Revisions to Computing the MultinormalDistribution density gives sometimes different values from in-built function

Det[c * var] = c^d * Det[var]

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edit approved Oct 17, 2023 at 2:05

9
3

This is less about accuracy (it is already good) but about getting rid of the General::munfl messages. Before the final number is computed, we should check whether the logarithm of the result is below (a multiple of) Log[$MinMachineNumber]; if yes, we simply set the result to 0.

multinormalDens[x_, mean_, var_] := Module[{t, det, d=Length[mean]},
   t = 0.5*(x - mean).LinearSolve[var, (x - mean)];
   det = Det[(2*Pi)^d*var]^Det[2*Pi*var]^(0.5);
   If[-t - Log[det] < 10. Log[$MinMachineNumber], 0., Exp[-t]/det]
   ];

This is less about accuracy (it is already good) but about getting rid of the General::munfl messages. Before the final number is computed, we should check whether the logarithm of the result is below (a multiple of) Log[$MinMachineNumber]; if yes, we simply set the result to 0.

multinormalDens[x_, mean_, var_] := Module[{t, det, d=Length[mean]},
   t = 0.5*(x - mean).LinearSolve[var, (x - mean)];
   det = Det[(2*Pi)^d*var]^(0.5);
   If[-t - Log[det] < 10. Log[$MinMachineNumber], 0., Exp[-t]/det]
   ];

This is less about accuracy (it is already good) but about getting rid of the General::munfl messages. Before the final number is computed, we should check whether the logarithm of the result is below (a multiple of) Log[$MinMachineNumber]; if yes, we simply set the result to 0.

multinormalDens[x_, mean_, var_] := Module[{t, det},
   t = 0.5*(x - mean).LinearSolve[var, (x - mean)];
   det = Det[2*Pi*var]^(0.5);
   If[-t - Log[det] < 10. Log[$MinMachineNumber], 0., Exp[-t]/det]
   ];

pretty late on this, but `2*Pi` should be `(2*Pi)^d`, where `d=Length[mean]` is the dimensionality of the variables

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edit approved Oct 16, 2023 at 15:44

sanchez

9
3

This is less about accuracy (it is already good) but about getting rid of the General::munfl messages. Before the final number is computed, we should check whether the logarithm of the result is below (a multiple of) Log[$MinMachineNumber]; if yes, we simply set the result to 0.

multinormalDens[x_, mean_, var_] := Module[{t, det, d=Length[mean]},
   t = 0.5*(x - mean).LinearSolve[var, (x - mean)];
   det = Det[2*Pi*var]^Det[(2*Pi)^d*var]^(0.5);
   If[-t - Log[det] < 10. Log[$MinMachineNumber], 0., Exp[-t]/det]
   ];

This is less about accuracy (it is already good) but about getting rid of the General::munfl messages. Before the final number is computed, we should check whether the logarithm of the result is below (a multiple of) Log[$MinMachineNumber]; if yes, we simply set the result to 0.

multinormalDens[x_, mean_, var_] := Module[{t, det},
   t = 0.5*(x - mean).LinearSolve[var, (x - mean)];
   det = Det[2*Pi*var]^(0.5);
   If[-t - Log[det] < 10. Log[$MinMachineNumber], 0., Exp[-t]/det]
   ];

This is less about accuracy (it is already good) but about getting rid of the General::munfl messages. Before the final number is computed, we should check whether the logarithm of the result is below (a multiple of) Log[$MinMachineNumber]; if yes, we simply set the result to 0.

multinormalDens[x_, mean_, var_] := Module[{t, det, d=Length[mean]},
   t = 0.5*(x - mean).LinearSolve[var, (x - mean)];
   det = Det[(2*Pi)^d*var]^(0.5);
   If[-t - Log[det] < 10. Log[$MinMachineNumber], 0., Exp[-t]/det]
   ];

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created Feb 12, 2019 at 9:06

Henrik Schumacher

109.4k
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This is less about accuracy (it is already good) but about getting rid of the General::munfl messages. Before the final number is computed, we should check whether the logarithm of the result is below (a multiple of) Log[$MinMachineNumber]; if yes, we simply set the result to 0.

multinormalDens[x_, mean_, var_] := Module[{t, det},
   t = 0.5*(x - mean).LinearSolve[var, (x - mean)];
   det = Det[2*Pi*var]^(0.5);
   If[-t - Log[det] < 10. Log[$MinMachineNumber], 0., Exp[-t]/det]
   ];

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