estimate_time_varying.md
In cfr: Estimate Disease Severity and Case Ascertainment

`Time varying CFR, basic expectations

Code
  head(tvcfr_naive, 15)
Output
           date severity_estimate severity_low severity_high
  1  1976-08-25                NA           NA            NA
  2  1976-08-26                NA           NA            NA
  3  1976-08-27                NA           NA            NA
  4  1976-08-28                NA           NA            NA
  5  1976-08-29                NA           NA            NA
  6  1976-08-30                NA           NA            NA
  7  1976-08-31                NA           NA            NA
  8  1976-09-01               0.0   0.00000000     0.9750000
  9  1976-09-02               0.0   0.00000000     0.9750000
  10 1976-09-03               0.0   0.00000000     0.9750000
  11 1976-09-04               0.0   0.00000000     0.6023646
  12 1976-09-05               0.0   0.00000000     0.9750000
  13 1976-09-06               0.0   0.00000000     0.9750000
  14 1976-09-07               0.0   0.00000000     0.7075982
  15 1976-09-08               0.5   0.01257912     0.9874209

Code
  tail(tvcfr_corrected, 15)
Output
           date severity_estimate severity_low severity_high
  59 1976-10-22               0.5   0.01257912     0.9874209
  60 1976-10-23               0.0   0.00000000     0.8418861
  61 1976-10-24               0.0   0.00000000     0.9750000
  62 1976-10-25               0.0   0.00000000     0.9750000
  63 1976-10-26                NA           NA            NA
  64 1976-10-27               0.0   0.00000000     0.9750000
  65 1976-10-28                NA           NA            NA
  66 1976-10-29               1.0   0.02500000     1.0000000
  67 1976-10-30               0.0   0.00000000     0.9750000
  68 1976-10-31                NA           NA            NA
  69 1976-11-01                NA           NA            NA
  70 1976-11-02                NA           NA            NA
  71 1976-11-03                NA           NA            NA
  72 1976-11-04                NA           NA            NA
  73 1976-11-05                NA           NA            NA

Time-varying CFR with smoothing and burn in

Code
  head(tvcfr_burnin_7, 15)
Output
           date severity_estimate severity_low severity_high
  1  2020-05-02                NA           NA            NA
  2  2020-05-03                NA           NA            NA
  3  2020-05-04                NA           NA            NA
  4  2020-05-05                NA           NA            NA
  5  2020-05-06                NA           NA            NA
  6  2020-05-07                NA           NA            NA
  7  2020-05-08                NA           NA            NA
  8  2020-05-09         0.1660945    0.1543704     0.1783364
  9  2020-05-10         0.1853786    0.1717610     0.1995996
  10 2020-05-11         0.2483871    0.2303268     0.2671293
  11 2020-05-12         0.2109542    0.1945696     0.2280666
  12 2020-05-13         0.1182171    0.1078615     0.1291948
  13 2020-05-14         0.1293255    0.1182376     0.1410532
  14 2020-05-15         0.1363363    0.1248545     0.1484608
  15 2020-05-16         0.1768061    0.1624015     0.1919339