl. Subsequently, we compared the inference results between Turing and Stan, and our comparison indicates that results are reproducible with two different implementations. In particular, we performed 3 sets of simulations using the Imperial COVID-19 model. The resulting estimates of real number of cases, in contrast to *recorded* number of cases, the reproduction number \\(R\_t\\), and expected number of deaths as a function of time and non-pharmaceutical interventions (NPIs) for each simulation are shown below. Note that \\(R\_t\\) has a different time-range than the other plots; following the original report, this shows the 100 days days following the country-specific `epidemic_start` which is defined to be 31 days prior to the first date of 10 cumulative deaths, while the other plots show the last 60 days for all countries.
+In summary, we replicated the Imperial COVID-19 model using Turing.jl. Subsequently, we compared the inference results between Turing and Stan, and our comparison indicates that results are reproducible with two different implementations. In particular, we performed 4 sets of simulations using the Imperial COVID-19 model. The resulting estimates of real number of cases, in contrast to *recorded* number of cases, the reproduction number \\(R\_t\\), and expected number of deaths as a function of time and non-pharmaceutical interventions (NPIs) for each simulation are shown below. Note that \\(R\_t\\) has a different time-range than the other plots; following the original report, this shows the 100 days days following the country-specific `epidemic_start` which is defined to be 31 days prior to the first date of 10 cumulative deaths, while the other plots show the last 60 days for all countries.
 
 {% include plotly.html id='simulation-1-Rt' json='../assets/figures/2020-05-04-Imperial-Report13-analysis/Rt_prior.json' %}
 
@@ -41,7 +41,7 @@ In summary, we replicated the Imperial COVID-19 model using Turing.jl. Subsequen
 
 **Simulation (d):** future simulation with when `lockdown` is lifted two weeks before the last observation. The black bar corresponds to the date of the last observation, and the red bar indicates when `lockdown` was lifted.
 
-Simulation (a) shows the prior modelling assumptions, determining the predicted numbed of cases, etc. before seeing any data. Simulation (b) predicts the trend of the number of cases, etc. using estimated parameters and by keeping all the non-pharmaceutical interventions in place. Simulation (c) shows the estimate in case all intervention measures are removed, e.g. such as lifting lockdown after the peak has passed. Simulation (d) shows the esimates in the case when lockdown was lifted two weeks prior to the last observation, while keeping all the other non-pharmaceutical interventions in place.
+Simulation (a) shows the prior modelling assumptions, and how these prior assumptions determine the predicted numbed of cases, etc. before seeing any data. Simulation (b) predicts the trend of the number of cases, etc. using estimated parameters and by keeping all the non-pharmaceutical interventions in place. Simulation (c) shows the estimate in case all intervention measures are removed, e.g. such as lifting lockdown after the peak has passed. Simulation (d) shows the esimates in the case when lockdown was lifted two weeks prior to the last observation, while keeping all the other non-pharmaceutical interventions in place.
 
 We want to emphasize that we do not yet provide additional analysis of the Imperial model and that the reader should look at the original paper rather than this post for developments and analysis of the model. Note that we are not aiming to make any claims about the validity or the implications of the model and refer to Imperial Report 13 for more details and a detailed analysis. This post’s purpose is solely to add validation to the *inference* performed in the paper by obtaining the same results using a different probabilistic programming language (PPL) and to explore whether or not Turing.jl can be useful for researchers working on these problems.